Notes made while working through Biostatistics by Example Using SAS Studio by Ron Cody, using the SAS programmer interface. All SAS content and materials belong to them, not me.

R will then be used to complete representative activities.

Chapters 1 - 4: Data Import Basics

Read-in bult-in dataset, import from text and CSV files, work with various delimiters and header profiles.

SAS Code, click to expand

SAS Code:

#  (&path1 and biostats libname previously defined)
/* copy built-in SAS dataset to an external file for download and use with R later */
/* run once only */
/* validvarname v6 for mainframe and v9 for R or Unix */
/* options validvarname=v6;   */
/* options validvarname=v9;   */
/*  proc copy in=sashelp out=biostats;   */
/*    select heart fish bweight;   */
/*    run;   */
/* options validvarname=v7; */

/* temp one time run
proc copy in=sashelp out=biostats;  
  select bweight; 
  run; 
*/

/*** Chapters 1 - 4: Data Import Basics ***/

/* examining a sample built-in dataset */
title1 "sample built-in dataset heart";
proc contents data=sashelp.heart order=varnum; run;
title1 "sample built-in dataset heart sample";
proc print u data=sashelp.heart (obs=25); run;
proc sort data=sashelp.heart out=work.heart_temp; by descending Systolic; run;
title1 "sample built-in dataset heart sample decreasing Systolic";
proc print u data=work.heart_temp (obs=25 keep=Sex Height Systolic Diastolic Weight); run;
title1 "sample built-in dataset heart sample decreasing Systolic Height > 70";
proc print u data=work.heart_temp (obs=25 keep=Sex Height Systolic Diastolic Weight
  where=(Height GT 70)); run;
title1 "sample built-in dataset heart";
proc freq data=sashelp.heart; 
  tables height / missing; run; 
title1;
proc delete data=work.heart_temp; run;

/* import xlsx file */
proc import datafile=" &path1.Grades.xlsx"
    dbms=xlsx
    out=work.grades_xlsx replace;
    getnames=yes;
run;
title1 "sample imported dataset grades";
proc contents data=work.grades_xlsx order=varnum; run;
proc print u data=work.grades_xlsx (obs=25); run;
title1;
proc delete data=work.grades_xlsx; run;

/* import xlsx file take 2 invalid sas names*/
options validvarname=v7;  /* need to force imports to sas naming standards */
proc import datafile=" &path1.Grades2.xlsx"
    dbms=xlsx
    out=work.grades2_xlsx replace;
    getnames=yes;
run;
title1 "sample imported dataset grades2";
proc contents data=work.grades2_xlsx order=varnum; run;
proc print u data=work.grades2_xlsx (obs=25); run;
title1 "sample imported dataset grades2 rename";
proc print u data=work.grades2_xlsx (obs=25 rename=(Stuent_Name=Student_Name _2015Final = Final_2015)); run;
title1;
proc delete data=work.grades2_xlsx; run;

/* import csv file */
proc import datafile=" &path1.Grades.csv"
    dbms=csv
    out=work.grades_csv replace;
    getnames=yes;
run;
title1 "sample imported dataset grades csv";
proc contents data=work.grades_csv order=varnum; run;
proc print u data=work.grades_csv (obs=25); run;
title1;
proc delete data=work.grades_csv; run;

/* import txt file with no column names*/
proc import datafile="&path1.Health_List.txt"
    dbms=dlm replace
    out=work.healthlist_txt replace;
    getnames=no;
    delimiter='20'x;
run;
title1 "sample imported dataset healthlist txt proc import terrible";
proc contents data=work.healthlist_txt order=varnum; run;
proc print u data=work.healthlist_txt (obs=25); run;

/* Better to use a list input which takes care of consecutive delimeters etc. */
data work.healthlist_txt;
  infile "&path1.Health_List.txt";
  input Subj Gender $ Age Heart_Rate SBP DBP Chol;
  label Subj = "Subject Number"
    Gender = "Gender (M or F)"
    Age = "Age in years"
    Heart_Rate = "Heart rate"
    SBP = "Systolic blood pressure"
    DBP = "Diastolic blood pressure"
    Chol = "Total cholesterol";
  run;
title1 "sample imported dataset healthlist txt list input is better";
proc contents data=work.healthlist_txt order=varnum; run;
proc print u data=work.healthlist_txt (obs=25); run;
title1;
proc delete data=work.healthlist_txt; run;

/* same data using list input with more explicit parameters */
data work.healthlist_txt;
  length Gender $1.; /* specify string length before input */
  infile "&path1.Health_List.txt" DLM='20'x; /* TAB is 09x */
  input Subj Gender $ Age Heart_Rate SBP DBP Chol;
  label Subj = "Subject Number"
    Gender = "Gender (M or F)"
    Age = "Age in years"
    Heart_Rate = "Heart rate"
    SBP = "Systolic blood pressure"
    DBP = "Diastolic blood pressure"
    Chol = "Total cholesterol";
  run;
title1 "sample import using list input treat mult delim as one";
proc contents data=work.healthlist_txt order=varnum; run;
proc print u data=work.healthlist_txt (obs=25); run;
title1;
proc delete data=work.healthlist_txt; run;

/* Use list input to read in CSV */
data work.health_csv;
  infile "&path1.Health.csv" DSD;
  input Subj Gender $ Age Heart_Rate SBP DBP Chol;
  label Subj = "Subject Number"
    Gender = "Gender (M or F)"
    Age = "Age in years"
    Heart_Rate = "Heart rate"
    SBP = "Systolic blood pressure"
    DBP = "Diastolic blood pressure"
    Chol = "Total cholesterol";
  run;
title1 "sample imported dataset health csv using list input";
proc contents data=work.health_csv order=varnum; run;
proc print u data=work.health_csv (obs=25); run;
title1;
proc delete data=work.health_csv; run;

/* read in text with fixed columns */
data work.health_txt;
  infile "&path1.Health.txt" pad;
  input 
    @1 Subj 3.
    @4 Gender $1.
    @5 Age 2.
    @7 Heart_Rate 2.
    @9 SBP 3.
    @12 DBP 3.
    @16 Chol 3.;
  label Subj = "Subject Number"
    Gender = "Gender (M or F)"
    Age = "Age in years"
    Heart_Rate = "Heart rate"
    SBP = "Systolic blood pressure"
    DBP = "Diastolic blood pressure"
    Chol = "Total cholesterol";
  run;
title1 "sample imported dataset health txt fixed columns";
proc contents data=work.health_txt order=varnum; run;
proc print u data=work.health_txt (obs=25); run;
title1;
proc delete data=work.health_txt; run;

/* read in tab delimited file*/
data work.bpressure_txt;
  length Drug $7.
    Gender $1.;
  infile "&path1.Blood_Pressure.txt" DLM='09'x DSD;
  input Drug $ Subj Gender $ SBP DBP;
  label Drug = "Drug"
    Subj = "Subject Number"
    Gender = "Gender (M or F)"
    SBP = "Systolic blood pressure"
    DBP = "Diastolic blood pressure";
  run;
title1 "sample import blood pressure tab delim text file";
proc contents data=work.bpressure_txt order=varnum; run;
proc print u data=work.bpressure_txt (obs=25); run;
title1;
proc delete data=work.bpressure_txt; run;

/* Import external files for exercises found in other chapters - start */

/* Distribution Practice 5-3 */
options validvarname=v7;  /* need to force imports to sas naming standards */
proc import datafile=" &path1.Blood_Pressure.xlsx"
    dbms=xlsx
    out=work.blood_pressure replace;
    getnames=yes;
run;
title1 "Blood Pressure Distribution Practice 5-3";
proc contents data=work.blood_pressure order=varnum; run;
proc print u data=work.blood_pressure (obs=25); run;

/*** Chapter 6: One-Sample Tests ***/
/* Performing a One-Sample t Test */
options validvarname=v7;  /* need to force imports to sas naming standards */
proc import datafile=" &path1.Perch.xlsx"
    dbms=xlsx
    out=work.perch replace;
    getnames=yes;
run;
title1 "Importing Perch data";
proc contents data=work.perch order=varnum; run;
proc print u data=work.perch (obs=25); run;

/* Paired t Test */
options validvarname=v7;  /* need to force imports to sas naming standards */
proc import datafile=" &path1.Yoga.xlsx"
    dbms=xlsx
    out=work.yoga replace;
    getnames=yes;
run;
title1 "Importing Yoga data";
proc contents data=work.yoga order=varnum; run;
proc print u data=work.yoga (obs=25); run;

title1;
/* proc delete data=work.blood_pressure; run; */
/* proc delete data=work.perch; run; */
/* proc delete data=work.yoga; run; */

/* Practice: One-way ANOVA with test for Tukey multiple comparisons, CHF - generated code - start 8.6 */
title1 "Practice: One-way ANOVA with test for Tukey multiple comparisons, CHF";
/* Placebo: 55 58 62 48 57 57 80 40 55 52 */ 
/* Calcium: 57 65 55 78 57 84 72 80 78 81 */ 
/* Lasix:   60 60 65 67 48 62 64 70 57 40 */ 
data work.congestive_heart_failure;
  do Group = 'Placebo','Calcium','Lasix';
    do Subj = 1 to 10;
      input LVEF @@;
      output; 
    end;
  end;
datalines;
  55 58 62 48 57 57 80 40 55 52
  57 65 55 78 57 84 72 80 78 81
  60 60 65 67 48 62 64 70 57 40
    ; 

title1;
proc print u data=work.congestive_heart_failure ; run; 
/* proc delete data=work.congestive_heart_failure; run; */

/* Practice: One-way ANOVA with test for Tukey multiple comparisons, CHF - generated code - end 8.6 */

/* Chapter 9: create sample dataset for Performing a Two-Way Analysis of Variance - generated code - start */

/* Create 25 pct sample without replacement using random seed 13579 */
proc surveyselect data=biostats.bweight out=work.Birth_Wt_Sample method=srs 
        samprate=0.25 seed=13579;
run;

/* The SASHELP library contains the Bweight dataset containing birth weights for 50,000 babies, along with several variables believed to be related to birth weight, such as race (coded as black or not black), mother's smoking status (smoking or non-smoking), and marital status.
Weight (in grams) is the Dependent variable
Black (0 = not black, 1=black)
MomSmoke (0=no, 1=yes)
Married (0=no, 1=yes) */

/* Chapter 9: create sample dataset for Performing a Two-Way Analysis of Variance - generated code - end */


/*** Chapter 10: Correlation ***/
/* Statistics Correlation */
proc import datafile=" &path1.Exercise.xls"
    dbms=xls
    out=work.exercise replace;
    getnames=yes;
run;
title1 "Importing Exercise data";
proc contents data=work.exercise order=varnum; run;
proc print u data=work.exercise (obs=25); run;

/* Chapter 12: Binary Logistic Regression data prep - start */
/* Create a categorical weight variable from arbitrary 3402 gram cutoff using non-missing weight from previously-created sample */
title1 "Logistic Regression data prep Birth_Wt_Sample to High_Low";
data WORK.High_Low;
   set WORK.Birth_Wt_Sample;
   where Weight is not missing; 
   *Wt_Group = 1 is lower weight group
   The median weight is 3402 grams; 
   if Weight lt 3402 then Wt_Group = 1;
   else Wt_Group = 0;
run; 
proc means data=WORK.High_Low; run;
proc print U data=WORK.High_Low (obs=10); run;
/* Chapter 12: Binary Logistic Regression data prep - end */

/* Chapter 13: Prepare generated dataset Heart_Attack - start */
title1 "Import generated dataset Heart_Attack";
proc import datafile=" &path1.Heart_Attack.xlsx"
    dbms=xlsx
    out=work.Heart_Attack replace;
    getnames=yes;
run;
proc print u data=work.Heart_Attack (obs=10); run;
proc freq data=work.Heart_Attack ;
  tables Gender Age_Group High_Chol Heart_Attack
  /list missing;
  run;
/* Formats for the Heart_Attack Dataset */ 
title1 "Sample Observations from Formatted Heart_Attack";
proc format;
   value $gender 'F' = 'Female'
                 'M' = 'Male';
   value Yesno 0 = 'No'
               1 = 'Yes';
   value Age_Group 1 = '< 60'
                   2 = '60-70'
                   3 = '71+';
  run; 
data work.Heart_Attack;
   set work.Heart_Attack;
   format Gender $Gender.
          Heart_Attack High_Chol Yesno.
          Age_Group Age_Group.;
  run; 
proc print u data=work.Heart_Attack (obs=10); run;
proc freq data=work.Heart_Attack ;
  tables Gender Age_Group High_Chol Heart_Attack
  /list missing;
  run;

/* Reformat the Heart_Attack Dataset */ 
title1 "Sample Observations from Reformatted Heart_Attack";
proc format;
   value $gender 'F' = '2:Female'
                 'M' = '1:Male';
   value Yesno 0 = '2:No'
               1 = '1:Yes';
   value Age_Group 1 = '< 60'
                   2 = '60-70'
                   3 = '71+';
  run; 
data work.Heart_Attack;
   set work.Heart_Attack;
   format Gender $Gender.
          Heart_Attack High_Chol Yesno.
          Age_Group Age_Group.;
  run; 
proc print u data=work.Heart_Attack (obs=10); run;
proc freq data=work.Heart_Attack order=formatted;
  tables Gender Age_Group High_Chol Heart_Attack
  /list missing;
  run;

title1;
/* Chapter 13: Prepare generated dataset Heart_Attack - end */

title1;
/* Import external files for exercises found in other chapters - end */

SAS Output

Results: biostats_by_ex_SAScode.sas

Results: biostats_by_ex_SAScode.sas

sample built-in dataset heart

The CONTENTS Procedure

The Contents Procedure

SASHELP.HEART

Attributes

Data Set Name SASHELP.HEART Observations 5209
Member Type DATA Variables 17
Engine V9 Indexes 0
Created 10/24/2018 21:21:26 Observation Length 168
Last Modified 10/24/2018 21:21:26 Deleted Observations 0
Protection   Compressed NO
Data Set Type   Sorted NO
Label Framingham Heart Study    
Data Representation SOLARIS_X86_64, LINUX_X86_64, ALPHA_TRU64, LINUX_IA64    
Encoding us-ascii ASCII (ANSI)    

Engine/Host Information

Engine/Host Dependent Information
Data Set Page Size 65536
Number of Data Set Pages 14
First Data Page 1
Max Obs per Page 389
Obs in First Data Page 365
Number of Data Set Repairs 0
Filename /pbr/sfw/sas/940/SASFoundation/9.4/sashelp/heart.sas7bdat
Release Created 9.0401M6
Host Created Linux
Inode Number 137812
Access Permission rw-r--r--
Owner Name odaowner
File Size 960KB
File Size (bytes) 983040

Varnum

Variables in Creation Order
# Variable Type Len Label
1 Status Char 5  
2 DeathCause Char 26 Cause of Death
3 AgeCHDdiag Num 8 Age CHD Diagnosed
4 Sex Char 6  
5 AgeAtStart Num 8 Age at Start
6 Height Num 8  
7 Weight Num 8  
8 Diastolic Num 8  
9 Systolic Num 8  
10 MRW Num 8 Metropolitan Relative Weight
11 Smoking Num 8  
12 AgeAtDeath Num 8 Age at Death
13 Cholesterol Num 8  
14 Chol_Status Char 10 Cholesterol Status
15 BP_Status Char 7 Blood Pressure Status
16 Weight_Status Char 11 Weight Status
17 Smoking_Status Char 17 Smoking Status

sample built-in dataset heart sample

The Print Procedure

Data Set SASHELP.HEART

Obs Status DeathCause AgeCHDdiag Sex AgeAtStart Height Weight Diastolic Systolic MRW Smoking AgeAtDeath Cholesterol Chol_Status BP_Status Weight_Status Smoking_Status
1 Dead Other . Female 29 62.50 140 78 124 121 0 55 .   Normal Overweight Non-smoker
2 Dead Cancer . Female 41 59.75 194 92 144 183 0 57 181 Desirable High Overweight Non-smoker
3 Alive   . Female 57 62.25 132 90 170 114 10 . 250 High High Overweight Moderate (6-15)
4 Alive   . Female 39 65.75 158 80 128 123 0 . 242 High Normal Overweight Non-smoker
5 Alive   . Male 42 66.00 156 76 110 116 20 . 281 High Optimal Overweight Heavy (16-25)
6 Alive   . Female 58 61.75 131 92 176 117 0 . 196 Desirable High Overweight Non-smoker
7 Alive   . Female 36 64.75 136 80 112 110 15 . 196 Desirable Normal Overweight Moderate (6-15)
8 Dead Other . Male 53 65.50 130 80 114 99 0 77 276 High Normal Normal Non-smoker
9 Alive   . Male 35 71.00 194 68 132 124 0 . 211 Borderline Normal Overweight Non-smoker
10 Dead Cerebral Vascular Disease . Male 52 62.50 129 78 124 106 5 82 284 High Normal Normal Light (1-5)
11 Alive   . Male 39 66.25 179 76 128 133 30 . 225 Borderline Normal Overweight Very Heavy (> 25)
12 Alive   57 Male 33 64.25 151 68 108 118 0 . 221 Borderline Optimal Overweight Non-smoker
13 Alive   55 Male 33 70.00 174 90 142 114 0 . 188 Desirable High Overweight Non-smoker
14 Alive   79 Male 57 67.25 165 76 128 118 15 . .   Normal Overweight Moderate (6-15)
15 Alive   66 Male 44 69.00 155 90 130 105 30 . 292 High High Normal Very Heavy (> 25)
16 Alive   . Female 37 64.50 134 76 120 108 10 . 196 Desirable Normal Normal Moderate (6-15)
17 Alive   . Male 40 66.25 151 72 132 112 30 . 192 Desirable Normal Overweight Very Heavy (> 25)
18 Dead Cancer 56 Male 56 67.25 122 72 120 87 15 72 194 Desirable Normal Underweight Moderate (6-15)
19 Alive   . Female 42 67.75 162 96 138 119 1 . 200 Borderline High Overweight Light (1-5)
20 Dead Coronary Heart Disease 74 Male 46 66.50 157 84 142 116 30 76 233 Borderline High Overweight Very Heavy (> 25)
21 Alive   . Female 37 66.25 148 78 110 112 15 . 192 Desirable Optimal Overweight Moderate (6-15)
22 Alive   . Female 45 64.00 147 74 120 119 5 . 209 Borderline Normal Overweight Light (1-5)
23 Alive   . Female 59 65.75 156 74 156 122 0 . 200 Borderline High Overweight Non-smoker
24 Alive   . Female 36 63.75 122 84 132 102 0 . 184 Desirable Normal Normal Non-smoker
25 Alive   . Female 50 67.50 185 88 150 136 15 . 228 Borderline High Overweight Moderate (6-15)

sample built-in dataset heart sample decreasing Systolic

The Print Procedure

Data Set WORK.HEART_TEMP

Obs Sex Height Weight Diastolic Systolic
1 Female 62.75 228 150 300
2 Female 62.00 153 144 294
3 Female 61.75 144 124 290
4 Female 60.00 204 104 286
5 Female 59.75 189 145 280
6 Male 66.50 186 112 276
7 Female 63.75 115 124 272
8 Female 60.75 202 135 270
9 Male 64.00 168 130 260
10 Female 61.00 200 145 260
11 Female 58.75 152 140 250
12 Male 65.00 155 140 250
13 Female 63.75 154 130 250
14 Female 59.50 113 115 250
15 Female 60.25 271 130 246
16 Female 60.25 235 134 246
17 Male 66.75 174 110 246
18 Female 62.75 241 150 242
19 Female 60.25 171 130 240
20 Female 61.25 150 138 240
21 Female 62.25 198 120 240
22 Female 59.00 172 112 240
23 Female 64.00 217 130 240
24 Female 64.00 129 140 236
25 Female 62.50 145 114 236

sample built-in dataset heart sample decreasing Systolic Height > 70

The Print Procedure

Data Set WORK.HEART_TEMP

Obs Sex Height Weight Diastolic Systolic
60 Male 70.50 229 126 216
106 Male 73.50 178 140 200
115 Male 72.00 227 110 200
149 Male 70.50 226 130 190
150 Male 72.00 191 110 190
181 Male 70.50 172 96 188
260 Male 72.25 273 120 180
291 Male 71.50 215 105 180
308 Male 73.50 182 100 178
320 Male 70.25 183 100 176
345 Male 70.50 181 120 175
392 Male 71.00 191 100 172
399 Male 70.50 180 120 172
402 Male 70.75 198 104 172
428 Male 70.50 203 120 170
461 Male 71.25 189 115 170
472 Male 70.25 133 55 170
506 Male 71.25 166 106 168
545 Male 70.75 198 104 166
563 Male 70.50 156 95 165
567 Male 72.50 213 110 165
592 Male 70.50 223 90 164
599 Male 70.50 169 85 164
608 Male 70.25 172 94 164
626 Male 70.25 243 90 162

sample built-in dataset heart

The FREQ Procedure

The Freq Procedure

Table Height

One-Way Frequencies

Height Frequency Percent Cumulative
Frequency		 Cumulative
Percent
. 6 0.12 6 0.12
51.5 1 0.02 7 0.13
53.75 1 0.02 8 0.15
54.75 2 0.04 10 0.19
55 2 0.04 12 0.23
55.5 2 0.04 14 0.27
55.75 2 0.04 16 0.31
56 3 0.06 19 0.36
56.25 2 0.04 21 0.40
56.5 14 0.27 35 0.67
56.75 10 0.19 45 0.86
57 4 0.08 49 0.94
57.25 9 0.17 58 1.11
57.5 12 0.23 70 1.34
57.75 7 0.13 77 1.48
58 26 0.50 103 1.98
58.25 23 0.44 126 2.42
58.5 33 0.63 159 3.05
58.75 22 0.42 181 3.47
59 63 1.21 244 4.68
59.25 34 0.65 278 5.34
59.5 70 1.34 348 6.68
59.75 39 0.75 387 7.43
60 86 1.65 473 9.08
60.25 68 1.31 541 10.39
60.5 95 1.82 636 12.21
60.75 62 1.19 698 13.40
61 122 2.34 820 15.74
61.25 88 1.69 908 17.43
61.5 125 2.40 1033 19.83
61.75 88 1.69 1121 21.52
62 165 3.17 1286 24.69
62.25 129 2.48 1415 27.16
62.5 175 3.36 1590 30.52
62.75 102 1.96 1692 32.48
63 161 3.09 1853 35.57
63.25 109 2.09 1962 37.67
63.5 146 2.80 2108 40.47
63.75 102 1.96 2210 42.43
64 147 2.82 2357 45.25
64.25 111 2.13 2468 47.38
64.5 169 3.24 2637 50.62
64.75 86 1.65 2723 52.27
65 170 3.26 2893 55.54
65.25 119 2.28 3012 57.82
65.5 139 2.67 3151 60.49
65.75 113 2.17 3264 62.66
66 124 2.38 3388 65.04
66.25 109 2.09 3497 67.13
66.5 107 2.05 3604 69.19
66.75 66 1.27 3670 70.45
67 119 2.28 3789 72.74
67.25 103 1.98 3892 74.72
67.5 114 2.19 4006 76.91
67.75 85 1.63 4091 78.54
68 84 1.61 4175 80.15
68.25 102 1.96 4277 82.11
68.5 100 1.92 4377 84.03
68.75 73 1.40 4450 85.43
69 84 1.61 4534 87.04
69.25 77 1.48 4611 88.52
69.5 81 1.56 4692 90.07
69.75 47 0.90 4739 90.98
70 68 1.31 4807 92.28
70.25 38 0.73 4845 93.01
70.5 62 1.19 4907 94.20
70.75 24 0.46 4931 94.66
71 55 1.06 4986 95.72
71.25 30 0.58 5016 96.29
71.5 29 0.56 5045 96.85
71.75 14 0.27 5059 97.12
72 34 0.65 5093 97.77
72.25 22 0.42 5115 98.20
72.5 22 0.42 5137 98.62
72.75 12 0.23 5149 98.85
73 17 0.33 5166 99.17
73.25 12 0.23 5178 99.40
73.5 7 0.13 5185 99.54
73.75 2 0.04 5187 99.58
74 4 0.08 5191 99.65
74.25 2 0.04 5193 99.69
74.5 6 0.12 5199 99.81
74.75 2 0.04 5201 99.85
75 1 0.02 5202 99.87
75.25 2 0.04 5204 99.90
75.5 2 0.04 5206 99.94
76 2 0.04 5208 99.98
76.5 1 0.02 5209 100.00

sample imported dataset grades

The CONTENTS Procedure

The Contents Procedure

WORK.GRADES_XLSX

Attributes

Data Set Name WORK.GRADES_XLSX Observations 3
Member Type DATA Variables 8
Engine V9 Indexes 0
Created 07/13/2022 10:51:34 Observation Length 72
Last Modified 07/13/2022 10:51:34 Deleted Observations 0
Protection   Compressed NO
Data Set Type   Sorted NO
Label      
Data Representation SOLARIS_X86_64, LINUX_X86_64, ALPHA_TRU64, LINUX_IA64    
Encoding utf-8 Unicode (UTF-8)    

Engine/Host Information

Engine/Host Dependent Information
Data Set Page Size 131072
Number of Data Set Pages 1
First Data Page 1
Max Obs per Page 1816
Obs in First Data Page 3
Number of Data Set Repairs 0
Filename /saswork/SAS_work03A00000A0C4_odaws03-usw2.oda.sas.com/SAS_work0E560000A0C4_odaws03-usw2.oda.sas.com/grades_xlsx.sas7bdat
Release Created 9.0401M6
Host Created Linux
Inode Number 2156762
Access Permission rw-r--r--
Owner Name u47386750
File Size 256KB
File Size (bytes) 262144

Varnum

Variables in Creation Order
# Variable Type Len Format Informat Label
1 Name Char 10 $10. $10. Name
2 ID Num 8 BEST.   ID
3 Quiz1 Num 8 BEST.   Quiz1
4 Quiz2 Num 8 BEST.   Quiz2
5 Midterm Num 8 BEST.   Midterm
6 Quiz3 Num 8 BEST.   Quiz3
7 Quiz4 Num 8 BEST.   Quiz4
8 Final Num 8 BEST.   Final

sample imported dataset grades

The Print Procedure

Data Set WORK.GRADES_XLSX

Obs Name ID Quiz1 Quiz2 Midterm Quiz3 Quiz4 Final
1 Jones 12345 88 80 76 88 90 82
2 Hildebrand 22222 95 92 91 94 90 96
3 O'Brien 33333 76 78 79 81 83 80

sample imported dataset grades2

The CONTENTS Procedure

The Contents Procedure

WORK.GRADES2_XLSX

Attributes

Data Set Name WORK.GRADES2_XLSX Observations 3
Member Type DATA Variables 8
Engine V9 Indexes 0
Created 07/13/2022 10:51:34 Observation Length 72
Last Modified 07/13/2022 10:51:34 Deleted Observations 0
Protection   Compressed NO
Data Set Type   Sorted NO
Label      
Data Representation SOLARIS_X86_64, LINUX_X86_64, ALPHA_TRU64, LINUX_IA64    
Encoding utf-8 Unicode (UTF-8)    

Engine/Host Information

Engine/Host Dependent Information
Data Set Page Size 131072
Number of Data Set Pages 1
First Data Page 1
Max Obs per Page 1816
Obs in First Data Page 3
Number of Data Set Repairs 0
Filename /saswork/SAS_work03A00000A0C4_odaws03-usw2.oda.sas.com/SAS_work0E560000A0C4_odaws03-usw2.oda.sas.com/grades2_xlsx.sas7bdat
Release Created 9.0401M6
Host Created Linux
Inode Number 2156762
Access Permission rw-r--r--
Owner Name u47386750
File Size 256KB
File Size (bytes) 262144

Varnum

Variables in Creation Order
# Variable Type Len Format Informat Label
1 Stuent_Name Char 10 $10. $10. Stuent Name
2 ID Num 8 BEST.   ID
3 Quiz_1 Num 8 BEST.   Quiz 1
4 Quiz_2 Num 8 BEST.   Quiz 2
5 Mid_Term Num 8 BEST.   Mid Term
6 Quiz_3 Num 8 BEST.   Quiz 3
7 Quiz_4 Num 8 BEST.   Quiz 4
8 _2015Final Num 8 BEST.   2015Final

sample imported dataset grades2

The Print Procedure

Data Set WORK.GRADES2_XLSX

Obs Stuent_Name ID Quiz_1 Quiz_2 Mid_Term Quiz_3 Quiz_4 _2015Final
1 Jones 12345 88 80 76 88 90 82
2 Hildebrand 22222 95 92 91 94 90 96
3 O'Brien 33333 76 78 79 81 83 80

sample imported dataset grades2 rename

The Print Procedure

Data Set WORK.GRADES2_XLSX

Obs Student_Name ID Quiz_1 Quiz_2 Mid_Term Quiz_3 Quiz_4 Final_2015
1 Jones 12345 88 80 76 88 90 82
2 Hildebrand 22222 95 92 91 94 90 96
3 O'Brien 33333 76 78 79 81 83 80

sample imported dataset grades csv

The CONTENTS Procedure

The Contents Procedure

WORK.GRADES_CSV

Attributes

Data Set Name WORK.GRADES_CSV Observations 3
Member Type DATA Variables 8
Engine V9 Indexes 0
Created 07/13/2022 10:51:34 Observation Length 88
Last Modified 07/13/2022 10:51:34 Deleted Observations 0
Protection   Compressed NO
Data Set Type   Sorted NO
Label      
Data Representation SOLARIS_X86_64, LINUX_X86_64, ALPHA_TRU64, LINUX_IA64    
Encoding utf-8 Unicode (UTF-8)    

Engine/Host Information

Engine/Host Dependent Information
Data Set Page Size 131072
Number of Data Set Pages 1
First Data Page 1
Max Obs per Page 1486
Obs in First Data Page 3
Number of Data Set Repairs 0
Filename /saswork/SAS_work03A00000A0C4_odaws03-usw2.oda.sas.com/SAS_work0E560000A0C4_odaws03-usw2.oda.sas.com/grades_csv.sas7bdat
Release Created 9.0401M6
Host Created Linux
Inode Number 2156770
Access Permission rw-r--r--
Owner Name u47386750
File Size 256KB
File Size (bytes) 262144

Varnum

Variables in Creation Order
# Variable Type Len Format Informat
1 Name Char 31 $31. $31.
2 ID Num 8 BEST12. BEST32.
3 Quiz1 Num 8 BEST12. BEST32.
4 Quiz2 Num 8 BEST12. BEST32.
5 Midterm Num 8 BEST12. BEST32.
6 Quiz3 Num 8 BEST12. BEST32.
7 Quiz4 Num 8 BEST12. BEST32.
8 Final Num 8 BEST12. BEST32.

sample imported dataset grades csv

The Print Procedure

Data Set WORK.GRADES_CSV

Obs Name ID Quiz1 Quiz2 Midterm Quiz3 Quiz4 Final
1 Jones 12345 88 80 76 88 90 82
2 Hildebrand 22222 95 92 91 94 90 96
3 O'Brien 33333 76 78 79 81 83 80

sample imported dataset healthlist txt proc import terrible

The CONTENTS Procedure

The Contents Procedure

WORK.HEALTHLIST_TXT

Attributes

Data Set Name WORK.HEALTHLIST_TXT Observations 6
Member Type DATA Variables 11
Engine V9 Indexes 0
Created 07/13/2022 10:51:34 Observation Length 72
Last Modified 07/13/2022 10:51:34 Deleted Observations 0
Protection   Compressed NO
Data Set Type   Sorted NO
Label      
Data Representation SOLARIS_X86_64, LINUX_X86_64, ALPHA_TRU64, LINUX_IA64    
Encoding utf-8 Unicode (UTF-8)    

Engine/Host Information

Engine/Host Dependent Information
Data Set Page Size 131072
Number of Data Set Pages 1
First Data Page 1
Max Obs per Page 1816
Obs in First Data Page 6
Number of Data Set Repairs 0
Filename /saswork/SAS_work03A00000A0C4_odaws03-usw2.oda.sas.com/SAS_work0E560000A0C4_odaws03-usw2.oda.sas.com/healthlist_txt.sas7bdat
Release Created 9.0401M6
Host Created Linux
Inode Number 2156770
Access Permission rw-r--r--
Owner Name u47386750
File Size 256KB
File Size (bytes) 262144

Varnum

Variables in Creation Order
# Variable Type Len Format Informat
1 VAR1 Num 8 BEST12. BEST32.
2 VAR2 Char 1 $1. $1.
3 VAR3 Char 2 $2. $2.
4 VAR4 Char 2 $2. $2.
5 VAR5 Num 8 BEST12. BEST32.
6 VAR6 Num 8 BEST12. BEST32.
7 VAR7 Num 8 BEST12. BEST32.
8 VAR8 Num 8 BEST12. BEST32.
9 VAR9 Num 8 BEST12. BEST32.
10 VAR10 Num 8 BEST12. BEST32.
11 VAR11 Num 8 BEST12. BEST32.

sample imported dataset healthlist txt proc import terrible

The Print Procedure

Data Set WORK.HEALTHLIST_TXT

Obs VAR1 VAR2 VAR3 VAR4 VAR5 VAR6 VAR7 VAR8 VAR9 VAR10 VAR11
1 1 M 23 68 120 90 128 . . . .
2 2   F 55 . 72 . . 180 90 170
3 3 F 18 58 118 72 122 . . . .
4 4 M   80 82 . . 220 . . .
5 5 F 34 62 128 80 . . . . .
6 6     F . 38 78 108 68 220 .

sample imported dataset healthlist txt list input is better

The CONTENTS Procedure

The Contents Procedure

WORK.HEALTHLIST_TXT

Attributes

Data Set Name WORK.HEALTHLIST_TXT Observations 6
Member Type DATA Variables 7
Engine V9 Indexes 0
Created 07/13/2022 10:51:34 Observation Length 56
Last Modified 07/13/2022 10:51:34 Deleted Observations 0
Protection   Compressed NO
Data Set Type   Sorted NO
Label      
Data Representation SOLARIS_X86_64, LINUX_X86_64, ALPHA_TRU64, LINUX_IA64    
Encoding utf-8 Unicode (UTF-8)    

Engine/Host Information

Engine/Host Dependent Information
Data Set Page Size 131072
Number of Data Set Pages 1
First Data Page 1
Max Obs per Page 2334
Obs in First Data Page 6
Number of Data Set Repairs 0
Filename /saswork/SAS_work03A00000A0C4_odaws03-usw2.oda.sas.com/SAS_work0E560000A0C4_odaws03-usw2.oda.sas.com/healthlist_txt.sas7bdat
Release Created 9.0401M6
Host Created Linux
Inode Number 2156762
Access Permission rw-r--r--
Owner Name u47386750
File Size 256KB
File Size (bytes) 262144

Varnum

Variables in Creation Order
# Variable Type Len Label
1 Subj Num 8 Subject Number
2 Gender Char 8 Gender (M or F)
3 Age Num 8 Age in years
4 Heart_Rate Num 8 Heart rate
5 SBP Num 8 Systolic blood pressure
6 DBP Num 8 Diastolic blood pressure
7 Chol Num 8 Total cholesterol

sample imported dataset healthlist txt list input is better

The Print Procedure

Data Set WORK.HEALTHLIST_TXT

Obs Subj Gender Age Heart_Rate SBP DBP Chol
1 1 M 23 68 120 90 128
2 2 F 55 72 180 90 170
3 3 F 18 58 118 72 122
4 4 M 80 82 . . 220
5 5 F 34 62 128 80 .
6 6 F 38 78 108 68 220

sample import using list input treat mult delim as one

The CONTENTS Procedure

The Contents Procedure

WORK.HEALTHLIST_TXT

Attributes

Data Set Name WORK.HEALTHLIST_TXT Observations 6
Member Type DATA Variables 7
Engine V9 Indexes 0
Created 07/13/2022 10:51:34 Observation Length 56
Last Modified 07/13/2022 10:51:34 Deleted Observations 0
Protection   Compressed NO
Data Set Type   Sorted NO
Label      
Data Representation SOLARIS_X86_64, LINUX_X86_64, ALPHA_TRU64, LINUX_IA64    
Encoding utf-8 Unicode (UTF-8)    

Engine/Host Information

Engine/Host Dependent Information
Data Set Page Size 131072
Number of Data Set Pages 1
First Data Page 1
Max Obs per Page 2334
Obs in First Data Page 6
Number of Data Set Repairs 0
Filename /saswork/SAS_work03A00000A0C4_odaws03-usw2.oda.sas.com/SAS_work0E560000A0C4_odaws03-usw2.oda.sas.com/healthlist_txt.sas7bdat
Release Created 9.0401M6
Host Created Linux
Inode Number 2156762
Access Permission rw-r--r--
Owner Name u47386750
File Size 256KB
File Size (bytes) 262144

Varnum

Variables in Creation Order
# Variable Type Len Label
1 Gender Char 1 Gender (M or F)
2 Subj Num 8 Subject Number
3 Age Num 8 Age in years
4 Heart_Rate Num 8 Heart rate
5 SBP Num 8 Systolic blood pressure
6 DBP Num 8 Diastolic blood pressure
7 Chol Num 8 Total cholesterol

sample import using list input treat mult delim as one

The Print Procedure

Data Set WORK.HEALTHLIST_TXT

Obs Gender Subj Age Heart_Rate SBP DBP Chol
1 M 1 23 68 120 90 128
2 F 2 55 72 180 90 170
3 F 3 18 58 118 72 122
4 M 4 80 82 . . 220
5 F 5 34 62 128 80 .
6 F 6 38 78 108 68 220

sample imported dataset health csv using list input

The CONTENTS Procedure

The Contents Procedure

WORK.HEALTH_CSV

Attributes

Data Set Name WORK.HEALTH_CSV Observations 6
Member Type DATA Variables 7
Engine V9 Indexes 0
Created 07/13/2022 10:51:34 Observation Length 56
Last Modified 07/13/2022 10:51:34 Deleted Observations 0
Protection   Compressed NO
Data Set Type   Sorted NO
Label      
Data Representation SOLARIS_X86_64, LINUX_X86_64, ALPHA_TRU64, LINUX_IA64    
Encoding utf-8 Unicode (UTF-8)    

Engine/Host Information

Engine/Host Dependent Information
Data Set Page Size 131072
Number of Data Set Pages 1
First Data Page 1
Max Obs per Page 2334
Obs in First Data Page 6
Number of Data Set Repairs 0
Filename /saswork/SAS_work03A00000A0C4_odaws03-usw2.oda.sas.com/SAS_work0E560000A0C4_odaws03-usw2.oda.sas.com/health_csv.sas7bdat
Release Created 9.0401M6
Host Created Linux
Inode Number 2156762
Access Permission rw-r--r--
Owner Name u47386750
File Size 256KB
File Size (bytes) 262144

Varnum

Variables in Creation Order
# Variable Type Len Label
1 Subj Num 8 Subject Number
2 Gender Char 8 Gender (M or F)
3 Age Num 8 Age in years
4 Heart_Rate Num 8 Heart rate
5 SBP Num 8 Systolic blood pressure
6 DBP Num 8 Diastolic blood pressure
7 Chol Num 8 Total cholesterol

sample imported dataset health csv using list input

The Print Procedure

Data Set WORK.HEALTH_CSV

Obs Subj Gender Age Heart_Rate SBP DBP Chol
1 1 M 23 68 120 90 128
2 2 F 55 72 180 90 170
3 3 F 18 58 118 72 122
4 4 M 80 82 . . 220
5 5 F 34 62 128 80 .
6 6 F 38 78 108 68 220

sample imported dataset health txt fixed columns

The CONTENTS Procedure

The Contents Procedure

WORK.HEALTH_TXT

Attributes

Data Set Name WORK.HEALTH_TXT Observations 6
Member Type DATA Variables 7
Engine V9 Indexes 0
Created 07/13/2022 10:51:34 Observation Length 56
Last Modified 07/13/2022 10:51:34 Deleted Observations 0
Protection   Compressed NO
Data Set Type   Sorted NO
Label      
Data Representation SOLARIS_X86_64, LINUX_X86_64, ALPHA_TRU64, LINUX_IA64    
Encoding utf-8 Unicode (UTF-8)    

Engine/Host Information

Engine/Host Dependent Information
Data Set Page Size 131072
Number of Data Set Pages 1
First Data Page 1
Max Obs per Page 2334
Obs in First Data Page 6
Number of Data Set Repairs 0
Filename /saswork/SAS_work03A00000A0C4_odaws03-usw2.oda.sas.com/SAS_work0E560000A0C4_odaws03-usw2.oda.sas.com/health_txt.sas7bdat
Release Created 9.0401M6
Host Created Linux
Inode Number 2156762
Access Permission rw-r--r--
Owner Name u47386750
File Size 256KB
File Size (bytes) 262144

Varnum

Variables in Creation Order
# Variable Type Len Label
1 Subj Num 8 Subject Number
2 Gender Char 1 Gender (M or F)
3 Age Num 8 Age in years
4 Heart_Rate Num 8 Heart rate
5 SBP Num 8 Systolic blood pressure
6 DBP Num 8 Diastolic blood pressure
7 Chol Num 8 Total cholesterol

sample imported dataset health txt fixed columns

The Print Procedure

Data Set WORK.HEALTH_TXT

Obs Subj Gender Age Heart_Rate SBP DBP Chol
1 1 M 23 68 120 90 28
2 2 F 55 72 180 90 70
3 3 F 18 58 118 72 22
4 4 M 80 82 . . 20
5 5 F 34 62 128 80 .
6 6 F 38 78 108 68 20

sample import blood pressure tab delim text file

The CONTENTS Procedure

The Contents Procedure

WORK.BPRESSURE_TXT

Attributes

Data Set Name WORK.BPRESSURE_TXT Observations 60
Member Type DATA Variables 5
Engine V9 Indexes 0
Created 07/13/2022 10:51:34 Observation Length 32
Last Modified 07/13/2022 10:51:34 Deleted Observations 0
Protection   Compressed NO
Data Set Type   Sorted NO
Label      
Data Representation SOLARIS_X86_64, LINUX_X86_64, ALPHA_TRU64, LINUX_IA64    
Encoding utf-8 Unicode (UTF-8)    

Engine/Host Information

Engine/Host Dependent Information
Data Set Page Size 131072
Number of Data Set Pages 1
First Data Page 1
Max Obs per Page 4078
Obs in First Data Page 60
Number of Data Set Repairs 0
Filename /saswork/SAS_work03A00000A0C4_odaws03-usw2.oda.sas.com/SAS_work0E560000A0C4_odaws03-usw2.oda.sas.com/bpressure_txt.sas7bdat
Release Created 9.0401M6
Host Created Linux
Inode Number 2156762
Access Permission rw-r--r--
Owner Name u47386750
File Size 256KB
File Size (bytes) 262144

Varnum

Variables in Creation Order
# Variable Type Len Label
1 Drug Char 7 Drug
2 Gender Char 1 Gender (M or F)
3 Subj Num 8 Subject Number
4 SBP Num 8 Systolic blood pressure
5 DBP Num 8 Diastolic blood pressure

sample import blood pressure tab delim text file

The Print Procedure

Data Set WORK.BPRESSURE_TXT

Obs Drug Gender Subj SBP DBP
1 Placebo F 1 138 86
2 Placebo M 2 124 82
3 Placebo F 3 150 72
4 Placebo   4 136 84
5 Placebo F 5 . .
6 Placebo M 6 132 84
7 Placebo F 7 130 84
8 Placebo F 8 146 88
9 Placebo F 9 134 82
10 Placebo M 10 138 88
11 Placebo F 11 144 84
12 Placebo F 12 130 88
13 Placebo M 13 134 80
14 Placebo M 14 132 90
15 Placebo F 15 . .
16 Placebo M 16 124 88
17 Placebo F 17 140 78
18 Placebo   18 156 86
19 Placebo F 19 120 80
20 Placebo M 20 142 90
21 Drug A F 21 126 76
22 Drug A M 22 134 86
23 Drug A F 23 118 78
24 Drug A F 24 132 80
25 Drug A F 25 . .

Blood Pressure Distribution Practice 5-3

The CONTENTS Procedure

The Contents Procedure

WORK.BLOOD_PRESSURE

Attributes

Data Set Name WORK.BLOOD_PRESSURE Observations 60
Member Type DATA Variables 5
Engine V9 Indexes 0
Created 07/13/2022 10:51:35 Observation Length 32
Last Modified 07/13/2022 10:51:35 Deleted Observations 0
Protection   Compressed NO
Data Set Type   Sorted NO
Label      
Data Representation SOLARIS_X86_64, LINUX_X86_64, ALPHA_TRU64, LINUX_IA64    
Encoding utf-8 Unicode (UTF-8)    

Engine/Host Information

Engine/Host Dependent Information
Data Set Page Size 131072
Number of Data Set Pages 1
First Data Page 1
Max Obs per Page 4078
Obs in First Data Page 60
Number of Data Set Repairs 0
Filename /saswork/SAS_work03A00000A0C4_odaws03-usw2.oda.sas.com/SAS_work0E560000A0C4_odaws03-usw2.oda.sas.com/blood_pressure.sas7bdat
Release Created 9.0401M6
Host Created Linux
Inode Number 2156762
Access Permission rw-r--r--
Owner Name u47386750
File Size 256KB
File Size (bytes) 262144

Varnum

Variables in Creation Order
# Variable Type Len Format Informat Label
1 Drug Char 7 $7. $7. Drug
2 Subj Num 8 BEST.   Subj
3 Gender Char 1 $1. $1. Gender
4 SBP Num 8 BEST.   SBP
5 DBP Num 8 BEST.   DBP

Blood Pressure Distribution Practice 5-3

The Print Procedure

Data Set WORK.BLOOD_PRESSURE

Obs Drug Subj Gender SBP DBP
1 Placebo 1 F 138 86
2 Placebo 2 M 124 82
3 Placebo 3 F 150 72
4 Placebo 4   136 84
5 Placebo 5 F . .
6 Placebo 6 M 132 84
7 Placebo 7 F 130 84
8 Placebo 8 F 146 88
9 Placebo 9 F 134 82
10 Placebo 10 M 138 88
11 Placebo 11 F 144 84
12 Placebo 12 F 130 88
13 Placebo 13 M 134 80
14 Placebo 14 M 132 90
15 Placebo 15 F . .
16 Placebo 16 M 124 88
17 Placebo 17 F 140 78
18 Placebo 18   156 86
19 Placebo 19 F 120 80
20 Placebo 20 M 142 90
21 Drug A 21 F 126 76
22 Drug A 22 M 134 86
23 Drug A 23 F 118 78
24 Drug A 24 F 132 80
25 Drug A 25 F . .

Importing Perch data

The CONTENTS Procedure

The Contents Procedure

WORK.PERCH

Attributes

Data Set Name WORK.PERCH Observations 56
Member Type DATA Variables 3
Engine V9 Indexes 0
Created 07/13/2022 10:51:35 Observation Length 24
Last Modified 07/13/2022 10:51:35 Deleted Observations 0
Protection   Compressed NO
Data Set Type   Sorted NO
Label      
Data Representation SOLARIS_X86_64, LINUX_X86_64, ALPHA_TRU64, LINUX_IA64    
Encoding utf-8 Unicode (UTF-8)    

Engine/Host Information

Engine/Host Dependent Information
Data Set Page Size 131072
Number of Data Set Pages 1
First Data Page 1
Max Obs per Page 5431
Obs in First Data Page 56
Number of Data Set Repairs 0
Filename /saswork/SAS_work03A00000A0C4_odaws03-usw2.oda.sas.com/SAS_work0E560000A0C4_odaws03-usw2.oda.sas.com/perch.sas7bdat
Release Created 9.0401M6
Host Created Linux
Inode Number 2156770
Access Permission rw-r--r--
Owner Name u47386750
File Size 256KB
File Size (bytes) 262144

Varnum

Variables in Creation Order
# Variable Type Len Format Label
1 Weight Num 8 BEST. Weight
2 Height Num 8 BEST. Height
3 Width Num 8 BEST. Width

Importing Perch data

The Print Procedure

Data Set WORK.PERCH

Obs Weight Height Width
1 5.9 2.112 1.408
2 32 3.528 1.9992
3 40 3.824 2.432
4 51.5 4.5924 2.6316
5 70 4.588 2.9415
6 100 5.2224 3.3216
7 78 5.1992 3.1234
8 80 5.6358 3.0502
9 85 5.1376 3.0368
10 85 5.082 2.772
11 110 5.6925 3.555
12 115 5.9175 3.3075
13 125 5.6925 3.6675
14 130 6.384 3.534
15 120 6.11 3.4075
16 120 5.64 3.525
17 130 6.11 3.525
18 135 5.875 3.525
19 110 5.5225 3.995
20 130 5.856 3.624
21 150 6.792 3.624
22 145 5.9532 3.63
23 150 5.2185 3.626
24 170 6.275 3.725
25 225 7.293 3.723

Importing Yoga data

The CONTENTS Procedure

The Contents Procedure

WORK.YOGA

Attributes

Data Set Name WORK.YOGA Observations 9
Member Type DATA Variables 3
Engine V9 Indexes 0
Created 07/13/2022 10:51:35 Observation Length 24
Last Modified 07/13/2022 10:51:35 Deleted Observations 0
Protection   Compressed NO
Data Set Type   Sorted NO
Label      
Data Representation SOLARIS_X86_64, LINUX_X86_64, ALPHA_TRU64, LINUX_IA64    
Encoding utf-8 Unicode (UTF-8)    

Engine/Host Information

Engine/Host Dependent Information
Data Set Page Size 131072
Number of Data Set Pages 1
First Data Page 1
Max Obs per Page 5431
Obs in First Data Page 9
Number of Data Set Repairs 0
Filename /saswork/SAS_work03A00000A0C4_odaws03-usw2.oda.sas.com/SAS_work0E560000A0C4_odaws03-usw2.oda.sas.com/yoga.sas7bdat
Release Created 9.0401M6
Host Created Linux
Inode Number 2156771
Access Permission rw-r--r--
Owner Name u47386750
File Size 256KB
File Size (bytes) 262144

Varnum

Variables in Creation Order
# Variable Type Len Format Label
1 Subj Num 8 BEST. Subj
2 Before Num 8 BEST. Before
3 After Num 8 BEST. After

Importing Yoga data

The Print Procedure

Data Set WORK.YOGA

Obs Subj Before After
1 1 78 74
2 2 68 68
3 3 76 70
4 4 58 57
5 5 83 73
6 6 80 77
7 7 69 61
8 8 77 76
9 9 77 72

Practice: One-way ANOVA with test for Tukey multiple comparisons, CHF

The Print Procedure

Data Set WORK.CONGESTIVE_HEART_FAILURE

Obs Group Subj LVEF
1 Placebo 1 55
2 Placebo 2 58
3 Placebo 3 62
4 Placebo 4 48
5 Placebo 5 57
6 Placebo 6 57
7 Placebo 7 80
8 Placebo 8 40
9 Placebo 9 55
10 Placebo 10 52
11 Calcium 1 57
12 Calcium 2 65
13 Calcium 3 55
14 Calcium 4 78
15 Calcium 5 57
16 Calcium 6 84
17 Calcium 7 72
18 Calcium 8 80
19 Calcium 9 78
20 Calcium 10 81
21 Lasix 1 60
22 Lasix 2 60
23 Lasix 3 65
24 Lasix 4 67
25 Lasix 5 48
26 Lasix 6 62
27 Lasix 7 64
28 Lasix 8 70
29 Lasix 9 57
30 Lasix 10 40

Chapter 9: create 25 pct sample w/o replacement for Two-Way Anova

The SURVEYSELECT Procedure

The Surveyselect Procedure

Sample Selection Method

Selection Method Simple Random Sampling

Sample Selection Summary

Input Data Set BWEIGHT
Random Number Seed 13579
Sampling Rate 0.25
Sample Size 12500
Selection Probability 0.25
Sampling Weight 4
Output Data Set BIRTH_WT_SAMPLE

Importing Exercise data

The CONTENTS Procedure

The Contents Procedure

WORK.EXERCISE

Attributes

Data Set Name WORK.EXERCISE Observations 50
Member Type DATA Variables 6
Engine V9 Indexes 0
Created 07/13/2022 10:51:35 Observation Length 48
Last Modified 07/13/2022 10:51:35 Deleted Observations 0
Protection   Compressed NO
Data Set Type   Sorted NO
Label      
Data Representation SOLARIS_X86_64, LINUX_X86_64, ALPHA_TRU64, LINUX_IA64    
Encoding utf-8 Unicode (UTF-8)    

Engine/Host Information

Engine/Host Dependent Information
Data Set Page Size 131072
Number of Data Set Pages 1
First Data Page 1
Max Obs per Page 2722
Obs in First Data Page 50
Number of Data Set Repairs 0
Filename /saswork/SAS_work03A00000A0C4_odaws03-usw2.oda.sas.com/SAS_work0E560000A0C4_odaws03-usw2.oda.sas.com/exercise.sas7bdat
Release Created 9.0401M6
Host Created Linux
Inode Number 2156778
Access Permission rw-r--r--
Owner Name u47386750
File Size 256KB
File Size (bytes) 262144

Varnum

Variables in Creation Order
# Variable Type Len Format Label
1 Subj Num 8 BEST12. Subj
2 Age Num 8 BEST12. Age
3 Pushups Num 8 BEST12. Pushups
4 Rest_Pulse Num 8 BEST12. Rest_Pulse
5 Max_Pulse Num 8 BEST12. Max_Pulse
6 Run_Pulse Num 8 BEST12. Run_Pulse

Importing Exercise data

The Print Procedure

Data Set WORK.EXERCISE

Obs Subj Age Pushups Rest_Pulse Max_Pulse Run_Pulse
1 1 68 19 75 124 121
2 2 64 36 61 107 110
3 3 76 11 74 115 105
4 4 44 35 59 111 108
5 5 55 24 76 115 110
6 6 57 14 74 121 118
7 7 64 21 69 106 103
8 8 30 48 60 114 110
9 9 35 25 55 107 107
10 10 49 9 88 137 134
11 11 63 51 55 102 103
12 12 63 30 73 126 125
13 13 19 34 65 118 110
14 14 51 23 66 114 110
15 15 54 7 59 113 111
16 16 48 43 77 119 117
17 17 49 11 68 118 113
18 18 43 29 78 122 120
19 19 31 50 55 100 101
20 20 81 16 86 127 119
21 21 26 52 49 100 95
22 22 84 11 75 114 108
23 23 73 12 77 119 116
24 24 36 25 66 117 117
25 25 73 8 67 112 111

Logistic Regression data prep Birth_Wt_Sample to High_Low

The MEANS Procedure

The Means Procedure

Summary statistics

Variable Label N Mean Std Dev Minimum Maximum
Weight
Black
Married
Boy
MomAge
MomSmoke
CigsPerDay
MomWtGain
Visit
MomEdLevel
Wt_Group
Infant Birth Weight
Black Mother
Married Mother
Baby Boy
Mother's Age
Smoking Mother
Cigarettes Per Day
Mother's Pregnancy Weight Gain
Prenatal Visit
Mother's Education Level
 
12500
12500
12500
12500
12500
12500
12500
12500
12500
12500
12500
3373.25
0.1578400
0.7095200
0.5106400
0.3813600
0.1319200
1.4786400
0.6145600
2.6988000
1.2204000
0.4940000
561.7217975
0.3646055
0.4540020
0.4999068
5.7031611
0.3384173
4.6137064
12.8152321
0.7155135
1.0928492
0.4999840
322.0000000
0
0
0
-9.0000000
0
0
-30.0000000
0
0
0
5970.00
1.0000000
1.0000000
1.0000000
18.0000000
1.0000000
40.0000000
68.0000000
3.0000000
3.0000000
1.0000000

Logistic Regression data prep Birth_Wt_Sample to High_Low

The Print Procedure

Data Set WORK.HIGH_LOW

Obs Weight Black Married Boy MomAge MomSmoke CigsPerDay MomWtGain Visit MomEdLevel Wt_Group
1 3430 1 1 1 -4 0 0 -6 3 0 0
2 3657 0 1 0 6 0 0 15 3 0 0
3 4054 0 1 1 -5 0 0 21 3 2 0
4 4536 1 0 1 3 0 0 -1 3 3 0
5 3295 0 1 1 6 0 0 -29 3 2 1
6 3458 0 1 1 8 0 0 -18 3 1 0
7 3714 0 0 1 2 0 0 25 1 1 0
8 2807 0 1 0 -5 1 1 13 3 0 1
9 3625 0 1 0 2 0 0 0 3 0 0
10 3884 0 1 1 -2 0 0 -10 3 0 0

Import generated dataset Heart_Attack

The Print Procedure

Data Set WORK.HEART_ATTACK

Obs Gender Age Age_Group Chol High_Chol Heart_Attack
1 F 63 2 211 1 0
2 M 69 2 249 1 0
3 F 69 2 139 0 0
4 M 59 1 239 1 0
5 F 71 3 195 0 0
6 M 50 1 193 0 0
7 F 57 1 179 0 0
8 M 75 3 186 0 1
9 F 60 2 164 0 0
10 M 52 1 237 1 1

Import generated dataset Heart_Attack

The FREQ Procedure

The Freq Procedure

Table Gender

One-Way Frequencies

Gender
Gender Frequency Percent Cumulative
Frequency		 Cumulative
Percent
F 250 50.00 250 50.00
M 250 50.00 500 100.00

Table Age_Group

One-Way Frequencies

Age_Group
Age_Group Frequency Percent Cumulative
Frequency		 Cumulative
Percent
1 146 29.20 146 29.20
2 180 36.00 326 65.20
3 174 34.80 500 100.00

Table High_Chol

One-Way Frequencies

High_Chol
High_Chol Frequency Percent Cumulative
Frequency		 Cumulative
Percent
0 245 49.00 245 49.00
1 255 51.00 500 100.00

Table Heart_Attack

One-Way Frequencies

Heart_Attack
Heart_Attack Frequency Percent Cumulative
Frequency		 Cumulative
Percent
0 442 88.40 442 88.40
1 58 11.60 500 100.00

Sample Observations from Formatted Heart_Attack

The Print Procedure

Data Set WORK.HEART_ATTACK

Obs Gender Age Age_Group Chol High_Chol Heart_Attack
1 Female 63 60-70 211 Yes No
2 Male 69 60-70 249 Yes No
3 Female 69 60-70 139 No No
4 Male 59 < 60 239 Yes No
5 Female 71 71+ 195 No No
6 Male 50 < 60 193 No No
7 Female 57 < 60 179 No No
8 Male 75 71+ 186 No Yes
9 Female 60 60-70 164 No No
10 Male 52 < 60 237 Yes Yes

Sample Observations from Formatted Heart_Attack

The FREQ Procedure

The Freq Procedure

Table Gender

One-Way Frequencies

Gender
Gender Frequency Percent Cumulative
Frequency		 Cumulative
Percent
Female 250 50.00 250 50.00
Male 250 50.00 500 100.00

Table Age_Group

One-Way Frequencies

Age_Group
Age_Group Frequency Percent Cumulative
Frequency		 Cumulative
Percent
< 60 146 29.20 146 29.20
60-70 180 36.00 326 65.20
71+ 174 34.80 500 100.00

Table High_Chol

One-Way Frequencies

High_Chol
High_Chol Frequency Percent Cumulative
Frequency		 Cumulative
Percent
No 245 49.00 245 49.00
Yes 255 51.00 500 100.00

Table Heart_Attack

One-Way Frequencies

Heart_Attack
Heart_Attack Frequency Percent Cumulative
Frequency		 Cumulative
Percent
No 442 88.40 442 88.40
Yes 58 11.60 500 100.00

Sample Observations from Reformatted Heart_Attack

The Print Procedure

Data Set WORK.HEART_ATTACK

Obs Gender Age Age_Group Chol High_Chol Heart_Attack
1 2:Female 63 60-70 211 1:Yes 2:No
2 1:Male 69 60-70 249 1:Yes 2:No
3 2:Female 69 60-70 139 2:No 2:No
4 1:Male 59 < 60 239 1:Yes 2:No
5 2:Female 71 71+ 195 2:No 2:No
6 1:Male 50 < 60 193 2:No 2:No
7 2:Female 57 < 60 179 2:No 2:No
8 1:Male 75 71+ 186 2:No 1:Yes
9 2:Female 60 60-70 164 2:No 2:No
10 1:Male 52 < 60 237 1:Yes 1:Yes

Sample Observations from Reformatted Heart_Attack

The FREQ Procedure

The Freq Procedure

Table Gender

One-Way Frequencies

Gender
Gender Frequency Percent Cumulative
Frequency		 Cumulative
Percent
1:Male 250 50.00 250 50.00
2:Female 250 50.00 500 100.00

Table Age_Group

One-Way Frequencies

Age_Group
Age_Group Frequency Percent Cumulative
Frequency		 Cumulative
Percent
60-70 180 36.00 180 36.00
71+ 174 34.80 354 70.80
< 60 146 29.20 500 100.00

Table High_Chol

One-Way Frequencies

High_Chol
High_Chol Frequency Percent Cumulative
Frequency		 Cumulative
Percent
1:Yes 255 51.00 255 51.00
2:No 245 49.00 500 100.00

Table Heart_Attack

One-Way Frequencies

Heart_Attack
Heart_Attack Frequency Percent Cumulative
Frequency		 Cumulative
Percent
1:Yes 58 11.60 58 11.60
2:No 442 88.40 500 100.00

Chapter 5: Descriptive Statistics - Univariate Analysis

Descriptive Statistics for Continuous Variables.

SAS Code, click to expand

SAS Code:

#  (&path1 and biostats libname previously defined)
/*** Chapter 5: Descriptive Statistics - Univariate Analysis  ***/

/* Descriptive Statistics for Continuous Variables - generated code - start */
ods noproctitle;
ods graphics / imagemap=on;

title1 "Descriptive Statistics for Continuous Variables";
proc means data=sashelp.heart chartype mean std min max median n nmiss 
        vardef=df clm alpha=0.05 qmethod=os;
    var Height Weight Diastolic Systolic;
run;

/* Graph template to construct combination histogram/boxplot */
proc template;
    define statgraph histobox;
        dynamic AVAR ByVarInfo;
        begingraph;
        entrytitle "Distribution of " AVAR ByVarInfo;
        layout lattice / rows=2 columndatarange=union rowgutter=0 rowweights=(0.75 
            0.25);
        layout overlay / yaxisopts=(offsetmax=0.1) xaxisopts=(display=none);
        histogram AVAR /;
        endlayout;
        layout overlay /;
        BoxPlot Y=AVAR / orient=horizontal;
        endlayout;
        endlayout;
        endgraph;
    end;
run;

/* Macro to subset data and create a histobox for every by group */
%macro byGroupHistobox(data=, level=, num_level=, byVars=, num_byvars=, avar=);
    %do j=1 %to &num_byvars;
        %let varName&j=%scan(%str(&byVars), &j);
    %end;

    %do i=1 %to &num_level;

        /* Get group variable values */
        data _null_;
            i=&i;
            set &level point=i;

            %do j=1 %to &num_byvars;
                call symputx("x&j", strip(&&varName&j), 'l');
            %end;
            stop;
        run;

        /* Build proc sql where clause */
        %let dsid=%sysfunc(open(&data));
        %let whereClause=;

        %do j=1 %to %eval(&num_byvars-1);
            %let varnum=%sysfunc(varnum(&dsid, &&varName&j));

            %if(%sysfunc(vartype(&dsid, &varnum))=C) %then
                %let whereClause=&whereClause.&&varName&j.="&&x&j"%str( and );
            %else
                %let whereClause=&whereClause.&&varName&j.=&&x&j.%str( and );
        %end;
        %let varnum=%sysfunc(varnum(&dsid, &&varName&num_byvars));

        %if(%sysfunc(vartype(&dsid, &varnum))=C) %then
            %let whereClause=&whereClause.&&varName&num_byvars.="&&x&num_byvars";
        %else
            %let whereClause=&whereClause.&&varName&num_byvars.=&&x&num_byvars;
        %let rc=%sysfunc(close(&dsid));

        /* Subset the data set */
        proc sql noprint;
            create table WORK.tempData as select * from &data
            where &whereClause;
        quit;

        /* Build plot group info */
        %let groupInfo=;

        %do j=1 %to %eval(&num_byvars-1);
            %let groupInfo=&groupInfo.&&varName&j.=&&x&j%str( );
        %end;
        %let groupInfo=&groupInfo.&&varName&num_byvars.=&&x&num_byvars;

        /* Create histogram/boxplot combo plot */
        proc sgrender data=WORK.tempData template=histobox;
            dynamic AVAR="&avar" ByVarInfo=" (&groupInfo)";
        run;

    %end;
%mend;

proc sgrender data=sashelp.heart template=histobox;
    dynamic AVAR="Height" ByVarInfo="";
run;

proc sgrender data=sashelp.heart template=histobox;
    dynamic AVAR="Weight" ByVarInfo="";
run;

proc sgrender data=sashelp.heart template=histobox;
    dynamic AVAR="Diastolic" ByVarInfo="";
run;

proc sgrender data=sashelp.heart template=histobox;
    dynamic AVAR="Systolic" ByVarInfo="";
run;

proc datasets library=WORK noprint;
    delete tempData;
    run;

title1;
/* Descriptive Statistics for Continuous Variables - generated code - end */

/* The histogram and box plot for Systolic is positively skewed, seen by the long tail on the right side of the histogram and by the outliers (circles) on the box plot.  The mean (diamond on the box plot) is to the right of the median (vertical line in the box), indicating that the data values are positively skewed.  Let's further investigate the distribution of systolic blood pressure. */

SAS Output

Results: biostats_by_ex_SAScode.sas

Results: biostats_by_ex_SAScode.sas

Descriptive Statistics for Continuous Variables

The Means Procedure

Summary statistics

Variable Mean Std Dev Minimum Maximum Median N N Miss Lower 95%
CL for Mean		 Upper 95%
CL for Mean
Height
Weight
Diastolic
Systolic
64.8131847
153.0866808
85.3586101
136.9095796
3.5827074
28.9154261
12.9730913
23.7395964
51.5000000
67.0000000
50.0000000
82.0000000
76.5000000
300.0000000
160.0000000
300.0000000
64.5000000
150.0000000
84.0000000
132.0000000
5203
5203
5209
5209
6
6
0
0
64.7158128
152.3008087
85.0062268
136.2647496
64.9105566
153.8725528
85.7109934
137.5544095

Descriptive Statistics for Continuous Variables

The SGRender Procedure

The SGRender Procedure

Height = 76.5 Percent = 0.0577 Height = 76.5 Percent = 0.0577 Height = 75.5 Percent = 0.0961 Height = 75.5 Percent = 0.0961 Height = 74.5 Percent = 0.2691 Height = 74.5 Percent = 0.2691 Height = 73.5 Percent = 0.7303 Height = 73.5 Percent = 0.7303 Height = 72.5 Percent = 1.7298 Height = 72.5 Percent = 1.7298 Height = 71.5 Percent = 2.4601 Height = 71.5 Percent = 2.4601 Height = 70.5 Percent = 3.6902 Height = 70.5 Percent = 3.6902 Height = 69.5 Percent = 5.5545 Height = 69.5 Percent = 5.5545 Height = 68.5 Percent = 6.8999 Height = 68.5 Percent = 6.8999 Height = 67.5 Percent = 8.0915 Height = 67.5 Percent = 8.0915 Height = 66.5 Percent = 7.8032 Height = 66.5 Percent = 7.8032 Height = 65.5 Percent = 10.398 Height = 65.5 Percent = 10.398 Height = 64.5 Percent = 9.8597 Height = 64.5 Percent = 9.8597 Height = 63.5 Percent = 9.9558 Height = 63.5 Percent = 9.9558 Height = 62.5 Percent = 10.974 Height = 62.5 Percent = 10.974 Height = 61.5 Percent = 8.1299 Height = 61.5 Percent = 8.1299 Height = 60.5 Percent = 5.9773 Height = 60.5 Percent = 5.9773 Height = 59.5 Percent = 3.9593 Height = 59.5 Percent = 3.9593 Height = 58.5 Percent = 1.9988 Height = 58.5 Percent = 1.9988 Height = 57.5 Percent = 0.615 Height = 57.5 Percent = 0.615 Height = 56.5 Percent = 0.5574 Height = 56.5 Percent = 0.5574 Height = 55.5 Percent = 0.1153 Height = 55.5 Percent = 0.1153 Height = 54.5 Percent = 0.0384 Height = 54.5 Percent = 0.0384 Height = 53.5 Percent = 0.0192 Height = 53.5 Percent = 0.0192 Height = 52.5 Percent = 0 Height = 52.5 Percent = 0 Height = 51.5 Percent = 0.0192 Height = 51.5 Percent = 0.0192 Height = 75.5 Height = 75.5 Height = 76 Height = 76 Height = 76.5 Height = 53.75 Height = 51.5 Data Minimum = 51.5 Minimum Whisker = 54.75 First Quartile = 62.25 Median = 64.5 Third Quartile = 67.5 Maximum Whisker = 75.25 Data Maximum = 76.5 Mean = 64.813 Standard Deviation = 3.5827 Number of Observations = 5203 Sum of Weight = . Data Minimum = 51.5 Minimum Whisker = 54.75 First Quartile = 62.25 Median = 64.5 Third Quartile = 67.5 Maximum Whisker = 75.25 Data Maximum = 76.5 Mean = 64.813 Standard Deviation = 3.5827 Number of Observations = 5203 Sum of Weight = . Data Minimum = 51.5 Minimum Whisker = 54.75 First Quartile = 62.25 Median = 64.5 Third Quartile = 67.5 Maximum Whisker = 75.25 Data Maximum = 76.5 Mean = 64.813 Standard Deviation = 3.5827 Number of Observations = 5203 Sum of Weight = . Data Minimum = 51.5 Minimum Whisker = 54.75 First Quartile = 62.25 Median = 64.5 Third Quartile = 67.5 Maximum Whisker = 75.25 Data Maximum = 76.5 Mean = 64.813 Standard Deviation = 3.5827 Number of Observations = 5203 Sum of Weight = . Data Minimum = 51.5 Minimum Whisker = 54.75 First Quartile = 62.25 Median = 64.5 Third Quartile = 67.5 Maximum Whisker = 75.25 Data Maximum = 76.5 Mean = 64.813 Standard Deviation = 3.5827 Number of Observations = 5203 Sum of Weight = . Data Minimum = 51.5 Minimum Whisker = 54.75 First Quartile = 62.25 Median = 64.5 Third Quartile = 67.5 Maximum Whisker = 75.25 Data Maximum = 76.5 Mean = 64.813 Standard Deviation = 3.5827 Number of Observations = 5203 Sum of Weight = . Data Minimum = 51.5 Minimum Whisker = 54.75 First Quartile = 62.25 Median = 64.5 Third Quartile = 67.5 Maximum Whisker = 75.25 Data Maximum = 76.5 Mean = 64.813 Standard Deviation = 3.5827 Number of Observations = 5203 Sum of Weight = . Data Minimum = 51.5 Minimum Whisker = 54.75 First Quartile = 62.25 Median = 64.5 Third Quartile = 67.5 Maximum Whisker = 75.25 Data Maximum = 76.5 Mean = 64.813 Standard Deviation = 3.5827 Number of Observations = 5203 Sum of Weight = .
The SGRender Procedure

Descriptive Statistics for Continuous Variables

The SGRender Procedure

The SGRender Procedure

Weight = 300 Percent = 0.0384 Weight = 300 Percent = 0.0384 Weight = 290 Percent = 0.0192 Weight = 290 Percent = 0.0192 Weight = 280 Percent = 0.0577 Weight = 280 Percent = 0.0577 Weight = 270 Percent = 0.0577 Weight = 270 Percent = 0.0577 Weight = 260 Percent = 0.0769 Weight = 260 Percent = 0.0769 Weight = 250 Percent = 0.1153 Weight = 250 Percent = 0.1153 Weight = 240 Percent = 0.4805 Weight = 240 Percent = 0.4805 Weight = 230 Percent = 0.6342 Weight = 230 Percent = 0.6342 Weight = 220 Percent = 1.134 Weight = 220 Percent = 1.134 Weight = 210 Percent = 2.0757 Weight = 210 Percent = 2.0757 Weight = 200 Percent = 3.4019 Weight = 200 Percent = 3.4019 Weight = 190 Percent = 5.9004 Weight = 190 Percent = 5.9004 Weight = 180 Percent = 8.745 Weight = 180 Percent = 8.745 Weight = 170 Percent = 10.263 Weight = 170 Percent = 10.263 Weight = 160 Percent = 10.936 Weight = 160 Percent = 10.936 Weight = 150 Percent = 13.761 Weight = 150 Percent = 13.761 Weight = 140 Percent = 14.472 Weight = 140 Percent = 14.472 Weight = 130 Percent = 11.935 Weight = 130 Percent = 11.935 Weight = 120 Percent = 8.6873 Weight = 120 Percent = 8.6873 Weight = 110 Percent = 4.9202 Weight = 110 Percent = 4.9202 Weight = 100 Percent = 1.7682 Weight = 100 Percent = 1.7682 Weight = 90 Percent = 0.4228 Weight = 90 Percent = 0.4228 Weight = 80 Percent = 0.0384 Weight = 80 Percent = 0.0384 Weight = 70 Percent = 0.0577 Weight = 70 Percent = 0.0577 Weight = 234 Weight = 234 Weight = 235 Weight = 235 Weight = 235 Weight = 235 Weight = 236 Weight = 236 Weight = 236 Weight = 236 Weight = 237 Weight = 237 Weight = 238 Weight = 238 Weight = 238 Weight = 239 Weight = 239 Weight = 239 Weight = 239 Weight = 240 Weight = 241 Weight = 241 Weight = 242 Weight = 243 Weight = 244 Weight = 244 Weight = 244 Weight = 245 Weight = 245 Weight = 246 Weight = 247 Weight = 250 Weight = 250 Weight = 255 Weight = 256 Weight = 260 Weight = 261 Weight = 269 Weight = 271 Weight = 273 Weight = 275 Weight = 276 Weight = 281 Weight = 293 Weight = 300 Weight = 300 Weight = 71 Weight = 67 Data Minimum = 67 Minimum Whisker = 72 First Quartile = 132 Median = 150 Third Quartile = 172 Maximum Whisker = 232 Data Maximum = 300 Mean = 153.09 Standard Deviation = 28.915 Number of Observations = 5203 Sum of Weight = . Data Minimum = 67 Minimum Whisker = 72 First Quartile = 132 Median = 150 Third Quartile = 172 Maximum Whisker = 232 Data Maximum = 300 Mean = 153.09 Standard Deviation = 28.915 Number of Observations = 5203 Sum of Weight = . Data Minimum = 67 Minimum Whisker = 72 First Quartile = 132 Median = 150 Third Quartile = 172 Maximum Whisker = 232 Data Maximum = 300 Mean = 153.09 Standard Deviation = 28.915 Number of Observations = 5203 Sum of Weight = . Data Minimum = 67 Minimum Whisker = 72 First Quartile = 132 Median = 150 Third Quartile = 172 Maximum Whisker = 232 Data Maximum = 300 Mean = 153.09 Standard Deviation = 28.915 Number of Observations = 5203 Sum of Weight = . Data Minimum = 67 Minimum Whisker = 72 First Quartile = 132 Median = 150 Third Quartile = 172 Maximum Whisker = 232 Data Maximum = 300 Mean = 153.09 Standard Deviation = 28.915 Number of Observations = 5203 Sum of Weight = . Data Minimum = 67 Minimum Whisker = 72 First Quartile = 132 Median = 150 Third Quartile = 172 Maximum Whisker = 232 Data Maximum = 300 Mean = 153.09 Standard Deviation = 28.915 Number of Observations = 5203 Sum of Weight = . Data Minimum = 67 Minimum Whisker = 72 First Quartile = 132 Median = 150 Third Quartile = 172 Maximum Whisker = 232 Data Maximum = 300 Mean = 153.09 Standard Deviation = 28.915 Number of Observations = 5203 Sum of Weight = . Data Minimum = 67 Minimum Whisker = 72 First Quartile = 132 Median = 150 Third Quartile = 172 Maximum Whisker = 232 Data Maximum = 300 Mean = 153.09 Standard Deviation = 28.915 Number of Observations = 5203 Sum of Weight = .
The SGRender Procedure

Descriptive Statistics for Continuous Variables

The SGRender Procedure

The SGRender Procedure

Diastolic = 160 Percent = 0.0192 Diastolic = 160 Percent = 0.0192 Diastolic = 155 Percent = 0.0192 Diastolic = 155 Percent = 0.0192 Diastolic = 150 Percent = 0.0576 Diastolic = 150 Percent = 0.0576 Diastolic = 145 Percent = 0.0768 Diastolic = 145 Percent = 0.0768 Diastolic = 140 Percent = 0.192 Diastolic = 140 Percent = 0.192 Diastolic = 135 Percent = 0.096 Diastolic = 135 Percent = 0.096 Diastolic = 130 Percent = 0.4031 Diastolic = 130 Percent = 0.4031 Diastolic = 125 Percent = 0.3648 Diastolic = 125 Percent = 0.3648 Diastolic = 120 Percent = 1.0559 Diastolic = 120 Percent = 1.0559 Diastolic = 115 Percent = 0.7487 Diastolic = 115 Percent = 0.7487 Diastolic = 110 Percent = 2.9756 Diastolic = 110 Percent = 2.9756 Diastolic = 105 Percent = 2.5341 Diastolic = 105 Percent = 2.5341 Diastolic = 100 Percent = 7.7174 Diastolic = 100 Percent = 7.7174 Diastolic = 95 Percent = 7.3527 Diastolic = 95 Percent = 7.3527 Diastolic = 90 Percent = 17.239 Diastolic = 90 Percent = 17.239 Diastolic = 85 Percent = 11.73 Diastolic = 85 Percent = 11.73 Diastolic = 80 Percent = 22.173 Diastolic = 80 Percent = 22.173 Diastolic = 75 Percent = 8.7541 Diastolic = 75 Percent = 8.7541 Diastolic = 70 Percent = 12.766 Diastolic = 70 Percent = 12.766 Diastolic = 65 Percent = 1.9965 Diastolic = 65 Percent = 1.9965 Diastolic = 60 Percent = 1.3438 Diastolic = 60 Percent = 1.3438 Diastolic = 55 Percent = 0.2496 Diastolic = 55 Percent = 0.2496 Diastolic = 50 Percent = 0.1344 Diastolic = 50 Percent = 0.1344 Diastolic = 118 Diastolic = 118 Diastolic = 118 Diastolic = 118 Diastolic = 118 Diastolic = 118 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 120 Diastolic = 122 Diastolic = 122 Diastolic = 124 Diastolic = 124 Diastolic = 124 Diastolic = 124 Diastolic = 124 Diastolic = 124 Diastolic = 124 Diastolic = 124 Diastolic = 124 Diastolic = 124 Diastolic = 124 Diastolic = 124 Diastolic = 125 Diastolic = 125 Diastolic = 125 Diastolic = 125 Diastolic = 126 Diastolic = 126 Diastolic = 126 Diastolic = 128 Diastolic = 130 Diastolic = 130 Diastolic = 130 Diastolic = 130 Diastolic = 130 Diastolic = 130 Diastolic = 130 Diastolic = 130 Diastolic = 130 Diastolic = 130 Diastolic = 130 Diastolic = 130 Diastolic = 130 Diastolic = 130 Diastolic = 130 Diastolic = 130 Diastolic = 130 Diastolic = 130 Diastolic = 130 Diastolic = 130 Diastolic = 134 Diastolic = 134 Diastolic = 134 Diastolic = 135 Diastolic = 136 Diastolic = 138 Diastolic = 138 Diastolic = 138 Diastolic = 140 Diastolic = 140 Diastolic = 140 Diastolic = 140 Diastolic = 140 Diastolic = 140 Diastolic = 140 Diastolic = 144 Diastolic = 145 Diastolic = 145 Diastolic = 145 Diastolic = 150 Diastolic = 150 Diastolic = 150 Diastolic = 155 Diastolic = 160 Diastolic = 50 Diastolic = 50 Diastolic = 50 Diastolic = 50 Diastolic = 50 Data Minimum = 50 Minimum Whisker = 52 First Quartile = 76 Median = 84 Third Quartile = 92 Maximum Whisker = 116 Data Maximum = 160 Mean = 85.359 Standard Deviation = 12.973 Number of Observations = 5209 Sum of Weight = . Data Minimum = 50 Minimum Whisker = 52 First Quartile = 76 Median = 84 Third Quartile = 92 Maximum Whisker = 116 Data Maximum = 160 Mean = 85.359 Standard Deviation = 12.973 Number of Observations = 5209 Sum of Weight = . Data Minimum = 50 Minimum Whisker = 52 First Quartile = 76 Median = 84 Third Quartile = 92 Maximum Whisker = 116 Data Maximum = 160 Mean = 85.359 Standard Deviation = 12.973 Number of Observations = 5209 Sum of Weight = . Data Minimum = 50 Minimum Whisker = 52 First Quartile = 76 Median = 84 Third Quartile = 92 Maximum Whisker = 116 Data Maximum = 160 Mean = 85.359 Standard Deviation = 12.973 Number of Observations = 5209 Sum of Weight = . Data Minimum = 50 Minimum Whisker = 52 First Quartile = 76 Median = 84 Third Quartile = 92 Maximum Whisker = 116 Data Maximum = 160 Mean = 85.359 Standard Deviation = 12.973 Number of Observations = 5209 Sum of Weight = . Data Minimum = 50 Minimum Whisker = 52 First Quartile = 76 Median = 84 Third Quartile = 92 Maximum Whisker = 116 Data Maximum = 160 Mean = 85.359 Standard Deviation = 12.973 Number of Observations = 5209 Sum of Weight = . Data Minimum = 50 Minimum Whisker = 52 First Quartile = 76 Median = 84 Third Quartile = 92 Maximum Whisker = 116 Data Maximum = 160 Mean = 85.359 Standard Deviation = 12.973 Number of Observations = 5209 Sum of Weight = . Data Minimum = 50 Minimum Whisker = 52 First Quartile = 76 Median = 84 Third Quartile = 92 Maximum Whisker = 116 Data Maximum = 160 Mean = 85.359 Standard Deviation = 12.973 Number of Observations = 5209 Sum of Weight = .
The SGRender Procedure

Descriptive Statistics for Continuous Variables

The SGRender Procedure

The SGRender Procedure

Systolic = 300 Percent = 0.0192 Systolic = 300 Percent = 0.0192 Systolic = 292 Percent = 0.0384 Systolic = 292 Percent = 0.0384 Systolic = 284 Percent = 0.0384 Systolic = 284 Percent = 0.0384 Systolic = 276 Percent = 0.0384 Systolic = 276 Percent = 0.0384 Systolic = 268 Percent = 0.0192 Systolic = 268 Percent = 0.0192 Systolic = 260 Percent = 0.0384 Systolic = 260 Percent = 0.0384 Systolic = 252 Percent = 0.0768 Systolic = 252 Percent = 0.0768 Systolic = 244 Percent = 0.1728 Systolic = 244 Percent = 0.1728 Systolic = 236 Percent = 0.0768 Systolic = 236 Percent = 0.0768 Systolic = 228 Percent = 0.2688 Systolic = 228 Percent = 0.2688 Systolic = 220 Percent = 0.384 Systolic = 220 Percent = 0.384 Systolic = 212 Percent = 0.5375 Systolic = 212 Percent = 0.5375 Systolic = 204 Percent = 0.5567 Systolic = 204 Percent = 0.5567 Systolic = 196 Percent = 0.5375 Systolic = 196 Percent = 0.5375 Systolic = 188 Percent = 1.4974 Systolic = 188 Percent = 1.4974 Systolic = 180 Percent = 2.1309 Systolic = 180 Percent = 2.1309 Systolic = 172 Percent = 3.6475 Systolic = 172 Percent = 3.6475 Systolic = 164 Percent = 5.2217 Systolic = 164 Percent = 5.2217 Systolic = 156 Percent = 5.5097 Systolic = 156 Percent = 5.5097 Systolic = 148 Percent = 9.3684 Systolic = 148 Percent = 9.3684 Systolic = 140 Percent = 15.07 Systolic = 140 Percent = 15.07 Systolic = 132 Percent = 17.259 Systolic = 132 Percent = 17.259 Systolic = 124 Percent = 17.739 Systolic = 124 Percent = 17.739 Systolic = 116 Percent = 10.29 Systolic = 116 Percent = 10.29 Systolic = 108 Percent = 7.2951 Systolic = 108 Percent = 7.2951 Systolic = 100 Percent = 1.747 Systolic = 100 Percent = 1.747 Systolic = 92 Percent = 0.384 Systolic = 92 Percent = 0.384 Systolic = 84 Percent = 0.0384 Systolic = 84 Percent = 0.0384 Systolic = 192 Systolic = 192 Systolic = 192 Systolic = 192 Systolic = 194 Systolic = 194 Systolic = 194 Systolic = 194 Systolic = 194 Systolic = 194 Systolic = 194 Systolic = 194 Systolic = 195 Systolic = 195 Systolic = 195 Systolic = 195 Systolic = 195 Systolic = 195 Systolic = 195 Systolic = 196 Systolic = 196 Systolic = 196 Systolic = 196 Systolic = 196 Systolic = 196 Systolic = 198 Systolic = 198 Systolic = 198 Systolic = 200 Systolic = 200 Systolic = 200 Systolic = 200 Systolic = 200 Systolic = 200 Systolic = 200 Systolic = 200 Systolic = 200 Systolic = 200 Systolic = 200 Systolic = 200 Systolic = 200 Systolic = 200 Systolic = 200 Systolic = 200 Systolic = 200 Systolic = 200 Systolic = 202 Systolic = 204 Systolic = 204 Systolic = 204 Systolic = 204 Systolic = 204 Systolic = 204 Systolic = 205 Systolic = 205 Systolic = 206 Systolic = 206 Systolic = 208 Systolic = 208 Systolic = 208 Systolic = 208 Systolic = 208 Systolic = 208 Systolic = 210 Systolic = 210 Systolic = 210 Systolic = 210 Systolic = 210 Systolic = 210 Systolic = 210 Systolic = 210 Systolic = 210 Systolic = 210 Systolic = 210 Systolic = 210 Systolic = 210 Systolic = 210 Systolic = 212 Systolic = 212 Systolic = 212 Systolic = 214 Systolic = 214 Systolic = 214 Systolic = 215 Systolic = 215 Systolic = 216 Systolic = 216 Systolic = 216 Systolic = 216 Systolic = 216 Systolic = 218 Systolic = 220 Systolic = 220 Systolic = 220 Systolic = 220 Systolic = 220 Systolic = 220 Systolic = 220 Systolic = 220 Systolic = 220 Systolic = 220 Systolic = 220 Systolic = 220 Systolic = 220 Systolic = 222 Systolic = 225 Systolic = 225 Systolic = 226 Systolic = 226 Systolic = 228 Systolic = 228 Systolic = 230 Systolic = 230 Systolic = 230 Systolic = 230 Systolic = 230 Systolic = 230 Systolic = 230 Systolic = 230 Systolic = 234 Systolic = 234 Systolic = 236 Systolic = 236 Systolic = 240 Systolic = 240 Systolic = 240 Systolic = 240 Systolic = 240 Systolic = 242 Systolic = 246 Systolic = 246 Systolic = 246 Systolic = 250 Systolic = 250 Systolic = 250 Systolic = 250 Systolic = 260 Systolic = 260 Systolic = 270 Systolic = 272 Systolic = 276 Systolic = 280 Systolic = 286 Systolic = 290 Systolic = 294 Systolic = 300 Data Minimum = 82 Minimum Whisker = 82 First Quartile = 120 Median = 132 Third Quartile = 148 Maximum Whisker = 190 Data Maximum = 300 Mean = 136.91 Standard Deviation = 23.74 Number of Observations = 5209 Sum of Weight = . Data Minimum = 82 Minimum Whisker = 82 First Quartile = 120 Median = 132 Third Quartile = 148 Maximum Whisker = 190 Data Maximum = 300 Mean = 136.91 Standard Deviation = 23.74 Number of Observations = 5209 Sum of Weight = . Data Minimum = 82 Minimum Whisker = 82 First Quartile = 120 Median = 132 Third Quartile = 148 Maximum Whisker = 190 Data Maximum = 300 Mean = 136.91 Standard Deviation = 23.74 Number of Observations = 5209 Sum of Weight = . Data Minimum = 82 Minimum Whisker = 82 First Quartile = 120 Median = 132 Third Quartile = 148 Maximum Whisker = 190 Data Maximum = 300 Mean = 136.91 Standard Deviation = 23.74 Number of Observations = 5209 Sum of Weight = . Data Minimum = 82 Minimum Whisker = 82 First Quartile = 120 Median = 132 Third Quartile = 148 Maximum Whisker = 190 Data Maximum = 300 Mean = 136.91 Standard Deviation = 23.74 Number of Observations = 5209 Sum of Weight = . Data Minimum = 82 Minimum Whisker = 82 First Quartile = 120 Median = 132 Third Quartile = 148 Maximum Whisker = 190 Data Maximum = 300 Mean = 136.91 Standard Deviation = 23.74 Number of Observations = 5209 Sum of Weight = . Data Minimum = 82 Minimum Whisker = 82 First Quartile = 120 Median = 132 Third Quartile = 148 Maximum Whisker = 190 Data Maximum = 300 Mean = 136.91 Standard Deviation = 23.74 Number of Observations = 5209 Sum of Weight = . Data Minimum = 82 Minimum Whisker = 82 First Quartile = 120 Median = 132 Third Quartile = 148 Maximum Whisker = 190 Data Maximum = 300 Mean = 136.91 Standard Deviation = 23.74 Number of Observations = 5209 Sum of Weight = .
The SGRender Procedure
  • The histogram and box plot for Systolic is positively skewed, seen by the long tail on the right side of the histogram and by the outliers (circles) on the box plot. The mean (diamond on the box plot) is to the right of the median (vertical line in the box), indicating that the data values are positively skewed. Let’s further investigate the distribution of systolic blood pressure.

Investigating the Distribution for Systolic Blood Pressure.

SAS Code, click to expand

SAS Code:

#  (&path1 and biostats libname previously defined)
/* Investigating the Distribution for Systolic Blood Pressure - start */
ods noproctitle;
ods graphics / imagemap=on;

title1 "Investigating the Distribution for Systolic Blood Pressure";
proc univariate data=sashelp.heart;
    ods select QQPlot;
    var Systolic;

    /* Checking for Normality */
    qqplot Systolic / normal(mu=est sigma=est);
    inset skewness kurtosis n / position=nw;
run;

title1;
/* Investigating the Distribution for Systolic Blood Pressure - end */

/* The straight line represents a normal distribution with the same mean and standard deviation as the variable Systolic.  Values for Skewness and Kurtosis close to zero result from distributions that are close to normal.  The theoretical normal distribution has a mean (Mu) of 136.91 and a standard deviation (Sigma) of 23.74.  The circles on the plot represent values of systolic blood pressure from the sample data.  The right side of the this Q-Q plot shows circles above the straight line, indicating that the sample data includes values of systolic blood pressure that are higher than expected if the values were normally distributed.  This confirms the strong positive skewness seen in the prior histogram.   Positive values for skewness indicate a positively skewed distribution (right tail).  Positive values for kurtosis indicate both that the distribution is too peaked (leptokurtic) and that the tails are too heavy.  (In contrast, negative values for kurtosis indicate that the distribution is too flat (platykurtic) and that the tails are too light. Modern interpretation of kurtosis puts emphasis on the tails being too heavy or too light and deemphasizes the concepts of the distribution being too peaked or too flat.) */

SAS Output

Results: biostats_by_ex_SAScode.sas

Results: biostats_by_ex_SAScode.sas

Investigating the Distribution for Systolic Blood Pressure

The Univariate Procedure

Systolic

Q-Q Plot 1

Panel 1

Q-Q plot for Systolic
  • The straight line represents a normal distribution with the same mean and standard deviation as the variable Systolic. Values for Skewness and Kurtosis close to zero result from distributions that are close to normal. The theoretical normal distribution has a mean (Mu) of 136.91 and a standard deviation (Sigma) of 23.74. The circles on the plot represent values of systolic blood pressure from the sample data. The right side of the this Q-Q plot shows circles above the straight line, indicating that the sample data includes values of systolic blood pressure that are higher than expected if the values were normally distributed. This confirms the strong positive skewness seen in the prior histogram. Positive values for skewness indicate a positively skewed distribution (right tail). Positive values for kurtosis indicate both that the distribution is too peaked (leptokurtic) and that the tails are too heavy. (In contrast, negative values for kurtosis indicate that the distribution is too flat (platykurtic) and that the tails are too light. Modern interpretation of kurtosis puts emphasis on the tails being too heavy or too light and deemphasizes the concepts of the distribution being too peaked or too flat.)

Adding a Classification Variable in the Summary Statistics.

SAS Code, click to expand

SAS Code:

#  (&path1 and biostats libname previously defined)
/* Adding a Classification Variable in the Summary Statistics - start */
ods noproctitle;
ods graphics / imagemap=on;

title1 "Adding a Classification Variable in the Summary Statistics";
proc means data=sashelp.heart chartype mean std min max median n nmiss 
        vardef=df clm alpha=0.05 qmethod=os;
    var Height;
    class Sex;
run;

proc univariate data=sashelp.heart vardef=df noprint;
    var Height;
    class Sex;
    histogram Height / normal(noprint);
run;

proc sort data=sashelp.heart out=WORK.TempSorted2236;
    by Sex;
run;

proc boxplot data=WORK.TempSorted2236;
    plot (Height)*Sex / boxstyle=schematic;
run;

proc datasets library=WORK noprint;
    delete TempSorted2236;
    run;
title1;
/* Adding a Classification Variable in the Summary Statistics - end */

/* The center of the distribution for Sex=Male is shifted to the right compared to the distribution for Sex=Female.  The box plots also show more outliers in the female distribution of Height compared to the male distribution.  This may be partly due to the smaller interquartile range (the distance from the top to the bottom of the box) for the females compared to the males. */

SAS Output

Results: biostats_by_ex_SAScode.sas

Results: biostats_by_ex_SAScode.sas

Adding a Classification Variable in the Summary Statistics

The Means Procedure

Summary statistics

Analysis Variable : Height
Sex N Obs Mean Std Dev Minimum Maximum Median N N Miss Lower 95%
CL for Mean		 Upper 95%
CL for Mean
Female 2873 62.5725863 2.4524112 51.5000000 70.7500000 62.5000000 2869 4 62.4828104 62.6623621
Male 2336 67.5673736 2.7321366 56.0000000 76.5000000 67.5000000 2334 2 67.4564752 67.6782721

Adding a Classification Variable in the Summary Statistics

The Univariate Procedure

Height

Histogram 1

Panel 1

Height = 77 Percent = 0 CurveLabel = Normal Height = 76.869 Percent = 0 CurveLabel = Normal Height = 76.869 Percent = 0 CurveLabel = Normal Height = 76.737 Percent = 0 CurveLabel = Normal Height = 76.737 Percent = 0 CurveLabel = Normal Height = 76.606 Percent = 0 CurveLabel = Normal Height = 76.606 Percent = 0 CurveLabel = Normal Height = 76.475 Percent = 0 CurveLabel = Normal Height = 76.475 Percent = 0 CurveLabel = Normal Height = 76.343 Percent = 0 CurveLabel = Normal Height = 76.343 Percent = 0 CurveLabel = Normal Height = 76.212 Percent = 0 CurveLabel = Normal Height = 76.212 Percent = 0 CurveLabel = Normal Height = 76.081 Percent = 0 CurveLabel = Normal Height = 76.081 Percent = 0 CurveLabel = Normal Height = 75.949 Percent = 0 CurveLabel = Normal Height = 75.949 Percent = 0 CurveLabel = Normal Height = 75.818 Percent = 0 CurveLabel = Normal Height = 75.818 Percent = 0 CurveLabel = Normal Height = 75.687 Percent = 0 CurveLabel = Normal Height = 75.687 Percent = 0 CurveLabel = Normal Height = 75.556 Percent = 0 CurveLabel = Normal Height = 75.556 Percent = 0 CurveLabel = Normal Height = 75.424 Percent = 0 CurveLabel = Normal Height = 75.424 Percent = 0 CurveLabel = Normal Height = 75.293 Percent = 0 CurveLabel = Normal Height = 75.293 Percent = 0 CurveLabel = Normal Height = 75.162 Percent = 0 CurveLabel = Normal Height = 75.162 Percent = 0 CurveLabel = Normal Height = 75.03 Percent = 0 CurveLabel = Normal Height = 75.03 Percent = 0 CurveLabel = Normal Height = 74.899 Percent = 0 CurveLabel = Normal Height = 74.899 Percent = 0 CurveLabel = Normal Height = 74.768 Percent = 0 CurveLabel = Normal Height = 74.768 Percent = 0 CurveLabel = Normal Height = 74.636 Percent = 0 CurveLabel = Normal Height = 74.636 Percent = 0 CurveLabel = Normal Height = 74.505 Percent = 0 CurveLabel = Normal Height = 74.505 Percent = 0 CurveLabel = Normal Height = 74.374 Percent = 0 CurveLabel = Normal Height = 74.374 Percent = 0 CurveLabel = Normal Height = 74.242 Percent = 0 CurveLabel = Normal Height = 74.242 Percent = 0 CurveLabel = Normal Height = 74.111 Percent = 0 CurveLabel = Normal Height = 74.111 Percent = 0 CurveLabel = Normal Height = 73.98 Percent = 0 CurveLabel = Normal Height = 73.98 Percent = 0 CurveLabel = Normal Height = 73.848 Percent = 0 CurveLabel = Normal Height = 73.848 Percent = 0 CurveLabel = Normal Height = 73.717 Percent = 0 CurveLabel = Normal Height = 73.717 Percent = 0 CurveLabel = Normal Height = 73.586 Percent = 0 CurveLabel = Normal Height = 73.586 Percent = 0 CurveLabel = Normal Height = 73.455 Percent = 0 CurveLabel = Normal Height = 73.455 Percent = 0 CurveLabel = Normal Height = 73.323 Percent = 0 CurveLabel = Normal Height = 73.323 Percent = 0 CurveLabel = Normal Height = 73.192 Percent = 0 CurveLabel = Normal Height = 73.192 Percent = 0 CurveLabel = Normal Height = 73.061 Percent = 0 CurveLabel = Normal Height = 73.061 Percent = 0 CurveLabel = Normal Height = 72.929 Percent = 0 CurveLabel = Normal Height = 72.929 Percent = 0 CurveLabel = Normal Height = 72.798 Percent = 0 CurveLabel = Normal Height = 72.798 Percent = 0 CurveLabel = Normal Height = 72.667 Percent = 0 CurveLabel = Normal Height = 72.667 Percent = 0 CurveLabel = Normal Height = 72.535 Percent = 0 CurveLabel = Normal Height = 72.535 Percent = 0 CurveLabel = Normal Height = 72.404 Percent = 0 CurveLabel = Normal Height = 72.404 Percent = 0 CurveLabel = Normal Height = 72.273 Percent = 0.0065 CurveLabel = Normal Height = 72.273 Percent = 0.0065 CurveLabel = Normal Height = 72.141 Percent = 0.008 CurveLabel = Normal Height = 72.141 Percent = 0.008 CurveLabel = Normal Height = 72.01 Percent = 0.0099 CurveLabel = Normal Height = 72.01 Percent = 0.0099 CurveLabel = Normal Height = 71.879 Percent = 0.0121 CurveLabel = Normal Height = 71.879 Percent = 0.0121 CurveLabel = Normal Height = 71.747 Percent = 0.0149 CurveLabel = Normal Height = 71.747 Percent = 0.0149 CurveLabel = Normal Height = 71.616 Percent = 0.0181 CurveLabel = Normal Height = 71.616 Percent = 0.0181 CurveLabel = Normal Height = 71.485 Percent = 0.0221 CurveLabel = Normal Height = 71.485 Percent = 0.0221 CurveLabel = Normal Height = 71.354 Percent = 0.0268 CurveLabel = Normal Height = 71.354 Percent = 0.0268 CurveLabel = Normal Height = 71.222 Percent = 0.0324 CurveLabel = Normal Height = 71.222 Percent = 0.0324 CurveLabel = Normal Height = 71.091 Percent = 0.039 CurveLabel = Normal Height = 71.091 Percent = 0.039 CurveLabel = Normal Height = 70.96 Percent = 0.0469 CurveLabel = Normal Height = 70.96 Percent = 0.0469 CurveLabel = Normal Height = 70.828 Percent = 0.0563 CurveLabel = Normal Height = 70.828 Percent = 0.0563 CurveLabel = Normal Height = 70.697 Percent = 0.0673 CurveLabel = Normal Height = 70.697 Percent = 0.0673 CurveLabel = Normal Height = 70.566 Percent = 0.0803 CurveLabel = Normal Height = 70.566 Percent = 0.0803 CurveLabel = Normal Height = 70.434 Percent = 0.0954 CurveLabel = Normal Height = 70.434 Percent = 0.0954 CurveLabel = Normal Height = 70.303 Percent = 0.1132 CurveLabel = Normal Height = 70.303 Percent = 0.1132 CurveLabel = Normal Height = 70.172 Percent = 0.1338 CurveLabel = Normal Height = 70.172 Percent = 0.1338 CurveLabel = Normal Height = 70.04 Percent = 0.1577 CurveLabel = Normal Height = 70.04 Percent = 0.1577 CurveLabel = Normal Height = 69.909 Percent = 0.1853 CurveLabel = Normal Height = 69.909 Percent = 0.1853 CurveLabel = Normal Height = 69.778 Percent = 0.2172 CurveLabel = Normal Height = 69.778 Percent = 0.2172 CurveLabel = Normal Height = 69.646 Percent = 0.2539 CurveLabel = Normal Height = 69.646 Percent = 0.2539 CurveLabel = Normal Height = 69.515 Percent = 0.2959 CurveLabel = Normal Height = 69.515 Percent = 0.2959 CurveLabel = Normal Height = 69.384 Percent = 0.3438 CurveLabel = Normal Height = 69.384 Percent = 0.3438 CurveLabel = Normal Height = 69.253 Percent = 0.3983 CurveLabel = Normal Height = 69.253 Percent = 0.3983 CurveLabel = Normal Height = 69.121 Percent = 0.4602 CurveLabel = Normal Height = 69.121 Percent = 0.4602 CurveLabel = Normal Height = 68.99 Percent = 0.5302 CurveLabel = Normal Height = 68.99 Percent = 0.5302 CurveLabel = Normal Height = 68.859 Percent = 0.6091 CurveLabel = Normal Height = 68.859 Percent = 0.6091 CurveLabel = Normal Height = 68.727 Percent = 0.6977 CurveLabel = Normal Height = 68.727 Percent = 0.6977 CurveLabel = Normal Height = 68.596 Percent = 0.7969 CurveLabel = Normal Height = 68.596 Percent = 0.7969 CurveLabel = Normal Height = 68.465 Percent = 0.9076 CurveLabel = Normal Height = 68.465 Percent = 0.9076 CurveLabel = Normal Height = 68.333 Percent = 1.0307 CurveLabel = Normal Height = 68.333 Percent = 1.0307 CurveLabel = Normal Height = 68.202 Percent = 1.1672 CurveLabel = Normal Height = 68.202 Percent = 1.1672 CurveLabel = Normal Height = 68.071 Percent = 1.3179 CurveLabel = Normal Height = 68.071 Percent = 1.3179 CurveLabel = Normal Height = 67.939 Percent = 1.4839 CurveLabel = Normal Height = 67.939 Percent = 1.4839 CurveLabel = Normal Height = 67.808 Percent = 1.666 CurveLabel = Normal Height = 67.808 Percent = 1.666 CurveLabel = Normal Height = 67.677 Percent = 1.865 CurveLabel = Normal Height = 67.677 Percent = 1.865 CurveLabel = Normal Height = 67.545 Percent = 2.0819 CurveLabel = Normal Height = 67.545 Percent = 2.0819 CurveLabel = Normal Height = 67.414 Percent = 2.3173 CurveLabel = Normal Height = 67.414 Percent = 2.3173 CurveLabel = Normal Height = 67.283 Percent = 2.572 CurveLabel = Normal Height = 67.283 Percent = 2.572 CurveLabel = Normal Height = 67.152 Percent = 2.8465 CurveLabel = Normal Height = 67.152 Percent = 2.8465 CurveLabel = Normal Height = 67.02 Percent = 3.1413 CurveLabel = Normal Height = 67.02 Percent = 3.1413 CurveLabel = Normal Height = 66.889 Percent = 3.4567 CurveLabel = Normal Height = 66.889 Percent = 3.4567 CurveLabel = Normal Height = 66.758 Percent = 3.7929 CurveLabel = Normal Height = 66.758 Percent = 3.7929 CurveLabel = Normal Height = 66.626 Percent = 4.1498 CurveLabel = Normal Height = 66.626 Percent = 4.1498 CurveLabel = Normal Height = 66.495 Percent = 4.5273 CurveLabel = Normal Height = 66.495 Percent = 4.5273 CurveLabel = Normal Height = 66.364 Percent = 4.9251 CurveLabel = Normal Height = 66.364 Percent = 4.9251 CurveLabel = Normal Height = 66.232 Percent = 5.3424 CurveLabel = Normal Height = 66.232 Percent = 5.3424 CurveLabel = Normal Height = 66.101 Percent = 5.7785 CurveLabel = Normal Height = 66.101 Percent = 5.7785 CurveLabel = Normal Height = 65.97 Percent = 6.2323 CurveLabel = Normal Height = 65.97 Percent = 6.2323 CurveLabel = Normal Height = 65.838 Percent = 6.7026 CurveLabel = Normal Height = 65.838 Percent = 6.7026 CurveLabel = Normal Height = 65.707 Percent = 7.1876 CurveLabel = Normal Height = 65.707 Percent = 7.1876 CurveLabel = Normal Height = 65.576 Percent = 7.6857 CurveLabel = Normal Height = 65.576 Percent = 7.6857 CurveLabel = Normal Height = 65.444 Percent = 8.1948 CurveLabel = Normal Height = 65.444 Percent = 8.1948 CurveLabel = Normal Height = 65.313 Percent = 8.7126 CurveLabel = Normal Height = 65.313 Percent = 8.7126 CurveLabel = Normal Height = 65.182 Percent = 9.2366 CurveLabel = Normal Height = 65.182 Percent = 9.2366 CurveLabel = Normal Height = 65.051 Percent = 9.764 CurveLabel = Normal Height = 65.051 Percent = 9.764 CurveLabel = Normal Height = 64.919 Percent = 10.292 CurveLabel = Normal Height = 64.919 Percent = 10.292 CurveLabel = Normal Height = 64.788 Percent = 10.818 CurveLabel = Normal Height = 64.788 Percent = 10.818 CurveLabel = Normal Height = 64.657 Percent = 11.337 CurveLabel = Normal Height = 64.657 Percent = 11.337 CurveLabel = Normal Height = 64.525 Percent = 11.848 CurveLabel = Normal Height = 64.525 Percent = 11.848 CurveLabel = Normal Height = 64.394 Percent = 12.347 CurveLabel = Normal Height = 64.394 Percent = 12.347 CurveLabel = Normal Height = 64.263 Percent = 12.829 CurveLabel = Normal Height = 64.263 Percent = 12.829 CurveLabel = Normal Height = 64.131 Percent = 13.292 CurveLabel = Normal Height = 64.131 Percent = 13.292 CurveLabel = Normal Height = 64 Percent = 13.733 CurveLabel = Normal Height = 64 Percent = 13.733 CurveLabel = Normal Height = 63.869 Percent = 14.147 CurveLabel = Normal Height = 63.869 Percent = 14.147 CurveLabel = Normal Height = 63.737 Percent = 14.532 CurveLabel = Normal Height = 63.737 Percent = 14.532 CurveLabel = Normal Height = 63.606 Percent = 14.885 CurveLabel = Normal Height = 63.606 Percent = 14.885 CurveLabel = Normal Height = 63.475 Percent = 15.203 CurveLabel = Normal Height = 63.475 Percent = 15.203 CurveLabel = Normal Height = 63.343 Percent = 15.483 CurveLabel = Normal Height = 63.343 Percent = 15.483 CurveLabel = Normal Height = 63.212 Percent = 15.724 CurveLabel = Normal Height = 63.212 Percent = 15.724 CurveLabel = Normal Height = 63.081 Percent = 15.922 CurveLabel = Normal Height = 63.081 Percent = 15.922 CurveLabel = Normal Height = 62.949 Percent = 16.076 CurveLabel = Normal Height = 62.949 Percent = 16.076 CurveLabel = Normal Height = 62.818 Percent = 16.186 CurveLabel = Normal Height = 62.818 Percent = 16.186 CurveLabel = Normal Height = 62.687 Percent = 16.25 CurveLabel = Normal Height = 62.687 Percent = 16.25 CurveLabel = Normal Height = 62.573 Percent = 16.267 CurveLabel = Normal Height = 62.573 Percent = 16.267 CurveLabel = Normal Height = 62.556 Percent = 16.267 CurveLabel = Normal Height = 62.556 Percent = 16.267 CurveLabel = Normal Height = 62.424 Percent = 16.238 CurveLabel = Normal Height = 62.424 Percent = 16.238 CurveLabel = Normal Height = 62.293 Percent = 16.162 CurveLabel = Normal Height = 62.293 Percent = 16.162 CurveLabel = Normal Height = 62.162 Percent = 16.041 CurveLabel = Normal Height = 62.162 Percent = 16.041 CurveLabel = Normal Height = 62.03 Percent = 15.874 CurveLabel = Normal Height = 62.03 Percent = 15.874 CurveLabel = Normal Height = 61.899 Percent = 15.665 CurveLabel = Normal Height = 61.899 Percent = 15.665 CurveLabel = Normal Height = 61.768 Percent = 15.414 CurveLabel = Normal Height = 61.768 Percent = 15.414 CurveLabel = Normal Height = 61.636 Percent = 15.124 CurveLabel = Normal Height = 61.636 Percent = 15.124 CurveLabel = Normal Height = 61.505 Percent = 14.797 CurveLabel = Normal Height = 61.505 Percent = 14.797 CurveLabel = Normal Height = 61.374 Percent = 14.435 CurveLabel = Normal Height = 61.374 Percent = 14.435 CurveLabel = Normal Height = 61.242 Percent = 14.042 CurveLabel = Normal Height = 61.242 Percent = 14.042 CurveLabel = Normal Height = 61.111 Percent = 13.621 CurveLabel = Normal Height = 61.111 Percent = 13.621 CurveLabel = Normal Height = 60.98 Percent = 13.174 CurveLabel = Normal Height = 60.98 Percent = 13.174 CurveLabel = Normal Height = 60.848 Percent = 12.706 CurveLabel = Normal Height = 60.848 Percent = 12.706 CurveLabel = Normal Height = 60.717 Percent = 12.219 CurveLabel = Normal Height = 60.717 Percent = 12.219 CurveLabel = Normal Height = 60.586 Percent = 11.717 CurveLabel = Normal Height = 60.586 Percent = 11.717 CurveLabel = Normal Height = 60.455 Percent = 11.203 CurveLabel = Normal Height = 60.455 Percent = 11.203 CurveLabel = Normal Height = 60.323 Percent = 10.682 CurveLabel = Normal Height = 60.323 Percent = 10.682 CurveLabel = Normal Height = 60.192 Percent = 10.155 CurveLabel = Normal Height = 60.192 Percent = 10.155 CurveLabel = Normal Height = 60.061 Percent = 9.627 CurveLabel = Normal Height = 60.061 Percent = 9.627 CurveLabel = Normal Height = 59.929 Percent = 9.1002 CurveLabel = Normal Height = 59.929 Percent = 9.1002 CurveLabel = Normal Height = 59.798 Percent = 8.5776 CurveLabel = Normal Height = 59.798 Percent = 8.5776 CurveLabel = Normal Height = 59.667 Percent = 8.0618 CurveLabel = Normal Height = 59.667 Percent = 8.0618 CurveLabel = Normal Height = 59.535 Percent = 7.5554 CurveLabel = Normal Height = 59.535 Percent = 7.5554 CurveLabel = Normal Height = 59.404 Percent = 7.0605 CurveLabel = Normal Height = 59.404 Percent = 7.0605 CurveLabel = Normal Height = 59.273 Percent = 6.5791 CurveLabel = Normal Height = 59.273 Percent = 6.5791 CurveLabel = Normal Height = 59.141 Percent = 6.113 CurveLabel = Normal Height = 59.141 Percent = 6.113 CurveLabel = Normal Height = 59.01 Percent = 5.6637 CurveLabel = Normal Height = 59.01 Percent = 5.6637 CurveLabel = Normal Height = 58.879 Percent = 5.2323 CurveLabel = Normal Height = 58.879 Percent = 5.2323 CurveLabel = Normal Height = 58.747 Percent = 4.82 CurveLabel = Normal Height = 58.747 Percent = 4.82 CurveLabel = Normal Height = 58.616 Percent = 4.4275 CurveLabel = Normal Height = 58.616 Percent = 4.4275 CurveLabel = Normal Height = 58.485 Percent = 4.0552 CurveLabel = Normal Height = 58.485 Percent = 4.0552 CurveLabel = Normal Height = 58.354 Percent = 3.7037 CurveLabel = Normal Height = 58.354 Percent = 3.7037 CurveLabel = Normal Height = 58.222 Percent = 3.3729 CurveLabel = Normal Height = 58.222 Percent = 3.3729 CurveLabel = Normal Height = 58.091 Percent = 3.0629 CurveLabel = Normal Height = 58.091 Percent = 3.0629 CurveLabel = Normal Height = 57.96 Percent = 2.7734 CurveLabel = Normal Height = 57.96 Percent = 2.7734 CurveLabel = Normal Height = 57.828 Percent = 2.5041 CurveLabel = Normal Height = 57.828 Percent = 2.5041 CurveLabel = Normal Height = 57.697 Percent = 2.2545 CurveLabel = Normal Height = 57.697 Percent = 2.2545 CurveLabel = Normal Height = 57.566 Percent = 2.0239 CurveLabel = Normal Height = 57.566 Percent = 2.0239 CurveLabel = Normal Height = 57.434 Percent = 1.8117 CurveLabel = Normal Height = 57.434 Percent = 1.8117 CurveLabel = Normal Height = 57.303 Percent = 1.6171 CurveLabel = Normal Height = 57.303 Percent = 1.6171 CurveLabel = Normal Height = 57.172 Percent = 1.4393 CurveLabel = Normal Height = 57.172 Percent = 1.4393 CurveLabel = Normal Height = 57.04 Percent = 1.2774 CurveLabel = Normal Height = 57.04 Percent = 1.2774 CurveLabel = Normal Height = 56.909 Percent = 1.1304 CurveLabel = Normal Height = 56.909 Percent = 1.1304 CurveLabel = Normal Height = 56.778 Percent = 0.9975 CurveLabel = Normal Height = 56.778 Percent = 0.9975 CurveLabel = Normal Height = 56.646 Percent = 0.8777 CurveLabel = Normal Height = 56.646 Percent = 0.8777 CurveLabel = Normal Height = 56.515 Percent = 0.7701 CurveLabel = Normal Height = 56.515 Percent = 0.7701 CurveLabel = Normal Height = 56.384 Percent = 0.6737 CurveLabel = Normal Height = 56.384 Percent = 0.6737 CurveLabel = Normal Height = 56.253 Percent = 0.5877 CurveLabel = Normal Height = 56.253 Percent = 0.5877 CurveLabel = Normal Height = 56.121 Percent = 0.5112 CurveLabel = Normal Height = 56.121 Percent = 0.5112 CurveLabel = Normal Height = 55.99 Percent = 0.4434 CurveLabel = Normal Height = 55.99 Percent = 0.4434 CurveLabel = Normal Height = 55.859 Percent = 0.3835 CurveLabel = Normal Height = 55.859 Percent = 0.3835 CurveLabel = Normal Height = 55.727 Percent = 0.3307 CurveLabel = Normal Height = 55.727 Percent = 0.3307 CurveLabel = Normal Height = 55.596 Percent = 0.2844 CurveLabel = Normal Height = 55.596 Percent = 0.2844 CurveLabel = Normal Height = 55.465 Percent = 0.2439 CurveLabel = Normal Height = 55.465 Percent = 0.2439 CurveLabel = Normal Height = 55.333 Percent = 0.2085 CurveLabel = Normal Height = 55.333 Percent = 0.2085 CurveLabel = Normal Height = 55.202 Percent = 0.1778 CurveLabel = Normal Height = 55.202 Percent = 0.1778 CurveLabel = Normal Height = 55.071 Percent = 0.1511 CurveLabel = Normal Height = 55.071 Percent = 0.1511 CurveLabel = Normal Height = 54.939 Percent = 0.1281 CurveLabel = Normal Height = 54.939 Percent = 0.1281 CurveLabel = Normal Height = 54.808 Percent = 0.1083 CurveLabel = Normal Height = 54.808 Percent = 0.1083 CurveLabel = Normal Height = 54.677 Percent = 0.0913 CurveLabel = Normal Height = 54.677 Percent = 0.0913 CurveLabel = Normal Height = 54.545 Percent = 0.0767 CurveLabel = Normal Height = 54.545 Percent = 0.0767 CurveLabel = Normal Height = 54.414 Percent = 0.0643 CurveLabel = Normal Height = 54.414 Percent = 0.0643 CurveLabel = Normal Height = 54.283 Percent = 0.0537 CurveLabel = Normal Height = 54.283 Percent = 0.0537 CurveLabel = Normal Height = 54.152 Percent = 0.0448 CurveLabel = Normal Height = 54.152 Percent = 0.0448 CurveLabel = Normal Height = 54.02 Percent = 0.0372 CurveLabel = Normal Height = 54.02 Percent = 0.0372 CurveLabel = Normal Height = 53.889 Percent = 0.0308 CurveLabel = Normal Height = 53.889 Percent = 0.0308 CurveLabel = Normal Height = 53.758 Percent = 0.0255 CurveLabel = Normal Height = 53.758 Percent = 0.0255 CurveLabel = Normal Height = 53.626 Percent = 0.021 CurveLabel = Normal Height = 53.626 Percent = 0.021 CurveLabel = Normal Height = 53.495 Percent = 0.0172 CurveLabel = Normal Height = 53.495 Percent = 0.0172 CurveLabel = Normal Height = 53.364 Percent = 0.0141 CurveLabel = Normal Height = 53.364 Percent = 0.0141 CurveLabel = Normal Height = 53.232 Percent = 0.0115 CurveLabel = Normal Height = 53.232 Percent = 0.0115 CurveLabel = Normal Height = 53.101 Percent = 0.0094 CurveLabel = Normal Height = 53.101 Percent = 0.0094 CurveLabel = Normal Height = 52.97 Percent = 0.0076 CurveLabel = Normal Height = 52.97 Percent = 0.0076 CurveLabel = Normal Height = 52.838 Percent = 0.0062 CurveLabel = Normal Height = 52.838 Percent = 0.0062 CurveLabel = Normal Height = 52.707 Percent = 0 CurveLabel = Normal Height = 52.707 Percent = 0 CurveLabel = Normal Height = 52.576 Percent = 0 CurveLabel = Normal Height = 52.576 Percent = 0 CurveLabel = Normal Height = 52.444 Percent = 0 CurveLabel = Normal Height = 52.444 Percent = 0 CurveLabel = Normal Height = 52.313 Percent = 0 CurveLabel = Normal Height = 52.313 Percent = 0 CurveLabel = Normal Height = 52.182 Percent = 0 CurveLabel = Normal Height = 52.182 Percent = 0 CurveLabel = Normal Height = 52.051 Percent = 0 CurveLabel = Normal Height = 52.051 Percent = 0 CurveLabel = Normal Height = 51.919 Percent = 0 CurveLabel = Normal Height = 51.919 Percent = 0 CurveLabel = Normal Height = 51.788 Percent = 0 CurveLabel = Normal Height = 51.788 Percent = 0 CurveLabel = Normal Height = 51.657 Percent = 0 CurveLabel = Normal Height = 51.657 Percent = 0 CurveLabel = Normal Height = 51.525 Percent = 0 CurveLabel = Normal Height = 51.525 Percent = 0 CurveLabel = Normal Height = 51.394 Percent = 0 CurveLabel = Normal Height = 51.394 Percent = 0 CurveLabel = Normal Height = 51.263 Percent = 0 CurveLabel = Normal Height = 51.263 Percent = 0 CurveLabel = Normal Height = 51.131 Percent = 0 CurveLabel = Normal Height = 51.131 Percent = 0 CurveLabel = Normal Height = 51 Percent = 0 CurveLabel = Normal Bin Midpoint = 76.5 Percent = 0 Bin Midpoint = 76.5 Percent = 0 Bin Midpoint = 75.5 Percent = 0 Bin Midpoint = 75.5 Percent = 0 Bin Midpoint = 74.5 Percent = 0 Bin Midpoint = 74.5 Percent = 0 Bin Midpoint = 73.5 Percent = 0 Bin Midpoint = 73.5 Percent = 0 Bin Midpoint = 72.5 Percent = 0 Bin Midpoint = 72.5 Percent = 0 Bin Midpoint = 71.5 Percent = 0 Bin Midpoint = 71.5 Percent = 0 Bin Midpoint = 70.5 Percent = 0.1046 Bin Midpoint = 70.5 Percent = 0.1046 Bin Midpoint = 69.5 Percent = 0.3834 Bin Midpoint = 69.5 Percent = 0.3834 Bin Midpoint = 68.5 Percent = 1.1502 Bin Midpoint = 68.5 Percent = 1.1502 Bin Midpoint = 67.5 Percent = 2.7536 Bin Midpoint = 67.5 Percent = 2.7536 Bin Midpoint = 66.5 Percent = 4.6009 Bin Midpoint = 66.5 Percent = 4.6009 Bin Midpoint = 65.5 Percent = 8.8184 Bin Midpoint = 65.5 Percent = 8.8184 Bin Midpoint = 64.5 Percent = 12.199 Bin Midpoint = 64.5 Percent = 12.199 Bin Midpoint = 63.5 Percent = 14.57 Bin Midpoint = 63.5 Percent = 14.57 Bin Midpoint = 62.5 Percent = 17.916 Bin Midpoint = 62.5 Percent = 17.916 Bin Midpoint = 61.5 Percent = 13.838 Bin Midpoint = 61.5 Percent = 13.838 Bin Midpoint = 60.5 Percent = 10.631 Bin Midpoint = 60.5 Percent = 10.631 Bin Midpoint = 59.5 Percent = 7.0756 Bin Midpoint = 59.5 Percent = 7.0756 Bin Midpoint = 58.5 Percent = 3.5552 Bin Midpoint = 58.5 Percent = 3.5552 Bin Midpoint = 57.5 Percent = 1.1154 Bin Midpoint = 57.5 Percent = 1.1154 Bin Midpoint = 56.5 Percent = 0.9411 Bin Midpoint = 56.5 Percent = 0.9411 Bin Midpoint = 55.5 Percent = 0.2091 Bin Midpoint = 55.5 Percent = 0.2091 Bin Midpoint = 54.5 Percent = 0.0697 Bin Midpoint = 54.5 Percent = 0.0697 Bin Midpoint = 53.5 Percent = 0.0349 Bin Midpoint = 53.5 Percent = 0.0349 Bin Midpoint = 52.5 Percent = 0 Bin Midpoint = 52.5 Percent = 0 Bin Midpoint = 51.5 Percent = 0.0349 Bin Midpoint = 51.5 Percent = 0.0349 Height = 77 Percent = 0.0377 CurveLabel = Normal Height = 76.869 Percent = 0.0444 CurveLabel = Normal Height = 76.869 Percent = 0.0444 CurveLabel = Normal Height = 76.737 Percent = 0.0523 CurveLabel = Normal Height = 76.737 Percent = 0.0523 CurveLabel = Normal Height = 76.606 Percent = 0.0613 CurveLabel = Normal Height = 76.606 Percent = 0.0613 CurveLabel = Normal Height = 76.475 Percent = 0.0718 CurveLabel = Normal Height = 76.475 Percent = 0.0718 CurveLabel = Normal Height = 76.343 Percent = 0.0839 CurveLabel = Normal Height = 76.343 Percent = 0.0839 CurveLabel = Normal Height = 76.212 Percent = 0.0978 CurveLabel = Normal Height = 76.212 Percent = 0.0978 CurveLabel = Normal Height = 76.081 Percent = 0.1138 CurveLabel = Normal Height = 76.081 Percent = 0.1138 CurveLabel = Normal Height = 75.949 Percent = 0.132 CurveLabel = Normal Height = 75.949 Percent = 0.132 CurveLabel = Normal Height = 75.818 Percent = 0.1528 CurveLabel = Normal Height = 75.818 Percent = 0.1528 CurveLabel = Normal Height = 75.687 Percent = 0.1764 CurveLabel = Normal Height = 75.687 Percent = 0.1764 CurveLabel = Normal Height = 75.556 Percent = 0.2033 CurveLabel = Normal Height = 75.556 Percent = 0.2033 CurveLabel = Normal Height = 75.424 Percent = 0.2337 CurveLabel = Normal Height = 75.424 Percent = 0.2337 CurveLabel = Normal Height = 75.293 Percent = 0.268 CurveLabel = Normal Height = 75.293 Percent = 0.268 CurveLabel = Normal Height = 75.162 Percent = 0.3067 CurveLabel = Normal Height = 75.162 Percent = 0.3067 CurveLabel = Normal Height = 75.03 Percent = 0.3501 CurveLabel = Normal Height = 75.03 Percent = 0.3501 CurveLabel = Normal Height = 74.899 Percent = 0.3988 CurveLabel = Normal Height = 74.899 Percent = 0.3988 CurveLabel = Normal Height = 74.768 Percent = 0.4531 CurveLabel = Normal Height = 74.768 Percent = 0.4531 CurveLabel = Normal Height = 74.636 Percent = 0.5137 CurveLabel = Normal Height = 74.636 Percent = 0.5137 CurveLabel = Normal Height = 74.505 Percent = 0.5811 CurveLabel = Normal Height = 74.505 Percent = 0.5811 CurveLabel = Normal Height = 74.374 Percent = 0.6558 CurveLabel = Normal Height = 74.374 Percent = 0.6558 CurveLabel = Normal Height = 74.242 Percent = 0.7383 CurveLabel = Normal Height = 74.242 Percent = 0.7383 CurveLabel = Normal Height = 74.111 Percent = 0.8294 CurveLabel = Normal Height = 74.111 Percent = 0.8294 CurveLabel = Normal Height = 73.98 Percent = 0.9295 CurveLabel = Normal Height = 73.98 Percent = 0.9295 CurveLabel = Normal Height = 73.848 Percent = 1.0393 CurveLabel = Normal Height = 73.848 Percent = 1.0393 CurveLabel = Normal Height = 73.717 Percent = 1.1593 CurveLabel = Normal Height = 73.717 Percent = 1.1593 CurveLabel = Normal Height = 73.586 Percent = 1.2903 CurveLabel = Normal Height = 73.586 Percent = 1.2903 CurveLabel = Normal Height = 73.455 Percent = 1.4327 CurveLabel = Normal Height = 73.455 Percent = 1.4327 CurveLabel = Normal Height = 73.323 Percent = 1.5873 CurveLabel = Normal Height = 73.323 Percent = 1.5873 CurveLabel = Normal Height = 73.192 Percent = 1.7544 CurveLabel = Normal Height = 73.192 Percent = 1.7544 CurveLabel = Normal Height = 73.061 Percent = 1.9346 CurveLabel = Normal Height = 73.061 Percent = 1.9346 CurveLabel = Normal Height = 72.929 Percent = 2.1284 CurveLabel = Normal Height = 72.929 Percent = 2.1284 CurveLabel = Normal Height = 72.798 Percent = 2.3362 CurveLabel = Normal Height = 72.798 Percent = 2.3362 CurveLabel = Normal Height = 72.667 Percent = 2.5584 CurveLabel = Normal Height = 72.667 Percent = 2.5584 CurveLabel = Normal Height = 72.535 Percent = 2.7953 CurveLabel = Normal Height = 72.535 Percent = 2.7953 CurveLabel = Normal Height = 72.404 Percent = 3.0471 CurveLabel = Normal Height = 72.404 Percent = 3.0471 CurveLabel = Normal Height = 72.273 Percent = 3.3139 CurveLabel = Normal Height = 72.273 Percent = 3.3139 CurveLabel = Normal Height = 72.141 Percent = 3.5957 CurveLabel = Normal Height = 72.141 Percent = 3.5957 CurveLabel = Normal Height = 72.01 Percent = 3.8925 CurveLabel = Normal Height = 72.01 Percent = 3.8925 CurveLabel = Normal Height = 71.879 Percent = 4.204 CurveLabel = Normal Height = 71.879 Percent = 4.204 CurveLabel = Normal Height = 71.747 Percent = 4.5301 CurveLabel = Normal Height = 71.747 Percent = 4.5301 CurveLabel = Normal Height = 71.616 Percent = 4.8701 CurveLabel = Normal Height = 71.616 Percent = 4.8701 CurveLabel = Normal Height = 71.485 Percent = 5.2236 CurveLabel = Normal Height = 71.485 Percent = 5.2236 CurveLabel = Normal Height = 71.354 Percent = 5.5898 CurveLabel = Normal Height = 71.354 Percent = 5.5898 CurveLabel = Normal Height = 71.222 Percent = 5.9679 CurveLabel = Normal Height = 71.222 Percent = 5.9679 CurveLabel = Normal Height = 71.091 Percent = 6.3568 CurveLabel = Normal Height = 71.091 Percent = 6.3568 CurveLabel = Normal Height = 70.96 Percent = 6.7555 CurveLabel = Normal Height = 70.96 Percent = 6.7555 CurveLabel = Normal Height = 70.828 Percent = 7.1627 CurveLabel = Normal Height = 70.828 Percent = 7.1627 CurveLabel = Normal Height = 70.697 Percent = 7.5768 CurveLabel = Normal Height = 70.697 Percent = 7.5768 CurveLabel = Normal Height = 70.566 Percent = 7.9964 CurveLabel = Normal Height = 70.566 Percent = 7.9964 CurveLabel = Normal Height = 70.434 Percent = 8.4197 CurveLabel = Normal Height = 70.434 Percent = 8.4197 CurveLabel = Normal Height = 70.303 Percent = 8.8451 CurveLabel = Normal Height = 70.303 Percent = 8.8451 CurveLabel = Normal Height = 70.172 Percent = 9.2704 CurveLabel = Normal Height = 70.172 Percent = 9.2704 CurveLabel = Normal Height = 70.04 Percent = 9.6938 CurveLabel = Normal Height = 70.04 Percent = 9.6938 CurveLabel = Normal Height = 69.909 Percent = 10.113 CurveLabel = Normal Height = 69.909 Percent = 10.113 CurveLabel = Normal Height = 69.778 Percent = 10.526 CurveLabel = Normal Height = 69.778 Percent = 10.526 CurveLabel = Normal Height = 69.646 Percent = 10.931 CurveLabel = Normal Height = 69.646 Percent = 10.931 CurveLabel = Normal Height = 69.515 Percent = 11.325 CurveLabel = Normal Height = 69.515 Percent = 11.325 CurveLabel = Normal Height = 69.384 Percent = 11.706 CurveLabel = Normal Height = 69.384 Percent = 11.706 CurveLabel = Normal Height = 69.253 Percent = 12.073 CurveLabel = Normal Height = 69.253 Percent = 12.073 CurveLabel = Normal Height = 69.121 Percent = 12.421 CurveLabel = Normal Height = 69.121 Percent = 12.421 CurveLabel = Normal Height = 68.99 Percent = 12.751 CurveLabel = Normal Height = 68.99 Percent = 12.751 CurveLabel = Normal Height = 68.859 Percent = 13.059 CurveLabel = Normal Height = 68.859 Percent = 13.059 CurveLabel = Normal Height = 68.727 Percent = 13.344 CurveLabel = Normal Height = 68.727 Percent = 13.344 CurveLabel = Normal Height = 68.596 Percent = 13.603 CurveLabel = Normal Height = 68.596 Percent = 13.603 CurveLabel = Normal Height = 68.465 Percent = 13.835 CurveLabel = Normal Height = 68.465 Percent = 13.835 CurveLabel = Normal Height = 68.333 Percent = 14.039 CurveLabel = Normal Height = 68.333 Percent = 14.039 CurveLabel = Normal Height = 68.202 Percent = 14.213 CurveLabel = Normal Height = 68.202 Percent = 14.213 CurveLabel = Normal Height = 68.071 Percent = 14.356 CurveLabel = Normal Height = 68.071 Percent = 14.356 CurveLabel = Normal Height = 67.939 Percent = 14.467 CurveLabel = Normal Height = 67.939 Percent = 14.467 CurveLabel = Normal Height = 67.808 Percent = 14.545 CurveLabel = Normal Height = 67.808 Percent = 14.545 CurveLabel = Normal Height = 67.677 Percent = 14.59 CurveLabel = Normal Height = 67.677 Percent = 14.59 CurveLabel = Normal Height = 67.567 Percent = 14.602 CurveLabel = Normal Height = 67.567 Percent = 14.602 CurveLabel = Normal Height = 67.545 Percent = 14.601 CurveLabel = Normal Height = 67.545 Percent = 14.601 CurveLabel = Normal Height = 67.414 Percent = 14.579 CurveLabel = Normal Height = 67.414 Percent = 14.579 CurveLabel = Normal Height = 67.283 Percent = 14.523 CurveLabel = Normal Height = 67.283 Percent = 14.523 CurveLabel = Normal Height = 67.152 Percent = 14.434 CurveLabel = Normal Height = 67.152 Percent = 14.434 CurveLabel = Normal Height = 67.02 Percent = 14.312 CurveLabel = Normal Height = 67.02 Percent = 14.312 CurveLabel = Normal Height = 66.889 Percent = 14.158 CurveLabel = Normal Height = 66.889 Percent = 14.158 CurveLabel = Normal Height = 66.758 Percent = 13.974 CurveLabel = Normal Height = 66.758 Percent = 13.974 CurveLabel = Normal Height = 66.626 Percent = 13.761 CurveLabel = Normal Height = 66.626 Percent = 13.761 CurveLabel = Normal Height = 66.495 Percent = 13.519 CurveLabel = Normal Height = 66.495 Percent = 13.519 CurveLabel = Normal Height = 66.364 Percent = 13.251 CurveLabel = Normal Height = 66.364 Percent = 13.251 CurveLabel = Normal Height = 66.232 Percent = 12.959 CurveLabel = Normal Height = 66.232 Percent = 12.959 CurveLabel = Normal Height = 66.101 Percent = 12.643 CurveLabel = Normal Height = 66.101 Percent = 12.643 CurveLabel = Normal Height = 65.97 Percent = 12.307 CurveLabel = Normal Height = 65.97 Percent = 12.307 CurveLabel = Normal Height = 65.838 Percent = 11.952 CurveLabel = Normal Height = 65.838 Percent = 11.952 CurveLabel = Normal Height = 65.707 Percent = 11.581 CurveLabel = Normal Height = 65.707 Percent = 11.581 CurveLabel = Normal Height = 65.576 Percent = 11.195 CurveLabel = Normal Height = 65.576 Percent = 11.195 CurveLabel = Normal Height = 65.444 Percent = 10.797 CurveLabel = Normal Height = 65.444 Percent = 10.797 CurveLabel = Normal Height = 65.313 Percent = 10.389 CurveLabel = Normal Height = 65.313 Percent = 10.389 CurveLabel = Normal Height = 65.182 Percent = 9.9737 CurveLabel = Normal Height = 65.182 Percent = 9.9737 CurveLabel = Normal Height = 65.051 Percent = 9.5528 CurveLabel = Normal Height = 65.051 Percent = 9.5528 CurveLabel = Normal Height = 64.919 Percent = 9.1285 CurveLabel = Normal Height = 64.919 Percent = 9.1285 CurveLabel = Normal Height = 64.788 Percent = 8.703 CurveLabel = Normal Height = 64.788 Percent = 8.703 CurveLabel = Normal Height = 64.657 Percent = 8.2781 CurveLabel = Normal Height = 64.657 Percent = 8.2781 CurveLabel = Normal Height = 64.525 Percent = 7.8558 CurveLabel = Normal Height = 64.525 Percent = 7.8558 CurveLabel = Normal Height = 64.394 Percent = 7.4379 CurveLabel = Normal Height = 64.394 Percent = 7.4379 CurveLabel = Normal Height = 64.263 Percent = 7.0259 CurveLabel = Normal Height = 64.263 Percent = 7.0259 CurveLabel = Normal Height = 64.131 Percent = 6.6214 CurveLabel = Normal Height = 64.131 Percent = 6.6214 CurveLabel = Normal Height = 64 Percent = 6.2259 CurveLabel = Normal Height = 64 Percent = 6.2259 CurveLabel = Normal Height = 63.869 Percent = 5.8404 CurveLabel = Normal Height = 63.869 Percent = 5.8404 CurveLabel = Normal Height = 63.737 Percent = 5.4662 CurveLabel = Normal Height = 63.737 Percent = 5.4662 CurveLabel = Normal Height = 63.606 Percent = 5.1041 CurveLabel = Normal Height = 63.606 Percent = 5.1041 CurveLabel = Normal Height = 63.475 Percent = 4.7551 CurveLabel = Normal Height = 63.475 Percent = 4.7551 CurveLabel = Normal Height = 63.343 Percent = 4.4196 CurveLabel = Normal Height = 63.343 Percent = 4.4196 CurveLabel = Normal Height = 63.212 Percent = 4.0984 CurveLabel = Normal Height = 63.212 Percent = 4.0984 CurveLabel = Normal Height = 63.081 Percent = 3.7917 CurveLabel = Normal Height = 63.081 Percent = 3.7917 CurveLabel = Normal Height = 62.949 Percent = 3.4999 CurveLabel = Normal Height = 62.949 Percent = 3.4999 CurveLabel = Normal Height = 62.818 Percent = 3.2231 CurveLabel = Normal Height = 62.818 Percent = 3.2231 CurveLabel = Normal Height = 62.687 Percent = 2.9614 CurveLabel = Normal Height = 62.687 Percent = 2.9614 CurveLabel = Normal Height = 62.556 Percent = 2.7146 CurveLabel = Normal Height = 62.556 Percent = 2.7146 CurveLabel = Normal Height = 62.424 Percent = 2.4826 CurveLabel = Normal Height = 62.424 Percent = 2.4826 CurveLabel = Normal Height = 62.293 Percent = 2.2653 CurveLabel = Normal Height = 62.293 Percent = 2.2653 CurveLabel = Normal Height = 62.162 Percent = 2.0622 CurveLabel = Normal Height = 62.162 Percent = 2.0622 CurveLabel = Normal Height = 62.03 Percent = 1.8729 CurveLabel = Normal Height = 62.03 Percent = 1.8729 CurveLabel = Normal Height = 61.899 Percent = 1.6971 CurveLabel = Normal Height = 61.899 Percent = 1.6971 CurveLabel = Normal Height = 61.768 Percent = 1.5343 CurveLabel = Normal Height = 61.768 Percent = 1.5343 CurveLabel = Normal Height = 61.636 Percent = 1.3839 CurveLabel = Normal Height = 61.636 Percent = 1.3839 CurveLabel = Normal Height = 61.505 Percent = 1.2453 CurveLabel = Normal Height = 61.505 Percent = 1.2453 CurveLabel = Normal Height = 61.374 Percent = 1.1181 CurveLabel = Normal Height = 61.374 Percent = 1.1181 CurveLabel = Normal Height = 61.242 Percent = 1.0015 CurveLabel = Normal Height = 61.242 Percent = 1.0015 CurveLabel = Normal Height = 61.111 Percent = 0.895 CurveLabel = Normal Height = 61.111 Percent = 0.895 CurveLabel = Normal Height = 60.98 Percent = 0.798 CurveLabel = Normal Height = 60.98 Percent = 0.798 CurveLabel = Normal Height = 60.848 Percent = 0.7099 CurveLabel = Normal Height = 60.848 Percent = 0.7099 CurveLabel = Normal Height = 60.717 Percent = 0.63 CurveLabel = Normal Height = 60.717 Percent = 0.63 CurveLabel = Normal Height = 60.586 Percent = 0.5578 CurveLabel = Normal Height = 60.586 Percent = 0.5578 CurveLabel = Normal Height = 60.455 Percent = 0.4928 CurveLabel = Normal Height = 60.455 Percent = 0.4928 CurveLabel = Normal Height = 60.323 Percent = 0.4343 CurveLabel = Normal Height = 60.323 Percent = 0.4343 CurveLabel = Normal Height = 60.192 Percent = 0.3819 CurveLabel = Normal Height = 60.192 Percent = 0.3819 CurveLabel = Normal Height = 60.061 Percent = 0.3351 CurveLabel = Normal Height = 60.061 Percent = 0.3351 CurveLabel = Normal Height = 59.929 Percent = 0.2933 CurveLabel = Normal Height = 59.929 Percent = 0.2933 CurveLabel = Normal Height = 59.798 Percent = 0.2561 CurveLabel = Normal Height = 59.798 Percent = 0.2561 CurveLabel = Normal Height = 59.667 Percent = 0.2231 CurveLabel = Normal Height = 59.667 Percent = 0.2231 CurveLabel = Normal Height = 59.535 Percent = 0.1939 CurveLabel = Normal Height = 59.535 Percent = 0.1939 CurveLabel = Normal Height = 59.404 Percent = 0.1682 CurveLabel = Normal Height = 59.404 Percent = 0.1682 CurveLabel = Normal Height = 59.273 Percent = 0.1455 CurveLabel = Normal Height = 59.273 Percent = 0.1455 CurveLabel = Normal Height = 59.141 Percent = 0.1256 CurveLabel = Normal Height = 59.141 Percent = 0.1256 CurveLabel = Normal Height = 59.01 Percent = 0.1082 CurveLabel = Normal Height = 59.01 Percent = 0.1082 CurveLabel = Normal Height = 58.879 Percent = 0.093 CurveLabel = Normal Height = 58.879 Percent = 0.093 CurveLabel = Normal Height = 58.747 Percent = 0.0797 CurveLabel = Normal Height = 58.747 Percent = 0.0797 CurveLabel = Normal Height = 58.616 Percent = 0.0682 CurveLabel = Normal Height = 58.616 Percent = 0.0682 CurveLabel = Normal Height = 58.485 Percent = 0.0582 CurveLabel = Normal Height = 58.485 Percent = 0.0582 CurveLabel = Normal Height = 58.354 Percent = 0.0495 CurveLabel = Normal Height = 58.354 Percent = 0.0495 CurveLabel = Normal Height = 58.222 Percent = 0.0421 CurveLabel = Normal Height = 58.222 Percent = 0.0421 CurveLabel = Normal Height = 58.091 Percent = 0.0356 CurveLabel = Normal Height = 58.091 Percent = 0.0356 CurveLabel = Normal Height = 57.96 Percent = 0.0301 CurveLabel = Normal Height = 57.96 Percent = 0.0301 CurveLabel = Normal Height = 57.828 Percent = 0.0254 CurveLabel = Normal Height = 57.828 Percent = 0.0254 CurveLabel = Normal Height = 57.697 Percent = 0.0214 CurveLabel = Normal Height = 57.697 Percent = 0.0214 CurveLabel = Normal Height = 57.566 Percent = 0.018 CurveLabel = Normal Height = 57.566 Percent = 0.018 CurveLabel = Normal Height = 57.434 Percent = 0.015 CurveLabel = Normal Height = 57.434 Percent = 0.015 CurveLabel = Normal Height = 57.303 Percent = 0.0126 CurveLabel = Normal Height = 57.303 Percent = 0.0126 CurveLabel = Normal Height = 57.172 Percent = 0.0105 CurveLabel = Normal Height = 57.172 Percent = 0.0105 CurveLabel = Normal Height = 57.04 Percent = 0.0087 CurveLabel = Normal Height = 57.04 Percent = 0.0087 CurveLabel = Normal Height = 56.909 Percent = 0.0072 CurveLabel = Normal Height = 56.909 Percent = 0.0072 CurveLabel = Normal Height = 56.778 Percent = 0.006 CurveLabel = Normal Height = 56.778 Percent = 0.006 CurveLabel = Normal Height = 56.646 Percent = 0.005 CurveLabel = Normal Height = 56.646 Percent = 0.005 CurveLabel = Normal Height = 56.515 Percent = 0 CurveLabel = Normal Height = 56.515 Percent = 0 CurveLabel = Normal Height = 56.384 Percent = 0 CurveLabel = Normal Height = 56.384 Percent = 0 CurveLabel = Normal Height = 56.253 Percent = 0 CurveLabel = Normal Height = 56.253 Percent = 0 CurveLabel = Normal Height = 56.121 Percent = 0 CurveLabel = Normal Height = 56.121 Percent = 0 CurveLabel = Normal Height = 55.99 Percent = 0 CurveLabel = Normal Height = 55.99 Percent = 0 CurveLabel = Normal Height = 55.859 Percent = 0 CurveLabel = Normal Height = 55.859 Percent = 0 CurveLabel = Normal Height = 55.727 Percent = 0 CurveLabel = Normal Height = 55.727 Percent = 0 CurveLabel = Normal Height = 55.596 Percent = 0 CurveLabel = Normal Height = 55.596 Percent = 0 CurveLabel = Normal Height = 55.465 Percent = 0 CurveLabel = Normal Height = 55.465 Percent = 0 CurveLabel = Normal Height = 55.333 Percent = 0 CurveLabel = Normal Height = 55.333 Percent = 0 CurveLabel = Normal Height = 55.202 Percent = 0 CurveLabel = Normal Height = 55.202 Percent = 0 CurveLabel = Normal Height = 55.071 Percent = 0 CurveLabel = Normal Height = 55.071 Percent = 0 CurveLabel = Normal Height = 54.939 Percent = 0 CurveLabel = Normal Height = 54.939 Percent = 0 CurveLabel = Normal Height = 54.808 Percent = 0 CurveLabel = Normal Height = 54.808 Percent = 0 CurveLabel = Normal Height = 54.677 Percent = 0 CurveLabel = Normal Height = 54.677 Percent = 0 CurveLabel = Normal Height = 54.545 Percent = 0 CurveLabel = Normal Height = 54.545 Percent = 0 CurveLabel = Normal Height = 54.414 Percent = 0 CurveLabel = Normal Height = 54.414 Percent = 0 CurveLabel = Normal Height = 54.283 Percent = 0 CurveLabel = Normal Height = 54.283 Percent = 0 CurveLabel = Normal Height = 54.152 Percent = 0 CurveLabel = Normal Height = 54.152 Percent = 0 CurveLabel = Normal Height = 54.02 Percent = 0 CurveLabel = Normal Height = 54.02 Percent = 0 CurveLabel = Normal Height = 53.889 Percent = 0 CurveLabel = Normal Height = 53.889 Percent = 0 CurveLabel = Normal Height = 53.758 Percent = 0 CurveLabel = Normal Height = 53.758 Percent = 0 CurveLabel = Normal Height = 53.626 Percent = 0 CurveLabel = Normal Height = 53.626 Percent = 0 CurveLabel = Normal Height = 53.495 Percent = 0 CurveLabel = Normal Height = 53.495 Percent = 0 CurveLabel = Normal Height = 53.364 Percent = 0 CurveLabel = Normal Height = 53.364 Percent = 0 CurveLabel = Normal Height = 53.232 Percent = 0 CurveLabel = Normal Height = 53.232 Percent = 0 CurveLabel = Normal Height = 53.101 Percent = 0 CurveLabel = Normal Height = 53.101 Percent = 0 CurveLabel = Normal Height = 52.97 Percent = 0 CurveLabel = Normal Height = 52.97 Percent = 0 CurveLabel = Normal Height = 52.838 Percent = 0 CurveLabel = Normal Height = 52.838 Percent = 0 CurveLabel = Normal Height = 52.707 Percent = 0 CurveLabel = Normal Height = 52.707 Percent = 0 CurveLabel = Normal Height = 52.576 Percent = 0 CurveLabel = Normal Height = 52.576 Percent = 0 CurveLabel = Normal Height = 52.444 Percent = 0 CurveLabel = Normal Height = 52.444 Percent = 0 CurveLabel = Normal Height = 52.313 Percent = 0 CurveLabel = Normal Height = 52.313 Percent = 0 CurveLabel = Normal Height = 52.182 Percent = 0 CurveLabel = Normal Height = 52.182 Percent = 0 CurveLabel = Normal Height = 52.051 Percent = 0 CurveLabel = Normal Height = 52.051 Percent = 0 CurveLabel = Normal Height = 51.919 Percent = 0 CurveLabel = Normal Height = 51.919 Percent = 0 CurveLabel = Normal Height = 51.788 Percent = 0 CurveLabel = Normal Height = 51.788 Percent = 0 CurveLabel = Normal Height = 51.657 Percent = 0 CurveLabel = Normal Height = 51.657 Percent = 0 CurveLabel = Normal Height = 51.525 Percent = 0 CurveLabel = Normal Height = 51.525 Percent = 0 CurveLabel = Normal Height = 51.394 Percent = 0 CurveLabel = Normal Height = 51.394 Percent = 0 CurveLabel = Normal Height = 51.263 Percent = 0 CurveLabel = Normal Height = 51.263 Percent = 0 CurveLabel = Normal Height = 51.131 Percent = 0 CurveLabel = Normal Height = 51.131 Percent = 0 CurveLabel = Normal Height = 51 Percent = 0 CurveLabel = Normal Bin Midpoint = 76.5 Percent = 0.1285 Bin Midpoint = 76.5 Percent = 0.1285 Bin Midpoint = 75.5 Percent = 0.2142 Bin Midpoint = 75.5 Percent = 0.2142 Bin Midpoint = 74.5 Percent = 0.5998 Bin Midpoint = 74.5 Percent = 0.5998 Bin Midpoint = 73.5 Percent = 1.6281 Bin Midpoint = 73.5 Percent = 1.6281 Bin Midpoint = 72.5 Percent = 3.856 Bin Midpoint = 72.5 Percent = 3.856 Bin Midpoint = 71.5 Percent = 5.4841 Bin Midpoint = 71.5 Percent = 5.4841 Bin Midpoint = 70.5 Percent = 8.0977 Bin Midpoint = 70.5 Percent = 8.0977 Bin Midpoint = 69.5 Percent = 11.911 Bin Midpoint = 69.5 Percent = 11.911 Bin Midpoint = 68.5 Percent = 13.967 Bin Midpoint = 68.5 Percent = 13.967 Bin Midpoint = 67.5 Percent = 14.653 Bin Midpoint = 67.5 Percent = 14.653 Bin Midpoint = 66.5 Percent = 11.74 Bin Midpoint = 66.5 Percent = 11.74 Bin Midpoint = 65.5 Percent = 12.339 Bin Midpoint = 65.5 Percent = 12.339 Bin Midpoint = 64.5 Percent = 6.9837 Bin Midpoint = 64.5 Percent = 6.9837 Bin Midpoint = 63.5 Percent = 4.2845 Bin Midpoint = 63.5 Percent = 4.2845 Bin Midpoint = 62.5 Percent = 2.4422 Bin Midpoint = 62.5 Percent = 2.4422 Bin Midpoint = 61.5 Percent = 1.114 Bin Midpoint = 61.5 Percent = 1.114 Bin Midpoint = 60.5 Percent = 0.2571 Bin Midpoint = 60.5 Percent = 0.2571 Bin Midpoint = 59.5 Percent = 0.1285 Bin Midpoint = 59.5 Percent = 0.1285 Bin Midpoint = 58.5 Percent = 0.0857 Bin Midpoint = 58.5 Percent = 0.0857 Bin Midpoint = 57.5 Percent = 0 Bin Midpoint = 57.5 Percent = 0 Bin Midpoint = 56.5 Percent = 0.0857 Bin Midpoint = 56.5 Percent = 0.0857 Bin Midpoint = 55.5 Percent = 0 Bin Midpoint = 55.5 Percent = 0 Bin Midpoint = 54.5 Percent = 0 Bin Midpoint = 54.5 Percent = 0 Bin Midpoint = 53.5 Percent = 0 Bin Midpoint = 53.5 Percent = 0 Bin Midpoint = 52.5 Percent = 0 Bin Midpoint = 52.5 Percent = 0 Bin Midpoint = 51.5 Percent = 0 Bin Midpoint = 51.5 Percent = 0
Histogram for Height

Adding a Classification Variable in the Summary Statistics

The Boxplot Procedure

Height

Panel 1

Sex = 1 Box Plot Feature Value = 76.5 Sex = 1 Box Plot Feature Value = 76 Sex = 1 Box Plot Feature Value = 76 Sex = 1 Box Plot Feature Value = 56 Sex = 1 Box Plot Feature Value = 56.5 Sex = 1 Box Plot Feature Value = 58.75 Sex = 1 Box Plot Feature Value = 58.75 Sex = 1 Box Plot Feature Value = 59.25 Sex = 1 Box Plot Feature Value = 59.25 Sex = 0 Box Plot Feature Value = 70.75 Sex = 0 Box Plot Feature Value = 70.5 Sex = 0 Box Plot Feature Value = 70 Sex = 0 Box Plot Feature Value = 69.75 Sex = 0 Box Plot Feature Value = 69.5 Sex = 0 Box Plot Feature Value = 69.5 Sex = 0 Box Plot Feature Value = 69.5 Sex = 0 Box Plot Feature Value = 69.5 Sex = 0 Box Plot Feature Value = 69.5 Sex = 0 Box Plot Feature Value = 69.25 Sex = 0 Box Plot Feature Value = 69.25 Sex = 0 Box Plot Feature Value = 51.5 Sex = 0 Box Plot Feature Value = 53.75 Sex = 0 Box Plot Feature Value = 54.75 Sex = 0 Box Plot Feature Value = 54.75 Sex = 0 Box Plot Feature Value = 55 Sex = 0 Box Plot Feature Value = 55 Sex = 0 Box Plot Feature Value = 55.5 Sex = 0 Box Plot Feature Value = 55.5 Sex = 0 Box Plot Feature Value = 55.75 Sex = 0 Box Plot Feature Value = 55.75 Sex = 0 Box Plot Feature Value = 56 Sex = 0 Box Plot Feature Value = 56 Sex = Male Minimum Whisker = 59.75 First Quartile = 65.5 Median = 67.5 Third Quartile = 69.5 Maximum Whisker = 75.5 Mean = 67.567 Standard Deviation = 2.7321 Number of Observations = 2334 Sex = Male Minimum Whisker = 59.75 First Quartile = 65.5 Median = 67.5 Third Quartile = 69.5 Maximum Whisker = 75.5 Mean = 67.567 Standard Deviation = 2.7321 Number of Observations = 2334 Sex = Male Minimum Whisker = 59.75 First Quartile = 65.5 Median = 67.5 Third Quartile = 69.5 Maximum Whisker = 75.5 Mean = 67.567 Standard Deviation = 2.7321 Number of Observations = 2334 Sex = Male Minimum Whisker = 59.75 First Quartile = 65.5 Median = 67.5 Third Quartile = 69.5 Maximum Whisker = 75.5 Mean = 67.567 Standard Deviation = 2.7321 Number of Observations = 2334 Sex = Male Minimum Whisker = 59.75 First Quartile = 65.5 Median = 67.5 Third Quartile = 69.5 Maximum Whisker = 75.5 Mean = 67.567 Standard Deviation = 2.7321 Number of Observations = 2334 Sex = Male Minimum Whisker = 59.75 First Quartile = 65.5 Median = 67.5 Third Quartile = 69.5 Maximum Whisker = 75.5 Mean = 67.567 Standard Deviation = 2.7321 Number of Observations = 2334 Sex = Male Minimum Whisker = 59.75 First Quartile = 65.5 Median = 67.5 Third Quartile = 69.5 Maximum Whisker = 75.5 Mean = 67.567 Standard Deviation = 2.7321 Number of Observations = 2334 Sex = Male Minimum Whisker = 59.75 First Quartile = 65.5 Median = 67.5 Third Quartile = 69.5 Maximum Whisker = 75.5 Mean = 67.567 Standard Deviation = 2.7321 Number of Observations = 2334 Sex = Female Minimum Whisker = 56.25 First Quartile = 61 Median = 62.5 Third Quartile = 64.25 Maximum Whisker = 69 Mean = 62.573 Standard Deviation = 2.4524 Number of Observations = 2869 Sex = Female Minimum Whisker = 56.25 First Quartile = 61 Median = 62.5 Third Quartile = 64.25 Maximum Whisker = 69 Mean = 62.573 Standard Deviation = 2.4524 Number of Observations = 2869 Sex = Female Minimum Whisker = 56.25 First Quartile = 61 Median = 62.5 Third Quartile = 64.25 Maximum Whisker = 69 Mean = 62.573 Standard Deviation = 2.4524 Number of Observations = 2869 Sex = Female Minimum Whisker = 56.25 First Quartile = 61 Median = 62.5 Third Quartile = 64.25 Maximum Whisker = 69 Mean = 62.573 Standard Deviation = 2.4524 Number of Observations = 2869 Sex = Female Minimum Whisker = 56.25 First Quartile = 61 Median = 62.5 Third Quartile = 64.25 Maximum Whisker = 69 Mean = 62.573 Standard Deviation = 2.4524 Number of Observations = 2869 Sex = Female Minimum Whisker = 56.25 First Quartile = 61 Median = 62.5 Third Quartile = 64.25 Maximum Whisker = 69 Mean = 62.573 Standard Deviation = 2.4524 Number of Observations = 2869 Sex = Female Minimum Whisker = 56.25 First Quartile = 61 Median = 62.5 Third Quartile = 64.25 Maximum Whisker = 69 Mean = 62.573 Standard Deviation = 2.4524 Number of Observations = 2869 Sex = Female Minimum Whisker = 56.25 First Quartile = 61 Median = 62.5 Third Quartile = 64.25 Maximum Whisker = 69 Mean = 62.573 Standard Deviation = 2.4524 Number of Observations = 2869
Box Plot for Height
  • The center of the distribution for Sex=Male is shifted to the right compared to the distribution for Sex=Female. The box plots also show more outliers in the female distribution of Height compared to the male distribution. This may be partly due to the smaller interquartile range (the distance from the top to the bottom of the box) for the females compared to the males.

Describing Categorical Variables.

SAS Code, click to expand

SAS Code:

#  (&path1 and biostats libname previously defined)
/* Describing Categorical Variables  - start */

title1 "Frequencies on Data from Health Data Set";
proc freq data=sashelp.heart;
    tables Status Sex Chol_Status / nocum missing plots=(freqplot);
run;
title1;

/* Describing Categorical Variables  - end */

SAS Output

Results: biostats_by_ex_SAScode.sas

Results: biostats_by_ex_SAScode.sas

Frequencies on Data from Health Data Set

The Freq Procedure

Table Status

One-Way Frequencies

Status Frequency Percent
Alive 3218 61.78
Dead 1991 38.22

Distribution Plots

Frequency Plot

Status = Dead Frequency = 1991 Percent = 38.222 Status = Alive Frequency = 3218 Percent = 61.778
Bar Chart of Frequencies for Status

Table Sex

One-Way Frequencies

Sex Frequency Percent
Female 2873 55.15
Male 2336 44.85

Distribution Plots

Frequency Plot

Sex = Male Frequency = 2336 Percent = 44.845 Sex = Female Frequency = 2873 Percent = 55.155
Bar Chart of Frequencies for Sex

Table Chol_Status

One-Way Frequencies

Cholesterol Status
Chol_Status Frequency Percent
  152 2.92
Borderline 1861 35.73
Desirable 1405 26.97
High 1791 34.38

Distribution Plots

Frequency Plot

Cholesterol Status = High Frequency = 1791 Percent = 34.383 Cholesterol Status = Desirable Frequency = 1405 Percent = 26.973 Cholesterol Status = Borderline Frequency = 1861 Percent = 35.727 Cholesterol Status = Frequency = 152 Percent = 2.918
Bar Chart of Frequencies for Chol_Status

Practice: Distribution of SBP (Systolic Blood Pressure) and DBP (Diastolic Blood Pressure) Values

SAS Code, click to expand

SAS Code:

#  (&path1 and biostats libname previously defined)
/* Distribution Practice 5-3  - start */

ods noproctitle;
ods graphics / imagemap=on;

proc univariate data=work.blood_pressure;
    ods select Histogram GoodnessOfFit QQPlot;
    var SBP DBP;
    /* Checking for Normality */
    histogram SBP DBP / normal(mu=est sigma=est);
    inset skewness kurtosis n / position=ne;
    qqplot SBP DBP / normal(mu=est sigma=est);
    inset skewness kurtosis n / position=nw;
run;
title1;

/* Practice Distribution 5-3  - end */

/* Using data from Blood_Pressure.xlsx, we examine the distribution of the two variables: SBP (Systolic Blood Pressure) and DBP (Diastolic Blood Pressure) with histogram and Q-Q plots.  Tests of normality (https://support.sas.com/documentation/cdl/en/procstat/63104/HTML/default/viewer.htm#procstat_univariate_sect037.htm) were requested, including and the [SAS-modified version of] Kolmogorov-Smirnov D test.  SBP (Systolic Blood Pressure) has a Kolmogorov-Smirnov D p-value of 0.111, exceeding our arbitrary significance level of 0.05 which means we cannot reject the null hypothesis, and cannot conclude that the data did not come from a normal distribution.  DBP (Diastolic Blood Pressure) has a Kolmogorov-Smirnov D p-value of 0.041, which is less than the predetermined critical value of 0.05, so we reject the null hypothesis and conclude that the data did not come from a normal distribution. */

SAS Output

Results: biostats_by_ex_SAScode.sas

Results: biostats_by_ex_SAScode.sas

The Univariate Procedure

SBP

Histogram 1

Panel 1

SBP = 160 Percent = 0.7633 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 159.72 Percent = 0.8183 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 159.72 Percent = 0.8183 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 159.43 Percent = 0.8768 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 159.43 Percent = 0.8768 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 159.15 Percent = 0.9388 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 159.15 Percent = 0.9388 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 158.87 Percent = 1.0045 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 158.87 Percent = 1.0045 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 158.59 Percent = 1.0741 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 158.59 Percent = 1.0741 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 158.3 Percent = 1.1477 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 158.3 Percent = 1.1477 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 158.02 Percent = 1.2255 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 158.02 Percent = 1.2255 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 157.74 Percent = 1.3078 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 157.74 Percent = 1.3078 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 157.45 Percent = 1.3946 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 157.45 Percent = 1.3946 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 157.17 Percent = 1.4862 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 157.17 Percent = 1.4862 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 156.89 Percent = 1.5828 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 156.89 Percent = 1.5828 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 156.61 Percent = 1.6844 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 156.61 Percent = 1.6844 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 156.32 Percent = 1.7915 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 156.32 Percent = 1.7915 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 156.04 Percent = 1.904 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 156.04 Percent = 1.904 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 155.76 Percent = 2.0223 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 155.76 Percent = 2.0223 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 155.47 Percent = 2.1464 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 155.47 Percent = 2.1464 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 155.19 Percent = 2.2767 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 155.19 Percent = 2.2767 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 154.91 Percent = 2.4132 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 154.91 Percent = 2.4132 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 154.63 Percent = 2.5562 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 154.63 Percent = 2.5562 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 154.34 Percent = 2.7058 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 154.34 Percent = 2.7058 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 154.06 Percent = 2.8623 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 154.06 Percent = 2.8623 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 153.78 Percent = 3.0258 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 153.78 Percent = 3.0258 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 153.49 Percent = 3.1965 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 153.49 Percent = 3.1965 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 153.21 Percent = 3.3746 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 153.21 Percent = 3.3746 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 152.93 Percent = 3.5602 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 152.93 Percent = 3.5602 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 152.65 Percent = 3.7534 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 152.65 Percent = 3.7534 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 152.36 Percent = 3.9545 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 152.36 Percent = 3.9545 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 152.08 Percent = 4.1636 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 152.08 Percent = 4.1636 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 151.8 Percent = 4.3808 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 151.8 Percent = 4.3808 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 151.52 Percent = 4.6062 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 151.52 Percent = 4.6062 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 151.23 Percent = 4.84 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 151.23 Percent = 4.84 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 150.95 Percent = 5.0822 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 150.95 Percent = 5.0822 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 150.67 Percent = 5.3329 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 150.67 Percent = 5.3329 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 150.38 Percent = 5.5923 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 150.38 Percent = 5.5923 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 150.1 Percent = 5.8603 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 150.1 Percent = 5.8603 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 149.82 Percent = 6.1371 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 149.82 Percent = 6.1371 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 149.54 Percent = 6.4226 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 149.54 Percent = 6.4226 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 149.25 Percent = 6.7168 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 149.25 Percent = 6.7168 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 148.97 Percent = 7.0199 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 148.97 Percent = 7.0199 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 148.69 Percent = 7.3317 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 148.69 Percent = 7.3317 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 148.4 Percent = 7.6522 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 148.4 Percent = 7.6522 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 148.12 Percent = 7.9813 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 148.12 Percent = 7.9813 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 147.84 Percent = 8.319 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 147.84 Percent = 8.319 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 147.56 Percent = 8.6652 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 147.56 Percent = 8.6652 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 147.27 Percent = 9.0197 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 147.27 Percent = 9.0197 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 146.99 Percent = 9.3824 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 146.99 Percent = 9.3824 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 146.71 Percent = 9.7531 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 146.71 Percent = 9.7531 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 146.42 Percent = 10.132 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 146.42 Percent = 10.132 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 146.14 Percent = 10.518 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 146.14 Percent = 10.518 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 145.86 Percent = 10.911 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 145.86 Percent = 10.911 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 145.58 Percent = 11.312 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 145.58 Percent = 11.312 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 145.29 Percent = 11.72 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 145.29 Percent = 11.72 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 145.01 Percent = 12.134 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 145.01 Percent = 12.134 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 144.73 Percent = 12.554 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 144.73 Percent = 12.554 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 144.44 Percent = 12.98 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 144.44 Percent = 12.98 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 144.16 Percent = 13.412 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 144.16 Percent = 13.412 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 143.88 Percent = 13.848 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 143.88 Percent = 13.848 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 143.6 Percent = 14.29 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 143.6 Percent = 14.29 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 143.31 Percent = 14.735 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 143.31 Percent = 14.735 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 143.03 Percent = 15.184 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 143.03 Percent = 15.184 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 142.75 Percent = 15.636 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 142.75 Percent = 15.636 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 142.46 Percent = 16.091 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 142.46 Percent = 16.091 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 142.18 Percent = 16.548 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 142.18 Percent = 16.548 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 141.9 Percent = 17.006 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 141.9 Percent = 17.006 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 141.62 Percent = 17.466 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 141.62 Percent = 17.466 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 141.33 Percent = 17.926 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 141.33 Percent = 17.926 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 141.05 Percent = 18.385 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 141.05 Percent = 18.385 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 140.77 Percent = 18.844 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 140.77 Percent = 18.844 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 140.48 Percent = 19.301 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 140.48 Percent = 19.301 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 140.2 Percent = 19.756 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 140.2 Percent = 19.756 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 139.92 Percent = 20.208 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 139.92 Percent = 20.208 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 139.64 Percent = 20.657 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 139.64 Percent = 20.657 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 139.35 Percent = 21.101 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 139.35 Percent = 21.101 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 139.07 Percent = 21.541 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 139.07 Percent = 21.541 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 138.79 Percent = 21.975 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 138.79 Percent = 21.975 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 138.51 Percent = 22.402 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 138.51 Percent = 22.402 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 138.22 Percent = 22.823 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 138.22 Percent = 22.823 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 137.94 Percent = 23.235 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 137.94 Percent = 23.235 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 137.66 Percent = 23.64 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 137.66 Percent = 23.64 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 137.37 Percent = 24.035 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 137.37 Percent = 24.035 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 137.09 Percent = 24.42 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 137.09 Percent = 24.42 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 136.81 Percent = 24.795 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 136.81 Percent = 24.795 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 136.53 Percent = 25.159 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 136.53 Percent = 25.159 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 136.24 Percent = 25.511 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 136.24 Percent = 25.511 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 135.96 Percent = 25.851 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 135.96 Percent = 25.851 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 135.68 Percent = 26.177 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 135.68 Percent = 26.177 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 135.39 Percent = 26.49 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 135.39 Percent = 26.49 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 135.11 Percent = 26.788 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 135.11 Percent = 26.788 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 134.83 Percent = 27.072 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 134.83 Percent = 27.072 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 134.55 Percent = 27.34 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 134.55 Percent = 27.34 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 134.26 Percent = 27.593 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 134.26 Percent = 27.593 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 133.98 Percent = 27.829 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 133.98 Percent = 27.829 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 133.7 Percent = 28.048 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 133.7 Percent = 28.048 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 133.41 Percent = 28.25 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 133.41 Percent = 28.25 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 133.13 Percent = 28.434 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 133.13 Percent = 28.434 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 132.85 Percent = 28.6 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 132.85 Percent = 28.6 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 132.57 Percent = 28.748 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 132.57 Percent = 28.748 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 132.28 Percent = 28.878 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 132.28 Percent = 28.878 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 132 Percent = 28.988 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 132 Percent = 28.988 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 131.72 Percent = 29.079 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 131.72 Percent = 29.079 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 131.43 Percent = 29.151 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 131.43 Percent = 29.151 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 131.15 Percent = 29.204 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 131.15 Percent = 29.204 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 130.87 Percent = 29.237 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 130.87 Percent = 29.237 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 130.59 Percent = 29.25 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 130.59 Percent = 29.25 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 130.54 Percent = 29.25 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 130.54 Percent = 29.25 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 130.3 Percent = 29.244 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 130.3 Percent = 29.244 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 130.02 Percent = 29.218 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 130.02 Percent = 29.218 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 129.74 Percent = 29.172 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 129.74 Percent = 29.172 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 129.45 Percent = 29.107 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 129.45 Percent = 29.107 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 129.17 Percent = 29.023 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 129.17 Percent = 29.023 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 128.89 Percent = 28.919 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 128.89 Percent = 28.919 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 128.61 Percent = 28.796 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 128.61 Percent = 28.796 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 128.32 Percent = 28.655 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 128.32 Percent = 28.655 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 128.04 Percent = 28.495 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 128.04 Percent = 28.495 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 127.76 Percent = 28.317 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 127.76 Percent = 28.317 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 127.47 Percent = 28.122 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 127.47 Percent = 28.122 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 127.19 Percent = 27.908 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 127.19 Percent = 27.908 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 126.91 Percent = 27.678 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 126.91 Percent = 27.678 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 126.63 Percent = 27.432 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 126.63 Percent = 27.432 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 126.34 Percent = 27.169 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 126.34 Percent = 27.169 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 126.06 Percent = 26.891 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 126.06 Percent = 26.891 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 125.78 Percent = 26.597 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 125.78 Percent = 26.597 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 125.49 Percent = 26.29 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 125.49 Percent = 26.29 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 125.21 Percent = 25.968 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 125.21 Percent = 25.968 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 124.93 Percent = 25.633 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 124.93 Percent = 25.633 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 124.65 Percent = 25.285 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 124.65 Percent = 25.285 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 124.36 Percent = 24.926 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 124.36 Percent = 24.926 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 124.08 Percent = 24.555 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 124.08 Percent = 24.555 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 123.8 Percent = 24.173 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 123.8 Percent = 24.173 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 123.52 Percent = 23.781 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 123.52 Percent = 23.781 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 123.23 Percent = 23.38 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 123.23 Percent = 23.38 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 122.95 Percent = 22.97 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 122.95 Percent = 22.97 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 122.67 Percent = 22.552 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 122.67 Percent = 22.552 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 122.38 Percent = 22.127 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 122.38 Percent = 22.127 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 122.1 Percent = 21.695 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 122.1 Percent = 21.695 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 121.82 Percent = 21.258 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 121.82 Percent = 21.258 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 121.54 Percent = 20.815 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 121.54 Percent = 20.815 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 121.25 Percent = 20.368 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 121.25 Percent = 20.368 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 120.97 Percent = 19.917 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 120.97 Percent = 19.917 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 120.69 Percent = 19.463 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 120.69 Percent = 19.463 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 120.4 Percent = 19.006 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 120.4 Percent = 19.006 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 120.12 Percent = 18.548 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 120.12 Percent = 18.548 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 119.84 Percent = 18.089 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 119.84 Percent = 18.089 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 119.56 Percent = 17.629 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 119.56 Percent = 17.629 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 119.27 Percent = 17.169 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 119.27 Percent = 17.169 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 118.99 Percent = 16.71 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 118.99 Percent = 16.71 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 118.71 Percent = 16.253 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 118.71 Percent = 16.253 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 118.42 Percent = 15.797 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 118.42 Percent = 15.797 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 118.14 Percent = 15.344 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 118.14 Percent = 15.344 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 117.86 Percent = 14.894 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 117.86 Percent = 14.894 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 117.58 Percent = 14.447 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 117.58 Percent = 14.447 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 117.29 Percent = 14.004 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 117.29 Percent = 14.004 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 117.01 Percent = 13.566 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 117.01 Percent = 13.566 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 116.73 Percent = 13.133 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 116.73 Percent = 13.133 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 116.44 Percent = 12.705 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 116.44 Percent = 12.705 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 116.16 Percent = 12.282 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 116.16 Percent = 12.282 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 115.88 Percent = 11.866 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 115.88 Percent = 11.866 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 115.6 Percent = 11.456 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 115.6 Percent = 11.456 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 115.31 Percent = 11.053 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 115.31 Percent = 11.053 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 115.03 Percent = 10.657 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 115.03 Percent = 10.657 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 114.75 Percent = 10.268 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 114.75 Percent = 10.268 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 114.46 Percent = 9.8865 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 114.46 Percent = 9.8865 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 114.18 Percent = 9.5129 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 114.18 Percent = 9.5129 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 113.9 Percent = 9.1473 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 113.9 Percent = 9.1473 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 113.62 Percent = 8.7899 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 113.62 Percent = 8.7899 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 113.33 Percent = 8.4408 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 113.33 Percent = 8.4408 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 113.05 Percent = 8.1001 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 113.05 Percent = 8.1001 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 112.77 Percent = 7.7679 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 112.77 Percent = 7.7679 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 112.48 Percent = 7.4443 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 112.48 Percent = 7.4443 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 112.2 Percent = 7.1294 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 112.2 Percent = 7.1294 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 111.92 Percent = 6.8233 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 111.92 Percent = 6.8233 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 111.64 Percent = 6.5259 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 111.64 Percent = 6.5259 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 111.35 Percent = 6.2373 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 111.35 Percent = 6.2373 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 111.07 Percent = 5.9574 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 111.07 Percent = 5.9574 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 110.79 Percent = 5.6863 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 110.79 Percent = 5.6863 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 110.51 Percent = 5.4239 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 110.51 Percent = 5.4239 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 110.22 Percent = 5.1701 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 110.22 Percent = 5.1701 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 109.94 Percent = 4.9249 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 109.94 Percent = 4.9249 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 109.66 Percent = 4.6881 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 109.66 Percent = 4.6881 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 109.37 Percent = 4.4598 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 109.37 Percent = 4.4598 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 109.09 Percent = 4.2397 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 109.09 Percent = 4.2397 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 108.81 Percent = 4.0277 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 108.81 Percent = 4.0277 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 108.53 Percent = 3.8238 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 108.53 Percent = 3.8238 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 108.24 Percent = 3.6278 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 108.24 Percent = 3.6278 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 107.96 Percent = 3.4395 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 107.96 Percent = 3.4395 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 107.68 Percent = 3.2588 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 107.68 Percent = 3.2588 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 107.39 Percent = 3.0855 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 107.39 Percent = 3.0855 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 107.11 Percent = 2.9195 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 107.11 Percent = 2.9195 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 106.83 Percent = 2.7605 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 106.83 Percent = 2.7605 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 106.55 Percent = 2.6085 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 106.55 Percent = 2.6085 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 106.26 Percent = 2.4631 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 106.26 Percent = 2.4631 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 105.98 Percent = 2.3243 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 105.98 Percent = 2.3243 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 105.7 Percent = 2.1919 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 105.7 Percent = 2.1919 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 105.41 Percent = 2.0656 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 105.41 Percent = 2.0656 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 105.13 Percent = 1.9453 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 105.13 Percent = 1.9453 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 104.85 Percent = 1.8307 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 104.85 Percent = 1.8307 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 104.57 Percent = 1.7218 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 104.57 Percent = 1.7218 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 104.28 Percent = 1.6182 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 104.28 Percent = 1.6182 CurveLabel = Normal(Mu=130.54 Sigma=10.911) SBP = 104 Percent = 1.5199 CurveLabel = Normal(Mu=130.54 Sigma=10.911) Bin Midpoint = 156 Percent = 1.7857 Bin Midpoint = 156 Percent = 1.7857 Bin Midpoint = 148 Percent = 8.9286 Bin Midpoint = 148 Percent = 8.9286 Bin Midpoint = 140 Percent = 26.786 Bin Midpoint = 140 Percent = 26.786 Bin Midpoint = 132 Percent = 25 Bin Midpoint = 132 Percent = 25 Bin Midpoint = 124 Percent = 21.429 Bin Midpoint = 124 Percent = 21.429 Bin Midpoint = 116 Percent = 12.5 Bin Midpoint = 116 Percent = 12.5 Bin Midpoint = 108 Percent = 3.5714 Bin Midpoint = 108 Percent = 3.5714
Histogram for SBP

Fitted Normal Distribution for SBP (SBP)

Normal Fit

Goodness of Fit

Goodness-of-Fit Tests for Normal Distribution
Test Statistic p Value
Kolmogorov-Smirnov D 0.10671056 Pr > D 0.111
Cramer-von Mises W-Sq 0.08450704 Pr > W-Sq 0.184
Anderson-Darling A-Sq 0.45548604 Pr > A-Sq >0.250

Q-Q Plot 1

Panel 1

Slope = 10.911 Y = 130.54 Quantile = 2.2865 SBP = 156 Quantile = 1.8974 SBP = 150 Quantile = 1.6781 SBP = 148 Quantile = 1.5185 SBP = 146 Quantile = 1.3903 SBP = 144 Quantile = 1.2816 SBP = 144 Quantile = 1.1862 SBP = 142 Quantile = 1.1005 SBP = 142 Quantile = 1.0222 SBP = 140 Quantile = 0.9498 SBP = 140 Quantile = 0.882 SBP = 140 Quantile = 0.818 SBP = 140 Quantile = 0.7573 SBP = 140 Quantile = 0.6992 SBP = 138 Quantile = 0.6433 SBP = 138 Quantile = 0.5895 SBP = 138 Quantile = 0.5372 SBP = 138 Quantile = 0.4864 SBP = 136 Quantile = 0.4368 SBP = 136 Quantile = 0.3883 SBP = 136 Quantile = 0.3407 SBP = 136 Quantile = 0.2938 SBP = 134 Quantile = 0.2476 SBP = 134 Quantile = 0.2019 SBP = 134 Quantile = 0.1566 SBP = 134 Quantile = 0.1116 SBP = 134 Quantile = 0.0669 SBP = 134 Quantile = 0.0223 SBP = 132 Quantile = -0.022 SBP = 132 Quantile = -0.067 SBP = 132 Quantile = -0.112 SBP = 130 Quantile = -0.157 SBP = 130 Quantile = -0.202 SBP = 130 Quantile = -0.248 SBP = 130 Quantile = -0.294 SBP = 128 Quantile = -0.341 SBP = 126 Quantile = -0.388 SBP = 126 Quantile = -0.437 SBP = 124 Quantile = -0.486 SBP = 124 Quantile = -0.537 SBP = 124 Quantile = -0.589 SBP = 124 Quantile = -0.643 SBP = 122 Quantile = -0.699 SBP = 120 Quantile = -0.757 SBP = 120 Quantile = -0.818 SBP = 120 Quantile = -0.882 SBP = 120 Quantile = -0.95 SBP = 120 Quantile = -1.022 SBP = 118 Quantile = -1.101 SBP = 118 Quantile = -1.186 SBP = 118 Quantile = -1.282 SBP = 114 Quantile = -1.39 SBP = 114 Quantile = -1.518 SBP = 112 Quantile = -1.678 SBP = 112 Quantile = -1.897 SBP = 110 Quantile = -2.287 SBP = 108
Q-Q plot for SBP

DBP

Histogram 1

Panel 1

DBP = 94 Percent = 1.9577 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 93.859 Percent = 2.0787 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 93.859 Percent = 2.0787 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 93.717 Percent = 2.2058 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 93.717 Percent = 2.2058 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 93.576 Percent = 2.3391 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 93.576 Percent = 2.3391 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 93.434 Percent = 2.4787 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 93.434 Percent = 2.4787 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 93.293 Percent = 2.6249 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 93.293 Percent = 2.6249 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 93.152 Percent = 2.7779 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 93.152 Percent = 2.7779 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 93.01 Percent = 2.9378 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 93.01 Percent = 2.9378 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 92.869 Percent = 3.1048 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 92.869 Percent = 3.1048 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 92.727 Percent = 3.2791 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 92.727 Percent = 3.2791 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 92.586 Percent = 3.4609 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 92.586 Percent = 3.4609 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 92.444 Percent = 3.6502 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 92.444 Percent = 3.6502 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 92.303 Percent = 3.8474 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 92.303 Percent = 3.8474 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 92.162 Percent = 4.0524 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 92.162 Percent = 4.0524 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 92.02 Percent = 4.2656 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 92.02 Percent = 4.2656 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 91.879 Percent = 4.4869 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 91.879 Percent = 4.4869 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 91.737 Percent = 4.7165 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 91.737 Percent = 4.7165 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 91.596 Percent = 4.9545 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 91.596 Percent = 4.9545 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 91.455 Percent = 5.2011 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 91.455 Percent = 5.2011 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 91.313 Percent = 5.4562 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 91.313 Percent = 5.4562 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 91.172 Percent = 5.72 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 91.172 Percent = 5.72 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 91.03 Percent = 5.9926 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 91.03 Percent = 5.9926 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 90.889 Percent = 6.2739 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 90.889 Percent = 6.2739 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 90.747 Percent = 6.5639 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 90.747 Percent = 6.5639 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 90.606 Percent = 6.8628 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 90.606 Percent = 6.8628 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 90.465 Percent = 7.1704 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 90.465 Percent = 7.1704 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 90.323 Percent = 7.4868 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 90.323 Percent = 7.4868 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 90.182 Percent = 7.8119 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 90.182 Percent = 7.8119 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 90.04 Percent = 8.1457 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 90.04 Percent = 8.1457 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 89.899 Percent = 8.4879 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 89.899 Percent = 8.4879 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 89.758 Percent = 8.8386 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 89.758 Percent = 8.8386 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 89.616 Percent = 9.1976 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 89.616 Percent = 9.1976 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 89.475 Percent = 9.5648 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 89.475 Percent = 9.5648 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 89.333 Percent = 9.9399 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 89.333 Percent = 9.9399 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 89.192 Percent = 10.323 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 89.192 Percent = 10.323 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 89.051 Percent = 10.713 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 89.051 Percent = 10.713 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 88.909 Percent = 11.111 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 88.909 Percent = 11.111 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 88.768 Percent = 11.516 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 88.768 Percent = 11.516 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 88.626 Percent = 11.927 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 88.626 Percent = 11.927 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 88.485 Percent = 12.345 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 88.485 Percent = 12.345 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 88.343 Percent = 12.769 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 88.343 Percent = 12.769 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 88.202 Percent = 13.198 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 88.202 Percent = 13.198 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 88.061 Percent = 13.633 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 88.061 Percent = 13.633 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 87.919 Percent = 14.072 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 87.919 Percent = 14.072 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 87.778 Percent = 14.516 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 87.778 Percent = 14.516 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 87.636 Percent = 14.964 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 87.636 Percent = 14.964 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 87.495 Percent = 15.416 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 87.495 Percent = 15.416 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 87.354 Percent = 15.87 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 87.354 Percent = 15.87 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 87.212 Percent = 16.327 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 87.212 Percent = 16.327 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 87.071 Percent = 16.785 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 87.071 Percent = 16.785 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 86.929 Percent = 17.245 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 86.929 Percent = 17.245 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 86.788 Percent = 17.706 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 86.788 Percent = 17.706 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 86.646 Percent = 18.166 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 86.646 Percent = 18.166 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 86.505 Percent = 18.626 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 86.505 Percent = 18.626 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 86.364 Percent = 19.085 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 86.364 Percent = 19.085 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 86.222 Percent = 19.542 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 86.222 Percent = 19.542 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 86.081 Percent = 19.997 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 86.081 Percent = 19.997 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 85.939 Percent = 20.448 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 85.939 Percent = 20.448 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 85.798 Percent = 20.895 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 85.798 Percent = 20.895 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 85.657 Percent = 21.338 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 85.657 Percent = 21.338 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 85.515 Percent = 21.775 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 85.515 Percent = 21.775 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 85.374 Percent = 22.207 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 85.374 Percent = 22.207 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 85.232 Percent = 22.632 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 85.232 Percent = 22.632 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 85.091 Percent = 23.049 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 85.091 Percent = 23.049 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 84.949 Percent = 23.459 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 84.949 Percent = 23.459 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 84.808 Percent = 23.859 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 84.808 Percent = 23.859 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 84.667 Percent = 24.25 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 84.667 Percent = 24.25 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 84.525 Percent = 24.631 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 84.525 Percent = 24.631 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 84.384 Percent = 25.001 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 84.384 Percent = 25.001 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 84.242 Percent = 25.36 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 84.242 Percent = 25.36 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 84.101 Percent = 25.706 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 84.101 Percent = 25.706 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 83.96 Percent = 26.04 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 83.96 Percent = 26.04 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 83.818 Percent = 26.36 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 83.818 Percent = 26.36 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 83.677 Percent = 26.666 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 83.677 Percent = 26.666 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 83.535 Percent = 26.957 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 83.535 Percent = 26.957 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 83.394 Percent = 27.234 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 83.394 Percent = 27.234 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 83.253 Percent = 27.494 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 83.253 Percent = 27.494 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 83.111 Percent = 27.739 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 83.111 Percent = 27.739 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 82.97 Percent = 27.967 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 82.97 Percent = 27.967 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 82.828 Percent = 28.178 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 82.828 Percent = 28.178 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 82.687 Percent = 28.371 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 82.687 Percent = 28.371 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 82.545 Percent = 28.546 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 82.545 Percent = 28.546 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 82.404 Percent = 28.703 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 82.404 Percent = 28.703 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 82.263 Percent = 28.842 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 82.263 Percent = 28.842 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 82.121 Percent = 28.962 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 82.121 Percent = 28.962 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 81.98 Percent = 29.062 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 81.98 Percent = 29.062 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 81.838 Percent = 29.144 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 81.838 Percent = 29.144 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 81.697 Percent = 29.206 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 81.697 Percent = 29.206 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 81.556 Percent = 29.248 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 81.556 Percent = 29.248 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 81.414 Percent = 29.271 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 81.414 Percent = 29.271 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 81.321 Percent = 29.275 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 81.321 Percent = 29.275 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 81.273 Percent = 29.274 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 81.273 Percent = 29.274 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 81.131 Percent = 29.257 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 81.131 Percent = 29.257 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 80.99 Percent = 29.221 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 80.99 Percent = 29.221 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 80.848 Percent = 29.165 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 80.848 Percent = 29.165 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 80.707 Percent = 29.09 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 80.707 Percent = 29.09 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 80.566 Percent = 28.995 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 80.566 Percent = 28.995 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 80.424 Percent = 28.881 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 80.424 Percent = 28.881 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 80.283 Percent = 28.748 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 80.283 Percent = 28.748 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 80.141 Percent = 28.597 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 80.141 Percent = 28.597 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 80 Percent = 28.427 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 80 Percent = 28.427 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 79.859 Percent = 28.24 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 79.859 Percent = 28.24 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 79.717 Percent = 28.034 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 79.717 Percent = 28.034 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 79.576 Percent = 27.812 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 79.576 Percent = 27.812 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 79.434 Percent = 27.572 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 79.434 Percent = 27.572 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 79.293 Percent = 27.317 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 79.293 Percent = 27.317 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 79.152 Percent = 27.045 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 79.152 Percent = 27.045 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 79.01 Percent = 26.758 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 79.01 Percent = 26.758 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 78.869 Percent = 26.456 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 78.869 Percent = 26.456 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 78.727 Percent = 26.141 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 78.727 Percent = 26.141 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 78.586 Percent = 25.811 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 78.586 Percent = 25.811 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 78.444 Percent = 25.469 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 78.444 Percent = 25.469 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 78.303 Percent = 25.114 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 78.303 Percent = 25.114 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 78.162 Percent = 24.747 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 78.162 Percent = 24.747 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 78.02 Percent = 24.37 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 78.02 Percent = 24.37 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 77.879 Percent = 23.982 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 77.879 Percent = 23.982 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 77.737 Percent = 23.584 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 77.737 Percent = 23.584 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 77.596 Percent = 23.177 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 77.596 Percent = 23.177 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 77.455 Percent = 22.762 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 77.455 Percent = 22.762 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 77.313 Percent = 22.34 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 77.313 Percent = 22.34 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 77.172 Percent = 21.91 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 77.172 Percent = 21.91 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 77.03 Percent = 21.475 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 77.03 Percent = 21.475 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 76.889 Percent = 21.033 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 76.889 Percent = 21.033 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 76.747 Percent = 20.587 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 76.747 Percent = 20.587 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 76.606 Percent = 20.137 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 76.606 Percent = 20.137 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 76.465 Percent = 19.684 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 76.465 Percent = 19.684 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 76.323 Percent = 19.228 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 76.323 Percent = 19.228 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 76.182 Percent = 18.769 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 76.182 Percent = 18.769 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 76.04 Percent = 18.31 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 76.04 Percent = 18.31 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 75.899 Percent = 17.849 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 75.899 Percent = 17.849 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 75.758 Percent = 17.389 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 75.758 Percent = 17.389 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 75.616 Percent = 16.928 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 75.616 Percent = 16.928 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 75.475 Percent = 16.469 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 75.475 Percent = 16.469 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 75.333 Percent = 16.012 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 75.333 Percent = 16.012 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 75.192 Percent = 15.557 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 75.192 Percent = 15.557 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 75.051 Percent = 15.105 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 75.051 Percent = 15.105 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 74.909 Percent = 14.655 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 74.909 Percent = 14.655 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 74.768 Percent = 14.21 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 74.768 Percent = 14.21 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 74.626 Percent = 13.769 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 74.626 Percent = 13.769 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 74.485 Percent = 13.333 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 74.485 Percent = 13.333 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 74.343 Percent = 12.902 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 74.343 Percent = 12.902 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 74.202 Percent = 12.476 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 74.202 Percent = 12.476 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 74.061 Percent = 12.056 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 74.061 Percent = 12.056 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 73.919 Percent = 11.643 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 73.919 Percent = 11.643 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 73.778 Percent = 11.236 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 73.778 Percent = 11.236 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 73.636 Percent = 10.836 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 73.636 Percent = 10.836 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 73.495 Percent = 10.443 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 73.495 Percent = 10.443 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 73.354 Percent = 10.058 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 73.354 Percent = 10.058 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 73.212 Percent = 9.6807 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 73.212 Percent = 9.6807 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 73.071 Percent = 9.311 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 73.071 Percent = 9.311 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 72.929 Percent = 8.9495 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 72.929 Percent = 8.9495 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 72.788 Percent = 8.5962 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 72.788 Percent = 8.5962 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 72.646 Percent = 8.2513 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 72.646 Percent = 8.2513 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 72.505 Percent = 7.9149 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 72.505 Percent = 7.9149 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 72.364 Percent = 7.5871 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 72.364 Percent = 7.5871 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 72.222 Percent = 7.268 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 72.222 Percent = 7.268 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 72.081 Percent = 6.9576 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 72.081 Percent = 6.9576 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 71.939 Percent = 6.656 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 71.939 Percent = 6.656 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 71.798 Percent = 6.3632 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 71.798 Percent = 6.3632 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 71.657 Percent = 6.0792 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 71.657 Percent = 6.0792 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 71.515 Percent = 5.8039 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 71.515 Percent = 5.8039 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 71.374 Percent = 5.5374 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 71.374 Percent = 5.5374 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 71.232 Percent = 5.2796 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 71.232 Percent = 5.2796 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 71.091 Percent = 5.0304 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 71.091 Percent = 5.0304 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 70.949 Percent = 4.7897 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 70.949 Percent = 4.7897 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 70.808 Percent = 4.5575 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 70.808 Percent = 4.5575 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 70.667 Percent = 4.3336 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 70.667 Percent = 4.3336 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 70.525 Percent = 4.1179 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 70.525 Percent = 4.1179 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 70.384 Percent = 3.9103 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 70.384 Percent = 3.9103 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 70.242 Percent = 3.7108 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 70.242 Percent = 3.7108 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 70.101 Percent = 3.519 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 70.101 Percent = 3.519 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 69.96 Percent = 3.3349 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 69.96 Percent = 3.3349 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 69.818 Percent = 3.1583 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 69.818 Percent = 3.1583 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 69.677 Percent = 2.989 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 69.677 Percent = 2.989 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 69.535 Percent = 2.8269 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 69.535 Percent = 2.8269 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 69.394 Percent = 2.6718 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 69.394 Percent = 2.6718 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 69.253 Percent = 2.5235 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 69.253 Percent = 2.5235 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 69.111 Percent = 2.3818 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 69.111 Percent = 2.3818 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 68.97 Percent = 2.2466 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 68.97 Percent = 2.2466 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 68.828 Percent = 2.1176 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 68.828 Percent = 2.1176 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 68.687 Percent = 1.9947 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 68.687 Percent = 1.9947 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 68.545 Percent = 1.8777 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 68.545 Percent = 1.8777 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 68.404 Percent = 1.7663 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 68.404 Percent = 1.7663 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 68.263 Percent = 1.6604 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 68.263 Percent = 1.6604 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 68.121 Percent = 1.5598 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 68.121 Percent = 1.5598 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 67.98 Percent = 1.4644 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 67.98 Percent = 1.4644 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 67.838 Percent = 1.3738 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 67.838 Percent = 1.3738 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 67.697 Percent = 1.288 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 67.697 Percent = 1.288 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 67.556 Percent = 1.2067 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 67.556 Percent = 1.2067 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 67.414 Percent = 1.1298 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 67.414 Percent = 1.1298 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 67.273 Percent = 1.0571 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 67.273 Percent = 1.0571 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 67.131 Percent = 0.9884 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 67.131 Percent = 0.9884 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 66.99 Percent = 0.9235 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 66.99 Percent = 0.9235 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 66.848 Percent = 0.8624 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 66.848 Percent = 0.8624 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 66.707 Percent = 0.8047 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 66.707 Percent = 0.8047 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 66.566 Percent = 0.7504 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 66.566 Percent = 0.7504 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 66.424 Percent = 0.6992 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 66.424 Percent = 0.6992 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 66.283 Percent = 0.6512 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 66.283 Percent = 0.6512 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 66.141 Percent = 0.606 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 66.141 Percent = 0.606 CurveLabel = Normal(Mu=81.321 Sigma=5.451) DBP = 66 Percent = 0.5636 CurveLabel = Normal(Mu=81.321 Sigma=5.451) Bin Midpoint = 92 Percent = 7.1429 Bin Midpoint = 92 Percent = 7.1429 Bin Midpoint = 88 Percent = 16.071 Bin Midpoint = 88 Percent = 16.071 Bin Midpoint = 84 Percent = 33.929 Bin Midpoint = 84 Percent = 33.929 Bin Midpoint = 80 Percent = 25 Bin Midpoint = 80 Percent = 25 Bin Midpoint = 76 Percent = 8.9286 Bin Midpoint = 76 Percent = 8.9286 Bin Midpoint = 72 Percent = 7.1429 Bin Midpoint = 72 Percent = 7.1429 Bin Midpoint = 68 Percent = 1.7857 Bin Midpoint = 68 Percent = 1.7857
Histogram for DBP

Fitted Normal Distribution for DBP (DBP)

Normal Fit

Goodness of Fit

Goodness-of-Fit Tests for Normal Distribution
Test Statistic p Value
Kolmogorov-Smirnov D 0.12096354 Pr > D 0.041
Cramer-von Mises W-Sq 0.10293193 Pr > W-Sq 0.101
Anderson-Darling A-Sq 0.59220879 Pr > A-Sq 0.122

Q-Q Plot 1

Panel 1

Slope = 5.451 Y = 81.321 Quantile = 2.2865 DBP = 92 Quantile = 1.8974 DBP = 90 Quantile = 1.6781 DBP = 90 Quantile = 1.5185 DBP = 90 Quantile = 1.3903 DBP = 88 Quantile = 1.2816 DBP = 88 Quantile = 1.1862 DBP = 88 Quantile = 1.1005 DBP = 88 Quantile = 1.0222 DBP = 88 Quantile = 0.9498 DBP = 86 Quantile = 0.882 DBP = 86 Quantile = 0.818 DBP = 86 Quantile = 0.7573 DBP = 86 Quantile = 0.6992 DBP = 84 Quantile = 0.6433 DBP = 84 Quantile = 0.5895 DBP = 84 Quantile = 0.5372 DBP = 84 Quantile = 0.4864 DBP = 84 Quantile = 0.4368 DBP = 84 Quantile = 0.3883 DBP = 84 Quantile = 0.3407 DBP = 84 Quantile = 0.2938 DBP = 84 Quantile = 0.2476 DBP = 82 Quantile = 0.2019 DBP = 82 Quantile = 0.1566 DBP = 82 Quantile = 0.1116 DBP = 82 Quantile = 0.0669 DBP = 82 Quantile = 0.0223 DBP = 82 Quantile = -0.022 DBP = 82 Quantile = -0.067 DBP = 82 Quantile = -0.112 DBP = 82 Quantile = -0.157 DBP = 82 Quantile = -0.202 DBP = 80 Quantile = -0.248 DBP = 80 Quantile = -0.294 DBP = 80 Quantile = -0.341 DBP = 80 Quantile = -0.388 DBP = 80 Quantile = -0.437 DBP = 80 Quantile = -0.486 DBP = 80 Quantile = -0.537 DBP = 78 Quantile = -0.589 DBP = 78 Quantile = -0.643 DBP = 78 Quantile = -0.699 DBP = 78 Quantile = -0.757 DBP = 78 Quantile = -0.818 DBP = 78 Quantile = -0.882 DBP = 78 Quantile = -0.95 DBP = 76 Quantile = -1.022 DBP = 76 Quantile = -1.101 DBP = 74 Quantile = -1.186 DBP = 74 Quantile = -1.282 DBP = 74 Quantile = -1.39 DBP = 72 Quantile = -1.518 DBP = 72 Quantile = -1.678 DBP = 70 Quantile = -1.897 DBP = 70 Quantile = -2.287 DBP = 68
Q-Q plot for DBP
  • Using data from Blood_Pressure.xlsx, we examine the distribution of the two variables: SBP (Systolic Blood Pressure) and DBP (Diastolic Blood Pressure) with histogram and Q-Q plots. Tests of normality were requested, including and the [SAS-modified version of] Kolmogorov-Smirnov D test. SBP (Systolic Blood Pressure) has a Kolmogorov-Smirnov D p-value of 0.111, exceeding our arbitrary significance level of 0.05 which means we cannot reject the null hypothesis, and cannot conclude that the data did not come from a normal distribution. DBP (Diastolic Blood Pressure) has a Kolmogorov-Smirnov D p-value of 0.041, which is less than the predetermined critical value of 0.05, so we reject the null hypothesis and conclude that the data did not come from a normal distribution.

Chapter 6: One-Sample Tests

Performing a One-Sample t Test.

SAS Code, click to expand

SAS Code:

#  (&path1 and biostats libname previously defined)
/*** Chapter 6: One-Sample Tests ***/

/* Performing a One-Sample t Test - generated code - start */

ods noproctitle;
ods graphics / imagemap=on;

/* You have 56 new measurements of perch and want to test if their mean weight is different from the historical mean value of 500. */

/* Test for normality */
title1 "Performing Tests for normality on Perch data";
proc univariate data=work.perch normal mu0=500;
    ods select TestsForNormality;
    var Weight;
run;

/* All of these tests reject the null hypothesis (at the α = .05 level).  One of the assumptions for one- or two-sample t tests is that the data values come from a population of values that are normally distributed.  At this point, you may be tempted to abandon the t test and choose a nonparametric alternative such as a sign test or a Wilcoxon rank sum test. The decision whether to use a parametric test should not be determined solely by these tests of normality. Before you decide to abandon the one-sample t test, you should take a look at the distribution of weights.  The one-sample t test task produces both a histogram and a Q-Q plot to help you understand how your data values are distributed. */

/* t test */
title1 "Performing a One-Sample t Test on Perch data";
proc ttest data=work.perch sides=2 h0=500 plots(showh0);
    var Weight;
run;

/* The 56 perch had a mean weight of 382.2 and a standard deviation of 347.6.  The 95% confidence limits are (293.1, 427.3), which does not include the historical mean of 500.  We see a t value of -2.54 and a p-value of .0141, which lets us reject the null hypothesis and state that that perch weights are lower than the historical value of 500 at a significance level α = .05.  */

/* "Output from the one-sample t test, shows a histogram with a normal distribution and a kernel distribution superimposed.  Although this is a skewed distribution, you may decide that with a sample size of 56, you can rely on the t test to decide if you should accept the alternative hypothesis (reject the null hypothesis).  You probably want to check the nonparametric test results." */

/* Performing a One-Sample t Test - generated code - end */

SAS Output

Results: biostats_by_ex_SAScode.sas

Results: biostats_by_ex_SAScode.sas

Performing Tests for normality on Perch data

Variable: Weight (Weight)

The Univariate Procedure

Weight

Tests For Normality

Tests for Normality
Test Statistic p Value
Shapiro-Wilk W 0.816849 Pr < W <0.0001
Kolmogorov-Smirnov D 0.239184 Pr > D <0.0100
Cramer-von Mises W-Sq 0.810687 Pr > W-Sq <0.0050
Anderson-Darling A-Sq 4.362138 Pr > A-Sq <0.0050

The Ttest Procedure

Weight

Performing a One-Sample t Test on Perch data

Variable: Weight (Weight)

 

 

Statistics

N Mean Std Dev Std Err Minimum Maximum
56 382.2 347.6 46.4524 5.9000 1100.0

Confidence Limits

Mean 95% CL Mean Std Dev 95% CL Std Dev
382.2 289.1 475.3 347.6 293.1 427.3

T-Tests

DF t Value Pr > |t|
55 -2.54 0.0141

Summary Panel

Weight = 1612.859375 Percent = 0.0904 Weight = 1604.3117187 Percent = 0.1015 Weight = 1604.3117187 Percent = 0.1015 Weight = 1595.7640625 Percent = 0.1137 Weight = 1595.7640625 Percent = 0.1137 Weight = 1587.2164062 Percent = 0.1273 Weight = 1587.2164062 Percent = 0.1273 Weight = 1578.66875 Percent = 0.1422 Weight = 1578.66875 Percent = 0.1422 Weight = 1570.1210937 Percent = 0.1587 Weight = 1570.1210937 Percent = 0.1587 Weight = 1561.5734375 Percent = 0.1767 Weight = 1561.5734375 Percent = 0.1767 Weight = 1553.0257812 Percent = 0.1965 Weight = 1553.0257812 Percent = 0.1965 Weight = 1544.478125 Percent = 0.2182 Weight = 1544.478125 Percent = 0.2182 Weight = 1535.9304687 Percent = 0.2418 Weight = 1535.9304687 Percent = 0.2418 Weight = 1527.3828125 Percent = 0.2676 Weight = 1527.3828125 Percent = 0.2676 Weight = 1518.8351562 Percent = 0.2957 Weight = 1518.8351562 Percent = 0.2957 Weight = 1510.2875 Percent = 0.3262 Weight = 1510.2875 Percent = 0.3262 Weight = 1501.7398437 Percent = 0.3593 Weight = 1501.7398437 Percent = 0.3593 Weight = 1493.1921875 Percent = 0.3952 Weight = 1493.1921875 Percent = 0.3952 Weight = 1484.6445312 Percent = 0.4339 Weight = 1484.6445312 Percent = 0.4339 Weight = 1476.096875 Percent = 0.4757 Weight = 1476.096875 Percent = 0.4757 Weight = 1467.5492187 Percent = 0.5207 Weight = 1467.5492187 Percent = 0.5207 Weight = 1459.0015625 Percent = 0.569 Weight = 1459.0015625 Percent = 0.569 Weight = 1450.4539062 Percent = 0.6209 Weight = 1450.4539062 Percent = 0.6209 Weight = 1441.90625 Percent = 0.6765 Weight = 1441.90625 Percent = 0.6765 Weight = 1433.3585937 Percent = 0.736 Weight = 1433.3585937 Percent = 0.736 Weight = 1424.8109375 Percent = 0.7994 Weight = 1424.8109375 Percent = 0.7994 Weight = 1416.2632812 Percent = 0.867 Weight = 1416.2632812 Percent = 0.867 Weight = 1407.715625 Percent = 0.9389 Weight = 1407.715625 Percent = 0.9389 Weight = 1399.1679687 Percent = 1.0152 Weight = 1399.1679687 Percent = 1.0152 Weight = 1390.6203125 Percent = 1.0961 Weight = 1390.6203125 Percent = 1.0961 Weight = 1382.0726562 Percent = 1.1816 Weight = 1382.0726562 Percent = 1.1816 Weight = 1373.525 Percent = 1.2719 Weight = 1373.525 Percent = 1.2719 Weight = 1364.9773437 Percent = 1.3671 Weight = 1364.9773437 Percent = 1.3671 Weight = 1356.4296875 Percent = 1.4673 Weight = 1356.4296875 Percent = 1.4673 Weight = 1347.8820312 Percent = 1.5724 Weight = 1347.8820312 Percent = 1.5724 Weight = 1339.334375 Percent = 1.6827 Weight = 1339.334375 Percent = 1.6827 Weight = 1330.7867187 Percent = 1.7981 Weight = 1330.7867187 Percent = 1.7981 Weight = 1322.2390625 Percent = 1.9186 Weight = 1322.2390625 Percent = 1.9186 Weight = 1313.6914062 Percent = 2.0442 Weight = 1313.6914062 Percent = 2.0442 Weight = 1305.14375 Percent = 2.175 Weight = 1305.14375 Percent = 2.175 Weight = 1296.5960937 Percent = 2.3108 Weight = 1296.5960937 Percent = 2.3108 Weight = 1288.0484375 Percent = 2.4517 Weight = 1288.0484375 Percent = 2.4517 Weight = 1279.5007812 Percent = 2.5975 Weight = 1279.5007812 Percent = 2.5975 Weight = 1270.953125 Percent = 2.7482 Weight = 1270.953125 Percent = 2.7482 Weight = 1253.8578125 Percent = 3.0634 Weight = 1253.8578125 Percent = 3.0634 Weight = 1236.7625 Percent = 3.3963 Weight = 1236.7625 Percent = 3.3963 Weight = 1219.6671875 Percent = 3.7451 Weight = 1219.6671875 Percent = 3.7451 Weight = 1100 Percent = 6.4329 Weight = 1100 Percent = 6.4329 Weight = 1074.3570312 Percent = 7.005 Weight = 1074.3570312 Percent = 7.005 Weight = 1057.2617187 Percent = 7.3729 Weight = 1057.2617187 Percent = 7.3729 Weight = 1040.1664062 Percent = 7.7262 Weight = 1040.1664062 Percent = 7.7262 Weight = 1023.0710937 Percent = 8.062 Weight = 1023.0710937 Percent = 8.062 Weight = 1014.5234375 Percent = 8.2224 Weight = 1014.5234375 Percent = 8.2224 Weight = 1005.9757812 Percent = 8.3775 Weight = 1005.9757812 Percent = 8.3775 Weight = 997.428125 Percent = 8.527 Weight = 997.428125 Percent = 8.527 Weight = 988.88046875 Percent = 8.6704 Weight = 988.88046875 Percent = 8.6704 Weight = 980.3328125 Percent = 8.8077 Weight = 980.3328125 Percent = 8.8077 Weight = 971.78515625 Percent = 8.9385 Weight = 971.78515625 Percent = 8.9385 Weight = 963.2375 Percent = 9.0626 Weight = 963.2375 Percent = 9.0626 Weight = 954.68984375 Percent = 9.1799 Weight = 954.68984375 Percent = 9.1799 Weight = 946.1421875 Percent = 9.2902 Weight = 946.1421875 Percent = 9.2902 Weight = 937.59453125 Percent = 9.3933 Weight = 937.59453125 Percent = 9.3933 Weight = 929.046875 Percent = 9.4892 Weight = 929.046875 Percent = 9.4892 Weight = 920.49921875 Percent = 9.5777 Weight = 920.49921875 Percent = 9.5777 Weight = 911.9515625 Percent = 9.6588 Weight = 911.9515625 Percent = 9.6588 Weight = 903.40390625 Percent = 9.7325 Weight = 903.40390625 Percent = 9.7325 Weight = 894.85625 Percent = 9.7988 Weight = 894.85625 Percent = 9.7988 Weight = 886.30859375 Percent = 9.8577 Weight = 886.30859375 Percent = 9.8577 Weight = 877.7609375 Percent = 9.9093 Weight = 877.7609375 Percent = 9.9093 Weight = 869.21328125 Percent = 9.9536 Weight = 869.21328125 Percent = 9.9536 Weight = 860.665625 Percent = 9.9908 Weight = 860.665625 Percent = 9.9908 Weight = 852.11796875 Percent = 10.021 Weight = 852.11796875 Percent = 10.021 Weight = 843.5703125 Percent = 10.045 Weight = 843.5703125 Percent = 10.045 Weight = 835.02265625 Percent = 10.062 Weight = 835.02265625 Percent = 10.062 Weight = 826.475 Percent = 10.072 Weight = 826.475 Percent = 10.072 Weight = 817.92734375 Percent = 10.077 Weight = 817.92734375 Percent = 10.077 Weight = 809.3796875 Percent = 10.076 Weight = 809.3796875 Percent = 10.076 Weight = 800.83203125 Percent = 10.07 Weight = 800.83203125 Percent = 10.07 Weight = 792.284375 Percent = 10.059 Weight = 792.284375 Percent = 10.059 Weight = 783.73671875 Percent = 10.043 Weight = 783.73671875 Percent = 10.043 Weight = 775.1890625 Percent = 10.023 Weight = 775.1890625 Percent = 10.023 Weight = 766.64140625 Percent = 10 Weight = 766.64140625 Percent = 10 Weight = 758.09375 Percent = 9.9738 Weight = 758.09375 Percent = 9.9738 Weight = 749.54609375 Percent = 9.945 Weight = 749.54609375 Percent = 9.945 Weight = 740.9984375 Percent = 9.9144 Weight = 740.9984375 Percent = 9.9144 Weight = 723.903125 Percent = 9.85 Weight = 723.903125 Percent = 9.85 Weight = 706.8078125 Percent = 9.786 Weight = 706.8078125 Percent = 9.786 Weight = 698.26015625 Percent = 9.7559 Weight = 698.26015625 Percent = 9.7559 Weight = 689.7125 Percent = 9.7282 Weight = 689.7125 Percent = 9.7282 Weight = 681.16484375 Percent = 9.7035 Weight = 681.16484375 Percent = 9.7035 Weight = 672.6171875 Percent = 9.6827 Weight = 672.6171875 Percent = 9.6827 Weight = 664.06953125 Percent = 9.6667 Weight = 664.06953125 Percent = 9.6667 Weight = 655.521875 Percent = 9.6563 Weight = 655.521875 Percent = 9.6563 Weight = 646.97421875 Percent = 9.6522 Weight = 646.97421875 Percent = 9.6522 Weight = 638.4265625 Percent = 9.6554 Weight = 638.4265625 Percent = 9.6554 Weight = 629.87890625 Percent = 9.6668 Weight = 629.87890625 Percent = 9.6668 Weight = 621.33125 Percent = 9.6872 Weight = 621.33125 Percent = 9.6872 Weight = 612.78359375 Percent = 9.7174 Weight = 612.78359375 Percent = 9.7174 Weight = 604.2359375 Percent = 9.7583 Weight = 604.2359375 Percent = 9.7583 Weight = 595.68828125 Percent = 9.8107 Weight = 595.68828125 Percent = 9.8107 Weight = 587.140625 Percent = 9.8754 Weight = 587.140625 Percent = 9.8754 Weight = 578.59296875 Percent = 9.9532 Weight = 578.59296875 Percent = 9.9532 Weight = 570.0453125 Percent = 10.045 Weight = 570.0453125 Percent = 10.045 Weight = 561.49765625 Percent = 10.151 Weight = 561.49765625 Percent = 10.151 Weight = 552.95 Percent = 10.272 Weight = 552.95 Percent = 10.272 Weight = 544.40234375 Percent = 10.409 Weight = 544.40234375 Percent = 10.409 Weight = 535.8546875 Percent = 10.562 Weight = 535.8546875 Percent = 10.562 Weight = 527.30703125 Percent = 10.732 Weight = 527.30703125 Percent = 10.732 Weight = 518.759375 Percent = 10.919 Weight = 518.759375 Percent = 10.919 Weight = 510.21171875 Percent = 11.123 Weight = 510.21171875 Percent = 11.123 Weight = 501.6640625 Percent = 11.345 Weight = 501.6640625 Percent = 11.345 Weight = 493.11640625 Percent = 11.585 Weight = 493.11640625 Percent = 11.585 Weight = 484.56875 Percent = 11.842 Weight = 484.56875 Percent = 11.842 Weight = 476.02109375 Percent = 12.117 Weight = 476.02109375 Percent = 12.117 Weight = 467.4734375 Percent = 12.41 Weight = 467.4734375 Percent = 12.41 Weight = 458.92578125 Percent = 12.719 Weight = 458.92578125 Percent = 12.719 Weight = 450.378125 Percent = 13.046 Weight = 450.378125 Percent = 13.046 Weight = 441.83046875 Percent = 13.388 Weight = 441.83046875 Percent = 13.388 Weight = 433.2828125 Percent = 13.746 Weight = 433.2828125 Percent = 13.746 Weight = 424.73515625 Percent = 14.119 Weight = 424.73515625 Percent = 14.119 Weight = 416.1875 Percent = 14.506 Weight = 416.1875 Percent = 14.506 Weight = 407.63984375 Percent = 14.906 Weight = 407.63984375 Percent = 14.906 Weight = 390.54453125 Percent = 15.74 Weight = 390.54453125 Percent = 15.74 Weight = 330.7109375 Percent = 18.861 Weight = 330.7109375 Percent = 18.861 Weight = 305.06796875 Percent = 20.191 Weight = 305.06796875 Percent = 20.191 Weight = 287.97265625 Percent = 21.036 Weight = 287.97265625 Percent = 21.036 Weight = 279.425 Percent = 21.44 Weight = 279.425 Percent = 21.44 Weight = 270.87734375 Percent = 21.828 Weight = 270.87734375 Percent = 21.828 Weight = 262.3296875 Percent = 22.2 Weight = 262.3296875 Percent = 22.2 Weight = 253.78203125 Percent = 22.552 Weight = 253.78203125 Percent = 22.552 Weight = 245.234375 Percent = 22.882 Weight = 245.234375 Percent = 22.882 Weight = 236.68671875 Percent = 23.19 Weight = 236.68671875 Percent = 23.19 Weight = 228.1390625 Percent = 23.473 Weight = 228.1390625 Percent = 23.473 Weight = 219.59140625 Percent = 23.73 Weight = 219.59140625 Percent = 23.73 Weight = 211.04375 Percent = 23.959 Weight = 211.04375 Percent = 23.959 Weight = 202.49609375 Percent = 24.158 Weight = 202.49609375 Percent = 24.158 Weight = 193.9484375 Percent = 24.327 Weight = 193.9484375 Percent = 24.327 Weight = 185.40078125 Percent = 24.463 Weight = 185.40078125 Percent = 24.463 Weight = 176.853125 Percent = 24.567 Weight = 176.853125 Percent = 24.567 Weight = 168.30546875 Percent = 24.638 Weight = 168.30546875 Percent = 24.638 Weight = 159.7578125 Percent = 24.673 Weight = 159.7578125 Percent = 24.673 Weight = 151.21015625 Percent = 24.674 Weight = 151.21015625 Percent = 24.674 Weight = 142.6625 Percent = 24.64 Weight = 142.6625 Percent = 24.64 Weight = 134.11484375 Percent = 24.57 Weight = 134.11484375 Percent = 24.57 Weight = 125.5671875 Percent = 24.465 Weight = 125.5671875 Percent = 24.465 Weight = 117.01953125 Percent = 24.325 Weight = 117.01953125 Percent = 24.325 Weight = 108.471875 Percent = 24.15 Weight = 108.471875 Percent = 24.15 Weight = 99.92421875 Percent = 23.94 Weight = 99.92421875 Percent = 23.94 Weight = 91.3765625 Percent = 23.697 Weight = 91.3765625 Percent = 23.697 Weight = 82.82890625 Percent = 23.421 Weight = 82.82890625 Percent = 23.421 Weight = 74.28125 Percent = 23.114 Weight = 74.28125 Percent = 23.114 Weight = 65.73359375 Percent = 22.776 Weight = 65.73359375 Percent = 22.776 Weight = 57.1859375 Percent = 22.409 Weight = 57.1859375 Percent = 22.409 Weight = 48.63828125 Percent = 22.014 Weight = 48.63828125 Percent = 22.014 Weight = 40.090625 Percent = 21.593 Weight = 40.090625 Percent = 21.593 Weight = 31.54296875 Percent = 21.148 Weight = 31.54296875 Percent = 21.148 Weight = 22.9953125 Percent = 20.679 Weight = 22.9953125 Percent = 20.679 Weight = 14.44765625 Percent = 20.19 Weight = 14.44765625 Percent = 20.19 Weight = 5.9 Percent = 19.682 Weight = 5.9 Percent = 19.682 Weight = -11.1953125 Percent = 18.616 Weight = -11.1953125 Percent = 18.616 Weight = -88.12421875 Percent = 13.403 Weight = -88.12421875 Percent = 13.403 Weight = -113.7671875 Percent = 11.673 Weight = -113.7671875 Percent = 11.673 Weight = -130.8625 Percent = 10.561 Weight = -130.8625 Percent = 10.561 Weight = -147.9578125 Percent = 9.4941 Weight = -147.9578125 Percent = 9.4941 Weight = -165.053125 Percent = 8.4798 Weight = -165.053125 Percent = 8.4798 Weight = -173.6007813 Percent = 7.9946 Weight = -173.6007813 Percent = 7.9946 Weight = -182.1484375 Percent = 7.525 Weight = -182.1484375 Percent = 7.525 Weight = -190.6960938 Percent = 7.0715 Weight = -190.6960938 Percent = 7.0715 Weight = -199.24375 Percent = 6.6346 Weight = -199.24375 Percent = 6.6346 Weight = -207.7914063 Percent = 6.2146 Weight = -207.7914063 Percent = 6.2146 Weight = -216.3390625 Percent = 5.8117 Weight = -216.3390625 Percent = 5.8117 Weight = -224.8867188 Percent = 5.4261 Weight = -224.8867188 Percent = 5.4261 Weight = -233.434375 Percent = 5.0578 Weight = -233.434375 Percent = 5.0578 Weight = -241.9820313 Percent = 4.7069 Weight = -241.9820313 Percent = 4.7069 Weight = -250.5296875 Percent = 4.3732 Weight = -250.5296875 Percent = 4.3732 Weight = -259.0773438 Percent = 4.0564 Weight = -259.0773438 Percent = 4.0564 Weight = -267.625 Percent = 3.7565 Weight = -267.625 Percent = 3.7565 Weight = -276.1726563 Percent = 3.4731 Weight = -276.1726563 Percent = 3.4731 Weight = -284.7203125 Percent = 3.2058 Weight = -284.7203125 Percent = 3.2058 Weight = -293.2679688 Percent = 2.9542 Weight = -293.2679688 Percent = 2.9542 Weight = -301.815625 Percent = 2.7179 Weight = -301.815625 Percent = 2.7179 Weight = -310.3632813 Percent = 2.4964 Weight = -310.3632813 Percent = 2.4964 Weight = -318.9109375 Percent = 2.2892 Weight = -318.9109375 Percent = 2.2892 Weight = -327.4585938 Percent = 2.0957 Weight = -327.4585938 Percent = 2.0957 Weight = -336.00625 Percent = 1.9155 Weight = -336.00625 Percent = 1.9155 Weight = -344.5539063 Percent = 1.7478 Weight = -344.5539063 Percent = 1.7478 Weight = -353.1015625 Percent = 1.5922 Weight = -353.1015625 Percent = 1.5922 Weight = -361.6492188 Percent = 1.4481 Weight = -361.6492188 Percent = 1.4481 Weight = -370.196875 Percent = 1.3148 Weight = -370.196875 Percent = 1.3148 Weight = -378.7445313 Percent = 1.1918 Weight = -378.7445313 Percent = 1.1918 Weight = -387.2921875 Percent = 1.0786 Weight = -387.2921875 Percent = 1.0786 Weight = -395.8398438 Percent = 0.9745 Weight = -395.8398438 Percent = 0.9745 Weight = -404.3875 Percent = 0.879 Weight = -404.3875 Percent = 0.879 Weight = -412.9351563 Percent = 0.7915 Weight = -412.9351563 Percent = 0.7915 Weight = -421.4828125 Percent = 0.7116 Weight = -421.4828125 Percent = 0.7116 Weight = -430.0304688 Percent = 0.6386 Weight = -430.0304688 Percent = 0.6386 Weight = -438.578125 Percent = 0.5722 Weight = -438.578125 Percent = 0.5722 Weight = -447.1257813 Percent = 0.5119 Weight = -447.1257813 Percent = 0.5119 Weight = -455.6734375 Percent = 0.4572 Weight = -455.6734375 Percent = 0.4572 Weight = -464.2210938 Percent = 0.4076 Weight = -464.2210938 Percent = 0.4076 Weight = -472.76875 Percent = 0.3628 Weight = -472.76875 Percent = 0.3628 Weight = -481.3164063 Percent = 0.3224 Weight = -481.3164063 Percent = 0.3224 Weight = -489.8640625 Percent = 0.286 Weight = -489.8640625 Percent = 0.286 Weight = -498.4117188 Percent = 0.2533 Weight = -498.4117188 Percent = 0.2533 Weight = -506.959375 Percent = 0.224 Weight = 1425.0924374 Percent = 0.255 Weight = 1414.5585672 Percent = 0.2791 Weight = 1414.5585672 Percent = 0.2791 Weight = 1404.024697 Percent = 0.3053 Weight = 1404.024697 Percent = 0.3053 Weight = 1393.4908268 Percent = 0.3336 Weight = 1393.4908268 Percent = 0.3336 Weight = 1382.9569566 Percent = 0.3641 Weight = 1382.9569566 Percent = 0.3641 Weight = 1372.4230863 Percent = 0.3971 Weight = 1372.4230863 Percent = 0.3971 Weight = 1361.8892161 Percent = 0.4327 Weight = 1361.8892161 Percent = 0.4327 Weight = 1351.3553459 Percent = 0.4711 Weight = 1351.3553459 Percent = 0.4711 Weight = 1340.8214757 Percent = 0.5124 Weight = 1340.8214757 Percent = 0.5124 Weight = 1330.2876055 Percent = 0.5568 Weight = 1330.2876055 Percent = 0.5568 Weight = 1319.7537352 Percent = 0.6045 Weight = 1319.7537352 Percent = 0.6045 Weight = 1309.219865 Percent = 0.6557 Weight = 1309.219865 Percent = 0.6557 Weight = 1298.6859948 Percent = 0.7105 Weight = 1298.6859948 Percent = 0.7105 Weight = 1288.1521246 Percent = 0.7693 Weight = 1288.1521246 Percent = 0.7693 Weight = 1277.6182544 Percent = 0.8321 Weight = 1277.6182544 Percent = 0.8321 Weight = 1267.0843841 Percent = 0.8992 Weight = 1267.0843841 Percent = 0.8992 Weight = 1256.5505139 Percent = 0.9709 Weight = 1256.5505139 Percent = 0.9709 Weight = 1246.0166437 Percent = 1.0473 Weight = 1246.0166437 Percent = 1.0473 Weight = 1235.4827735 Percent = 1.1287 Weight = 1235.4827735 Percent = 1.1287 Weight = 1224.9489033 Percent = 1.2153 Weight = 1224.9489033 Percent = 1.2153 Weight = 1214.415033 Percent = 1.3073 Weight = 1214.415033 Percent = 1.3073 Weight = 1203.8811628 Percent = 1.405 Weight = 1203.8811628 Percent = 1.405 Weight = 1193.3472926 Percent = 1.5087 Weight = 1193.3472926 Percent = 1.5087 Weight = 1182.8134224 Percent = 1.6185 Weight = 1182.8134224 Percent = 1.6185 Weight = 1172.2795522 Percent = 1.7346 Weight = 1172.2795522 Percent = 1.7346 Weight = 1161.7456819 Percent = 1.8575 Weight = 1161.7456819 Percent = 1.8575 Weight = 1151.2118117 Percent = 1.9872 Weight = 1151.2118117 Percent = 1.9872 Weight = 1140.6779415 Percent = 2.124 Weight = 1140.6779415 Percent = 2.124 Weight = 1130.1440713 Percent = 2.2681 Weight = 1130.1440713 Percent = 2.2681 Weight = 1119.6102011 Percent = 2.4198 Weight = 1119.6102011 Percent = 2.4198 Weight = 1109.0763308 Percent = 2.5792 Weight = 1109.0763308 Percent = 2.5792 Weight = 1098.5424606 Percent = 2.7467 Weight = 1098.5424606 Percent = 2.7467 Weight = 1088.0085904 Percent = 2.9223 Weight = 1088.0085904 Percent = 2.9223 Weight = 1077.4747202 Percent = 3.1063 Weight = 1077.4747202 Percent = 3.1063 Weight = 1066.94085 Percent = 3.2989 Weight = 1066.94085 Percent = 3.2989 Weight = 1056.4069798 Percent = 3.5002 Weight = 1056.4069798 Percent = 3.5002 Weight = 1045.8731095 Percent = 3.7104 Weight = 1045.8731095 Percent = 3.7104 Weight = 1035.3392393 Percent = 3.9295 Weight = 1035.3392393 Percent = 3.9295 Weight = 1024.8053691 Percent = 4.1578 Weight = 1024.8053691 Percent = 4.1578 Weight = 1014.2714989 Percent = 4.3954 Weight = 1014.2714989 Percent = 4.3954 Weight = 1003.7376287 Percent = 4.6422 Weight = 1003.7376287 Percent = 4.6422 Weight = 993.20375844 Percent = 4.8984 Weight = 993.20375844 Percent = 4.8984 Weight = 982.66988822 Percent = 5.164 Weight = 982.66988822 Percent = 5.164 Weight = 972.136018 Percent = 5.439 Weight = 972.136018 Percent = 5.439 Weight = 961.60214778 Percent = 5.7234 Weight = 961.60214778 Percent = 5.7234 Weight = 951.06827756 Percent = 6.0171 Weight = 951.06827756 Percent = 6.0171 Weight = 930.00053712 Percent = 6.6322 Weight = 930.00053712 Percent = 6.6322 Weight = 908.93279668 Percent = 7.2834 Weight = 908.93279668 Percent = 7.2834 Weight = 887.86505624 Percent = 7.9693 Weight = 887.86505624 Percent = 7.9693 Weight = 866.7973158 Percent = 8.6877 Weight = 866.7973158 Percent = 8.6877 Weight = 845.72957536 Percent = 9.4362 Weight = 845.72957536 Percent = 9.4362 Weight = 687.72152207 Percent = 15.601 Weight = 687.72152207 Percent = 15.601 Weight = 656.11991142 Percent = 16.828 Weight = 656.11991142 Percent = 16.828 Weight = 635.05217098 Percent = 17.619 Weight = 635.05217098 Percent = 17.619 Weight = 613.98443054 Percent = 18.379 Weight = 613.98443054 Percent = 18.379 Weight = 592.9166901 Percent = 19.102 Weight = 592.9166901 Percent = 19.102 Weight = 582.38281988 Percent = 19.447 Weight = 582.38281988 Percent = 19.447 Weight = 571.84894966 Percent = 19.78 Weight = 571.84894966 Percent = 19.78 Weight = 561.31507944 Percent = 20.101 Weight = 561.31507944 Percent = 20.101 Weight = 550.78120922 Percent = 20.408 Weight = 550.78120922 Percent = 20.408 Weight = 540.247339 Percent = 20.7 Weight = 540.247339 Percent = 20.7 Weight = 529.71346878 Percent = 20.978 Weight = 529.71346878 Percent = 20.978 Weight = 519.17959857 Percent = 21.239 Weight = 519.17959857 Percent = 21.239 Weight = 508.64572835 Percent = 21.484 Weight = 508.64572835 Percent = 21.484 Weight = 498.11185813 Percent = 21.713 Weight = 498.11185813 Percent = 21.713 Weight = 487.57798791 Percent = 21.923 Weight = 487.57798791 Percent = 21.923 Weight = 477.04411769 Percent = 22.115 Weight = 477.04411769 Percent = 22.115 Weight = 466.51024747 Percent = 22.288 Weight = 466.51024747 Percent = 22.288 Weight = 455.97637725 Percent = 22.442 Weight = 455.97637725 Percent = 22.442 Weight = 445.44250703 Percent = 22.577 Weight = 445.44250703 Percent = 22.577 Weight = 434.90863681 Percent = 22.691 Weight = 434.90863681 Percent = 22.691 Weight = 424.37476659 Percent = 22.785 Weight = 424.37476659 Percent = 22.785 Weight = 413.84089637 Percent = 22.858 Weight = 413.84089637 Percent = 22.858 Weight = 403.30702615 Percent = 22.911 Weight = 403.30702615 Percent = 22.911 Weight = 392.77315593 Percent = 22.942 Weight = 392.77315593 Percent = 22.942 Weight = 382.23928571 Percent = 22.953 Weight = 382.23928571 Percent = 22.953 Weight = 371.70541549 Percent = 22.942 Weight = 371.70541549 Percent = 22.942 Weight = 361.17154528 Percent = 22.911 Weight = 361.17154528 Percent = 22.911 Weight = 350.63767506 Percent = 22.858 Weight = 350.63767506 Percent = 22.858 Weight = 340.10380484 Percent = 22.785 Weight = 340.10380484 Percent = 22.785 Weight = 329.56993462 Percent = 22.691 Weight = 329.56993462 Percent = 22.691 Weight = 319.0360644 Percent = 22.577 Weight = 319.0360644 Percent = 22.577 Weight = 308.50219418 Percent = 22.442 Weight = 308.50219418 Percent = 22.442 Weight = 297.96832396 Percent = 22.288 Weight = 297.96832396 Percent = 22.288 Weight = 287.43445374 Percent = 22.115 Weight = 287.43445374 Percent = 22.115 Weight = 276.90058352 Percent = 21.923 Weight = 276.90058352 Percent = 21.923 Weight = 266.3667133 Percent = 21.713 Weight = 266.3667133 Percent = 21.713 Weight = 255.83284308 Percent = 21.484 Weight = 255.83284308 Percent = 21.484 Weight = 245.29897286 Percent = 21.239 Weight = 245.29897286 Percent = 21.239 Weight = 234.76510264 Percent = 20.978 Weight = 234.76510264 Percent = 20.978 Weight = 224.23123242 Percent = 20.7 Weight = 224.23123242 Percent = 20.7 Weight = 213.69736221 Percent = 20.408 Weight = 213.69736221 Percent = 20.408 Weight = 203.16349199 Percent = 20.101 Weight = 203.16349199 Percent = 20.101 Weight = 192.62962177 Percent = 19.78 Weight = 192.62962177 Percent = 19.78 Weight = 182.09575155 Percent = 19.447 Weight = 182.09575155 Percent = 19.447 Weight = 171.56188133 Percent = 19.102 Weight = 171.56188133 Percent = 19.102 Weight = 150.49414089 Percent = 18.379 Weight = 150.49414089 Percent = 18.379 Weight = 129.42640045 Percent = 17.619 Weight = 129.42640045 Percent = 17.619 Weight = 3.0199578184 Percent = 12.659 Weight = 3.0199578184 Percent = 12.659 Weight = -39.11552306 Percent = 11.01 Weight = -39.11552306 Percent = 11.01 Weight = -70.71713372 Percent = 9.8208 Weight = -70.71713372 Percent = 9.8208 Weight = -91.78487416 Percent = 9.0584 Weight = -91.78487416 Percent = 9.0584 Weight = -112.8526146 Percent = 8.3246 Weight = -112.8526146 Percent = 8.3246 Weight = -133.920355 Percent = 7.6221 Weight = -133.920355 Percent = 7.6221 Weight = -154.9880955 Percent = 6.9534 Weight = -154.9880955 Percent = 6.9534 Weight = -176.0558359 Percent = 6.3201 Weight = -176.0558359 Percent = 6.3201 Weight = -186.5897061 Percent = 6.0171 Weight = -186.5897061 Percent = 6.0171 Weight = -197.1235763 Percent = 5.7234 Weight = -197.1235763 Percent = 5.7234 Weight = -207.6574466 Percent = 5.439 Weight = -207.6574466 Percent = 5.439 Weight = -218.1913168 Percent = 5.164 Weight = -218.1913168 Percent = 5.164 Weight = -228.725187 Percent = 4.8984 Weight = -228.725187 Percent = 4.8984 Weight = -239.2590572 Percent = 4.6422 Weight = -239.2590572 Percent = 4.6422 Weight = -249.7929274 Percent = 4.3954 Weight = -249.7929274 Percent = 4.3954 Weight = -260.3267977 Percent = 4.1578 Weight = -260.3267977 Percent = 4.1578 Weight = -270.8606679 Percent = 3.9295 Weight = -270.8606679 Percent = 3.9295 Weight = -281.3945381 Percent = 3.7104 Weight = -281.3945381 Percent = 3.7104 Weight = -291.9284083 Percent = 3.5002 Weight = -291.9284083 Percent = 3.5002 Weight = -302.4622785 Percent = 3.2989 Weight = -302.4622785 Percent = 3.2989 Weight = -312.9961488 Percent = 3.1063 Weight = -312.9961488 Percent = 3.1063 Weight = -323.530019 Percent = 2.9223 Weight = -323.530019 Percent = 2.9223 Weight = -334.0638892 Percent = 2.7467 Weight = -334.0638892 Percent = 2.7467 Weight = -344.5977594 Percent = 2.5792 Weight = -344.5977594 Percent = 2.5792 Weight = -355.1316296 Percent = 2.4198 Weight = -355.1316296 Percent = 2.4198 Weight = -365.6654999 Percent = 2.2681 Weight = -365.6654999 Percent = 2.2681 Weight = -376.1993701 Percent = 2.124 Weight = -376.1993701 Percent = 2.124 Weight = -386.7332403 Percent = 1.9872 Weight = -386.7332403 Percent = 1.9872 Weight = -397.2671105 Percent = 1.8575 Weight = -397.2671105 Percent = 1.8575 Weight = -407.8009807 Percent = 1.7346 Weight = -407.8009807 Percent = 1.7346 Weight = -418.334851 Percent = 1.6185 Weight = -418.334851 Percent = 1.6185 Weight = -428.8687212 Percent = 1.5087 Weight = -428.8687212 Percent = 1.5087 Weight = -439.4025914 Percent = 1.405 Weight = -439.4025914 Percent = 1.405 Weight = -449.9364616 Percent = 1.3073 Weight = -449.9364616 Percent = 1.3073 Weight = -460.4703318 Percent = 1.2153 Weight = -460.4703318 Percent = 1.2153 Weight = -471.0042021 Percent = 1.1287 Weight = -471.0042021 Percent = 1.1287 Weight = -481.5380723 Percent = 1.0473 Weight = -481.5380723 Percent = 1.0473 Weight = -492.0719425 Percent = 0.9709 Weight = -492.0719425 Percent = 0.9709 Weight = -502.6058127 Percent = 0.8992 Weight = -502.6058127 Percent = 0.8992 Weight = -513.1396829 Percent = 0.8321 Weight = -513.1396829 Percent = 0.8321 Weight = -523.6735531 Percent = 0.7693 Weight = -523.6735531 Percent = 0.7693 Weight = -534.2074234 Percent = 0.7105 Weight = -534.2074234 Percent = 0.7105 Weight = -544.7412936 Percent = 0.6557 Weight = -544.7412936 Percent = 0.6557 Weight = -555.2751638 Percent = 0.6045 Weight = -555.2751638 Percent = 0.6045 Weight = -565.809034 Percent = 0.5568 Weight = -565.809034 Percent = 0.5568 Weight = -576.3429042 Percent = 0.5124 Weight = -576.3429042 Percent = 0.5124 Weight = -586.8767745 Percent = 0.4711 Weight = -586.8767745 Percent = 0.4711 Weight = -597.4106447 Percent = 0.4327 Weight = -597.4106447 Percent = 0.4327 Weight = -607.9445149 Percent = 0.3971 Weight = -607.9445149 Percent = 0.3971 Weight = -618.4783851 Percent = 0.3641 Weight = -618.4783851 Percent = 0.3641 Weight = -629.0122553 Percent = 0.3336 Weight = -629.0122553 Percent = 0.3336 Weight = -639.5461256 Percent = 0.3053 Weight = -639.5461256 Percent = 0.3053 Weight = -650.0799958 Percent = 0.2791 Weight = -650.0799958 Percent = 0.2791 Weight = -660.613866 Percent = 0.255 Weight = 1100 Percent = 10.714 Weight = 1100 Percent = 10.714 Weight = 900 Percent = 10.714 Weight = 900 Percent = 10.714 Weight = 700 Percent = 8.9286 Weight = 700 Percent = 8.9286 Weight = 500 Percent = 3.5714 Weight = 500 Percent = 3.5714 Weight = 300 Percent = 16.071 Weight = 300 Percent = 16.071 Weight = 100 Percent = 50 Weight = 100 Percent = 50 Data Minimum = 5.9 Minimum Whisker = 5.9 First Quartile = 120 Median = 207.5 Third Quartile = 695 Maximum Whisker = 1100 Data Maximum = 1100 Mean = 382.23928571 Standard Deviation = 347.61771724 Number of Observations = 56 Sum of Weight = . Data Minimum = 5.9 Minimum Whisker = 5.9 First Quartile = 120 Median = 207.5 Third Quartile = 695 Maximum Whisker = 1100 Data Maximum = 1100 Mean = 382.23928571 Standard Deviation = 347.61771724 Number of Observations = 56 Sum of Weight = . Data Minimum = 5.9 Minimum Whisker = 5.9 First Quartile = 120 Median = 207.5 Third Quartile = 695 Maximum Whisker = 1100 Data Maximum = 1100 Mean = 382.23928571 Standard Deviation = 347.61771724 Number of Observations = 56 Sum of Weight = . Data Minimum = 5.9 Minimum Whisker = 5.9 First Quartile = 120 Median = 207.5 Third Quartile = 695 Maximum Whisker = 1100 Data Maximum = 1100 Mean = 382.23928571 Standard Deviation = 347.61771724 Number of Observations = 56 Sum of Weight = . Data Minimum = 5.9 Minimum Whisker = 5.9 First Quartile = 120 Median = 207.5 Third Quartile = 695 Maximum Whisker = 1100 Data Maximum = 1100 Mean = 382.23928571 Standard Deviation = 347.61771724 Number of Observations = 56 Sum of Weight = . Data Minimum = 5.9 Minimum Whisker = 5.9 First Quartile = 120 Median = 207.5 Third Quartile = 695 Maximum Whisker = 1100 Data Maximum = 1100 Mean = 382.23928571 Standard Deviation = 347.61771724 Number of Observations = 56 Sum of Weight = . Data Minimum = 5.9 Minimum Whisker = 5.9 First Quartile = 120 Median = 207.5 Third Quartile = 695 Maximum Whisker = 1100 Data Maximum = 1100 Mean = 382.23928571 Standard Deviation = 347.61771724 Number of Observations = 56 Sum of Weight = . Data Minimum = 5.9 Minimum Whisker = 5.9 First Quartile = 120 Median = 207.5 Third Quartile = 695 Maximum Whisker = 1100 Data Maximum = 1100 Mean = 382.23928571 Standard Deviation = 347.61771724 Number of Observations = 56 Sum of Weight = . Null Value = 500 Lower Confidence Limit = 289.15 Upper Confidence Limit = 475.33 Lower Confidence Limit = 289.15 Upper Confidence Limit = 475.33 Lower Confidence Limit = 289.15 Upper Confidence Limit = 475.33 Lower Confidence Limit = 289.15 Upper Confidence Limit = 475.33 Lower Confidence Limit = 289.15 Upper Confidence Limit = 475.33 Lower Confidence Limit = 289.15 Upper Confidence Limit = 475.33 Lower Confidence Limit = 289.15 Upper Confidence Limit = 475.33 Lower Confidence Limit = 289.15 Upper Confidence Limit = 475.33 Lower Confidence Limit = 289.15 Upper Confidence Limit = 475.33 Lower Confidence Limit = 289.15 Upper Confidence Limit = 475.33 Lower Confidence Limit = 289.15 Upper Confidence Limit = 475.33 Lower Confidence Limit = 289.15 Upper Confidence Limit = 475.33 Lower Confidence Limit = 289.15 Upper Confidence Limit = 475.33 Lower Confidence Limit = 289.15 Upper Confidence Limit = 475.33 Lower Confidence Limit = 289.15 Upper Confidence Limit = 475.33 Lower Confidence Limit = 289.15 Upper Confidence Limit = 475.33 Lower Confidence Limit = 289.15 Upper Confidence Limit = 475.33 Lower Confidence Limit = 289.15 Upper Confidence Limit = 475.33 Lower Confidence Limit = 289.15 Upper Confidence Limit = 475.33 Lower Confidence Limit = 289.15 Upper Confidence Limit = 475.33 Lower Confidence Limit = 289.15 Upper Confidence Limit = 475.33 Lower Confidence Limit = 289.15 Upper Confidence Limit = 475.33 Lower Confidence Limit = 289.15 Upper Confidence Limit = 475.33 Lower Confidence Limit = 289.15 Upper Confidence Limit = 475.33 Lower Confidence Limit = 289.15 Upper Confidence Limit = 475.33 Lower Confidence Limit = 289.15 Upper Confidence Limit = 475.33 Lower Confidence Limit = 289.15 Upper Confidence Limit = 475.33
Summary Panel for Weight

Q-Q Plot

Quantile = 2.2865 Weight = 1100 Quantile = 1.8974 Weight = 1100 Quantile = 1.6781 Weight = 1015 Quantile = 1.5185 Weight = 1000 Quantile = 1.3903 Weight = 1000 Quantile = 1.2816 Weight = 1000 Quantile = 1.1862 Weight = 900 Quantile = 1.1005 Weight = 900 Quantile = 1.0222 Weight = 850 Quantile = 0.9498 Weight = 840 Quantile = 0.882 Weight = 820 Quantile = 0.818 Weight = 820 Quantile = 0.7573 Weight = 700 Quantile = 0.6992 Weight = 700 Quantile = 0.6433 Weight = 690 Quantile = 0.5895 Weight = 685 Quantile = 0.5372 Weight = 650 Quantile = 0.4864 Weight = 556 Quantile = 0.4368 Weight = 514 Quantile = 0.3883 Weight = 320 Quantile = 0.3407 Weight = 300 Quantile = 0.2938 Weight = 300 Quantile = 0.2476 Weight = 265 Quantile = 0.2019 Weight = 260 Quantile = 0.1566 Weight = 250 Quantile = 0.1116 Weight = 250 Quantile = 0.0669 Weight = 225 Quantile = 0.0223 Weight = 218 Quantile = -0.022 Weight = 197 Quantile = -0.067 Weight = 188 Quantile = -0.112 Weight = 180 Quantile = -0.157 Weight = 170 Quantile = -0.202 Weight = 150 Quantile = -0.248 Weight = 150 Quantile = -0.294 Weight = 145 Quantile = -0.341 Weight = 145 Quantile = -0.388 Weight = 135 Quantile = -0.437 Weight = 130 Quantile = -0.486 Weight = 130 Quantile = -0.537 Weight = 130 Quantile = -0.589 Weight = 125 Quantile = -0.643 Weight = 120 Quantile = -0.699 Weight = 120 Quantile = -0.757 Weight = 115 Quantile = -0.818 Weight = 110 Quantile = -0.882 Weight = 110 Quantile = -0.95 Weight = 100 Quantile = -1.022 Weight = 85 Quantile = -1.101 Weight = 85 Quantile = -1.186 Weight = 80 Quantile = -1.282 Weight = 78 Quantile = -1.39 Weight = 70 Quantile = -1.518 Weight = 51.5 Quantile = -1.678 Weight = 40 Quantile = -1.897 Weight = 32 Quantile = -2.287 Weight = 5.9 Slope = 347.62 Y = 382.24
Q-Q Plot for Weight
  • You have 56 new measurements of perch and want to test if their mean weight is different from the historical mean value of 500.
  • All 4 tests for normality reject the null hypothesis (at the α = .05 level). “One of the assumptions for one- or two-sample t tests is that the data values come from a population of values that are normally distributed. At this point, you may be tempted to abandon the t test and choose a nonparametric alternative such as a sign test or a Wilcoxon rank sum test. The decision whether to use a parametric test should not be determined solely by these tests of normality. Before you decide to abandon the one-sample t test, you should take a look at the distribution of weights. The one-sample t test task produces both a histogram and a Q-Q plot to help you understand how your data values are distributed.”
  • The 56 perch had a mean weight of 382.2 and a standard deviation of 347.6. The 95% confidence limits are (293.1, 427.3), which does not include the historical mean of 500. We see a t value of -2.54 and a p-value of .0141, which lets us reject the null hypothesis and state that that perch weights are lower than the historical value of 500 at a significance level α = .05.
  • “Output from the one-sample t test, shows a histogram with a normal distribution and a kernel distribution superimposed. Although this is a skewed distribution, you may decide that with a sample size of 56, you can rely on the t test to decide if you should accept the alternative hypothesis (reject the null hypothesis). You probably want to check the nonparametric test results.”

“Perform some nonparametric tests to confirm conclusion from the one-sample t test because distribution of weights is significantly different from a normal distribution.”

SAS Code, click to expand

SAS Code:

#  (&path1 and biostats libname previously defined)
/* Nonparametric One-sample Tests - generated code - start */

/* "Perform some nonparametric tests to confirm conclusion from the one-sample t test because distribution of weights is significantly different from a normal distribution." */

/* Nonparametric test */
title1 "Performing Nonparametric One-sample Tests on Perch data";
proc univariate data=work.perch mu0=500;
    ods select TestsForLocation;
    var Weight;
run;
title1;

/* "Both the sign test (https://en.wikipedia.org/wiki/Sign_test) and the Wilcoxon Signed Rank test (https://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test) show p-values less than .05, confirming conclusion from the prior one-sample t test." */

/* Nonparametric One-sample Tests - generated code - end */

SAS Output

Results: biostats_by_ex_SAScode.sas

Results: biostats_by_ex_SAScode.sas

Performing Nonparametric One-sample Tests on Perch data

Variable: Weight (Weight)

The Univariate Procedure

Weight

Tests For Location

Tests for Location: Mu0=500
Test Statistic p Value
Student's t t -2.53509 Pr > |t| 0.0141
Sign M -9 Pr >= |M| 0.0222
Signed Rank S -275 Pr >= |S| 0.0235

Chapter 7: Two-Sample Tests

Unpaired t Test (t Test for Independent Groups).

SAS Code, click to expand

SAS Code:

#  (&path1 and biostats libname previously defined)
/*** Chapter 7: Two-Sample Tests ***/

/* Unpaired t Test (t Test for Independent Groups) - generated code - start */

ods noproctitle;
ods graphics / imagemap=on;

/* Test for normality */
title1 "Performing Normality Tests on Heart / Weight Data by Sex";
proc univariate data=sashelp.heart normal mu0=0;
    ods select TestsForNormality;
    class Sex;
    var Weight;
run;

/* t test */
title1 "Performing Unpaired t Test on Heart / Weight Data by Sex";
proc ttest data=sashelp.heart sides=2 h0=0 plots(showh0);
    class Sex;
    var Weight;
run;

/* Nonparametric test */
title1 "Nonparametric Two-sample Tests on Heart / Weight Data by Sex";
proc npar1way data=sashelp.heart wilcoxon plots=wilcoxonplot;
    class Sex;
    var Weight;
run;
title1;

/* "The three tests for normality, for both values of Sex, show p-values less than .05, leading us to reject the null hypothesis that the distribution of weight for females and males is normally distributed.  Look at the histogram and Q-Q plots to determine if parametric tests are appropriate. */

/* "There are two different confidence limits listed and two t- and p-values in the table; one set of values is computed assuming that the two groups have equal variance; the other set of values is computed assuming unequal variance.  The most common strategy to choose Which set of values is to examine the F test, which tests the equality of variances for the groups.  (The null hypothesis is that the variances are equal; the alternative hypothesis is that they are not equal.)  If the p-value for this test is less than .05, you choose the t- and p- values under the assumption of unequal variances (labeled Satterthwaite); if the p-value is greater than .05 (in this case it is .0503), you use the values based on equal variances (labeled Pooled) which has t-value of -36.20 and p-value of <.0001.  Based on the test of homogeneity of variance p-value of .0503, we use the pooled values in the table.  We reject the null hypothesis that the populations from which you took the female and male weight samples have equal means, and conclude that the female mean was less than the male mean." */

/* (Nonparametric Two-sample Tests performed on same data for optional reference.) */

/* Unpaired t Test (t Test for Independent Groups) - generated code - end */

SAS Output

Results: biostats_by_ex_SAScode.sas

Results: biostats_by_ex_SAScode.sas

Performing Normality Tests on Heart / Weight Data by Sex

Variable: Weight

Sex = Female

The Univariate Procedure

Weight

Sex = Female

Tests For Normality

Tests for Normality
Test Statistic p Value
Kolmogorov-Smirnov D 0.077525 Pr > D <0.0100
Cramer-von Mises W-Sq 4.91407 Pr > W-Sq <0.0050
Anderson-Darling A-Sq 29.30832 Pr > A-Sq <0.0050

Performing Normality Tests on Heart / Weight Data by Sex

Variable: Weight

Sex = Male

Sex = Male

Tests For Normality

Tests for Normality
Test Statistic p Value
Kolmogorov-Smirnov D 0.033472 Pr > D <0.0100
Cramer-von Mises W-Sq 0.559512 Pr > W-Sq <0.0050
Anderson-Darling A-Sq 4.016874 Pr > A-Sq <0.0050

The Ttest Procedure

Weight

Performing Unpaired t Test on Heart / Weight Data by Sex

Variable: Weight

 

 

Statistics

Sex Method N Mean Std Dev Std Err Minimum Maximum
Female   2869 141.4 26.2880 0.4908 67.0000 300.0
Male   2334 167.5 25.2907 0.5235 99.0000 276.0
Diff (1-2) Pooled   -26.0775 25.8454 0.7204    
Diff (1-2) Satterthwaite   -26.0775   0.7176    

Confidence Limits

Sex Method Mean 95% CL Mean Std Dev 95% CL Std Dev
Female   141.4 140.4 142.4 26.2880 25.6251 26.9865
Male   167.5 166.4 168.5 25.2907 24.5855 26.0379
Diff (1-2) Pooled -26.0775 -27.4899 -24.6652 25.8454 25.3582 26.3519
Diff (1-2) Satterthwaite -26.0775 -27.4843 -24.6708      

T-Tests

Method Variances DF t Value Pr > |t|
Pooled Equal 5201 -36.20 <.0001
Satterthwaite Unequal 5057.9 -36.34 <.0001

Equality of Variances

Equality of Variances
Method Num DF Den DF F Value Pr > F
Folded F 2868 2333 1.08 0.0503

Summary Panel

Weight = 312.74 Percent = 0.0025 Weight = 310.92 Percent = 0.006 Weight = 310.92 Percent = 0.006 Weight = 309.1 Percent = 0.0126 Weight = 309.1 Percent = 0.0126 Weight = 307.28 Percent = 0.0234 Weight = 307.28 Percent = 0.0234 Weight = 305.46 Percent = 0.0382 Weight = 305.46 Percent = 0.0382 Weight = 303.64 Percent = 0.0549 Weight = 303.64 Percent = 0.0549 Weight = 301.82 Percent = 0.07 Weight = 301.82 Percent = 0.07 Weight = 300 Percent = 0.0799 Weight = 300 Percent = 0.0799 Weight = 298.18 Percent = 0.0826 Weight = 298.18 Percent = 0.0826 Weight = 296.36 Percent = 0.0784 Weight = 296.36 Percent = 0.0784 Weight = 294.54 Percent = 0.0694 Weight = 294.54 Percent = 0.0694 Weight = 292.72 Percent = 0.0585 Weight = 292.72 Percent = 0.0585 Weight = 290.9 Percent = 0.0481 Weight = 290.9 Percent = 0.0481 Weight = 289.08 Percent = 0.0404 Weight = 289.08 Percent = 0.0404 Weight = 287.26 Percent = 0.0369 Weight = 287.26 Percent = 0.0369 Weight = 285.44 Percent = 0.0385 Weight = 285.44 Percent = 0.0385 Weight = 283.62 Percent = 0.0444 Weight = 283.62 Percent = 0.0444 Weight = 281.8 Percent = 0.0532 Weight = 281.8 Percent = 0.0532 Weight = 279.98 Percent = 0.0634 Weight = 279.98 Percent = 0.0634 Weight = 278.16 Percent = 0.074 Weight = 278.16 Percent = 0.074 Weight = 276.34 Percent = 0.0842 Weight = 276.34 Percent = 0.0842 Weight = 274.52 Percent = 0.0927 Weight = 274.52 Percent = 0.0927 Weight = 272.7 Percent = 0.0978 Weight = 272.7 Percent = 0.0978 Weight = 270.88 Percent = 0.0979 Weight = 270.88 Percent = 0.0979 Weight = 269.05 Percent = 0.0925 Weight = 269.05 Percent = 0.0925 Weight = 267.23 Percent = 0.0831 Weight = 267.23 Percent = 0.0831 Weight = 265.41 Percent = 0.0723 Weight = 265.41 Percent = 0.0723 Weight = 263.59 Percent = 0.0621 Weight = 263.59 Percent = 0.0621 Weight = 261.77 Percent = 0.0536 Weight = 261.77 Percent = 0.0536 Weight = 259.95 Percent = 0.0468 Weight = 259.95 Percent = 0.0468 Weight = 258.13 Percent = 0.0418 Weight = 258.13 Percent = 0.0418 Weight = 256.31 Percent = 0.0393 Weight = 256.31 Percent = 0.0393 Weight = 254.49 Percent = 0.0401 Weight = 254.49 Percent = 0.0401 Weight = 252.67 Percent = 0.0446 Weight = 252.67 Percent = 0.0446 Weight = 250.85 Percent = 0.0531 Weight = 250.85 Percent = 0.0531 Weight = 249.03 Percent = 0.0664 Weight = 249.03 Percent = 0.0664 Weight = 247.21 Percent = 0.0862 Weight = 247.21 Percent = 0.0862 Weight = 245.39 Percent = 0.1142 Weight = 245.39 Percent = 0.1142 Weight = 243.57 Percent = 0.1509 Weight = 243.57 Percent = 0.1509 Weight = 241.75 Percent = 0.1947 Weight = 241.75 Percent = 0.1947 Weight = 236.29 Percent = 0.3408 Weight = 236.29 Percent = 0.3408 Weight = 234.47 Percent = 0.3866 Weight = 234.47 Percent = 0.3866 Weight = 232.65 Percent = 0.4267 Weight = 232.65 Percent = 0.4267 Weight = 230.83 Percent = 0.4582 Weight = 230.83 Percent = 0.4582 Weight = 229.01 Percent = 0.4803 Weight = 229.01 Percent = 0.4803 Weight = 227.19 Percent = 0.496 Weight = 227.19 Percent = 0.496 Weight = 225.37 Percent = 0.5127 Weight = 225.37 Percent = 0.5127 Weight = 223.55 Percent = 0.5391 Weight = 223.55 Percent = 0.5391 Weight = 221.73 Percent = 0.5816 Weight = 221.73 Percent = 0.5816 Weight = 219.91 Percent = 0.6424 Weight = 219.91 Percent = 0.6424 Weight = 218.09 Percent = 0.7194 Weight = 218.09 Percent = 0.7194 Weight = 212.63 Percent = 0.9951 Weight = 212.63 Percent = 0.9951 Weight = 210.8 Percent = 1.0786 Weight = 210.8 Percent = 1.0786 Weight = 208.98 Percent = 1.1516 Weight = 208.98 Percent = 1.1516 Weight = 207.16 Percent = 1.2209 Weight = 207.16 Percent = 1.2209 Weight = 205.34 Percent = 1.3001 Weight = 205.34 Percent = 1.3001 Weight = 203.52 Percent = 1.4025 Weight = 203.52 Percent = 1.4025 Weight = 201.7 Percent = 1.5344 Weight = 201.7 Percent = 1.5344 Weight = 199.88 Percent = 1.6931 Weight = 199.88 Percent = 1.6931 Weight = 198.06 Percent = 1.8721 Weight = 198.06 Percent = 1.8721 Weight = 196.24 Percent = 2.067 Weight = 196.24 Percent = 2.067 Weight = 194.42 Percent = 2.2786 Weight = 194.42 Percent = 2.2786 Weight = 192.6 Percent = 2.5134 Weight = 192.6 Percent = 2.5134 Weight = 190.78 Percent = 2.7813 Weight = 190.78 Percent = 2.7813 Weight = 188.96 Percent = 3.0931 Weight = 188.96 Percent = 3.0931 Weight = 187.14 Percent = 3.4558 Weight = 187.14 Percent = 3.4558 Weight = 185.32 Percent = 3.8667 Weight = 185.32 Percent = 3.8667 Weight = 181.68 Percent = 4.7566 Weight = 181.68 Percent = 4.7566 Weight = 179.86 Percent = 5.1837 Weight = 179.86 Percent = 5.1837 Weight = 178.04 Percent = 5.5768 Weight = 178.04 Percent = 5.5768 Weight = 176.22 Percent = 5.9361 Weight = 176.22 Percent = 5.9361 Weight = 174.4 Percent = 6.2696 Weight = 174.4 Percent = 6.2696 Weight = 170.76 Percent = 6.9037 Weight = 170.76 Percent = 6.9037 Weight = 168.94 Percent = 7.2439 Weight = 168.94 Percent = 7.2439 Weight = 167.12 Percent = 7.6467 Weight = 167.12 Percent = 7.6467 Weight = 165.3 Percent = 8.1581 Weight = 165.3 Percent = 8.1581 Weight = 163.48 Percent = 8.8164 Weight = 163.48 Percent = 8.8164 Weight = 161.66 Percent = 9.6349 Weight = 161.66 Percent = 9.6349 Weight = 159.84 Percent = 10.593 Weight = 159.84 Percent = 10.593 Weight = 156.2 Percent = 12.693 Weight = 156.2 Percent = 12.693 Weight = 154.38 Percent = 13.688 Weight = 154.38 Percent = 13.688 Weight = 152.55 Percent = 14.574 Weight = 152.55 Percent = 14.574 Weight = 150.73 Percent = 15.34 Weight = 150.73 Percent = 15.34 Weight = 147.09 Percent = 16.716 Weight = 147.09 Percent = 16.716 Weight = 145.27 Percent = 17.481 Weight = 145.27 Percent = 17.481 Weight = 143.45 Percent = 18.364 Weight = 143.45 Percent = 18.364 Weight = 141.63 Percent = 19.328 Weight = 141.63 Percent = 19.328 Weight = 139.81 Percent = 20.26 Weight = 139.81 Percent = 20.26 Weight = 137.99 Percent = 21.015 Weight = 137.99 Percent = 21.015 Weight = 136.17 Percent = 21.481 Weight = 136.17 Percent = 21.481 Weight = 134.35 Percent = 21.62 Weight = 134.35 Percent = 21.62 Weight = 132.53 Percent = 21.473 Weight = 132.53 Percent = 21.473 Weight = 130.71 Percent = 21.114 Weight = 130.71 Percent = 21.114 Weight = 128.89 Percent = 20.609 Weight = 128.89 Percent = 20.609 Weight = 127.07 Percent = 20 Weight = 127.07 Percent = 20 Weight = 125.25 Percent = 19.31 Weight = 125.25 Percent = 19.31 Weight = 123.43 Percent = 18.552 Weight = 123.43 Percent = 18.552 Weight = 121.61 Percent = 17.729 Weight = 121.61 Percent = 17.729 Weight = 119.79 Percent = 16.827 Weight = 119.79 Percent = 16.827 Weight = 117.97 Percent = 15.821 Weight = 117.97 Percent = 15.821 Weight = 116.15 Percent = 14.695 Weight = 116.15 Percent = 14.695 Weight = 110.69 Percent = 10.897 Weight = 110.69 Percent = 10.897 Weight = 108.87 Percent = 9.6592 Weight = 108.87 Percent = 9.6592 Weight = 107.05 Percent = 8.4765 Weight = 107.05 Percent = 8.4765 Weight = 105.23 Percent = 7.3421 Weight = 105.23 Percent = 7.3421 Weight = 103.41 Percent = 6.2519 Weight = 103.41 Percent = 6.2519 Weight = 101.59 Percent = 5.2166 Weight = 101.59 Percent = 5.2166 Weight = 99.766 Percent = 4.2602 Weight = 99.766 Percent = 4.2602 Weight = 97.945 Percent = 3.4086 Weight = 97.945 Percent = 3.4086 Weight = 96.125 Percent = 2.6796 Weight = 96.125 Percent = 2.6796 Weight = 94.305 Percent = 2.0782 Weight = 94.305 Percent = 2.0782 Weight = 92.484 Percent = 1.597 Weight = 92.484 Percent = 1.597 Weight = 90.664 Percent = 1.2199 Weight = 90.664 Percent = 1.2199 Weight = 88.844 Percent = 0.926 Weight = 88.844 Percent = 0.926 Weight = 87.023 Percent = 0.6956 Weight = 87.023 Percent = 0.6956 Weight = 85.203 Percent = 0.5132 Weight = 85.203 Percent = 0.5132 Weight = 83.383 Percent = 0.3691 Weight = 83.383 Percent = 0.3691 Weight = 81.563 Percent = 0.2586 Weight = 81.563 Percent = 0.2586 Weight = 79.742 Percent = 0.1795 Weight = 79.742 Percent = 0.1795 Weight = 77.922 Percent = 0.1295 Weight = 77.922 Percent = 0.1295 Weight = 76.102 Percent = 0.1041 Weight = 76.102 Percent = 0.1041 Weight = 74.281 Percent = 0.0961 Weight = 74.281 Percent = 0.0961 Weight = 72.461 Percent = 0.0963 Weight = 72.461 Percent = 0.0963 Weight = 70.641 Percent = 0.0964 Weight = 70.641 Percent = 0.0964 Weight = 68.82 Percent = 0.091 Weight = 68.82 Percent = 0.091 Weight = 67 Percent = 0.0788 Weight = 67 Percent = 0.0788 Weight = 65.18 Percent = 0.0619 Weight = 65.18 Percent = 0.0619 Weight = 63.359 Percent = 0.0437 Weight = 63.359 Percent = 0.0437 Weight = 61.539 Percent = 0.0277 Weight = 61.539 Percent = 0.0277 Weight = 59.719 Percent = 0.0157 Weight = 59.719 Percent = 0.0157 Weight = 57.898 Percent = 0.0079 Weight = 57.898 Percent = 0.0079 Weight = 56.078 Percent = 0.0036 Weight = 56.078 Percent = 0.0036 Weight = 54.258 Percent = 0.0014 Weight = 306 Percent = 5.6E-8 Weight = 304.77 Percent = 7.5E-8 Weight = 304.77 Percent = 7.5E-8 Weight = 303.54 Percent = 1.0E-7 Weight = 303.54 Percent = 1.0E-7 Weight = 302.31 Percent = 1.3E-7 Weight = 302.31 Percent = 1.3E-7 Weight = 301.08 Percent = 1.8E-7 Weight = 301.08 Percent = 1.8E-7 Weight = 299.85 Percent = 2.3E-7 Weight = 299.85 Percent = 2.3E-7 Weight = 298.62 Percent = 3.1E-7 Weight = 298.62 Percent = 3.1E-7 Weight = 297.39 Percent = 4.1E-7 Weight = 297.39 Percent = 4.1E-7 Weight = 296.16 Percent = 5.4E-7 Weight = 296.16 Percent = 5.4E-7 Weight = 294.93 Percent = 7.1E-7 Weight = 294.93 Percent = 7.1E-7 Weight = 293.7 Percent = 9.3E-7 Weight = 293.7 Percent = 9.3E-7 Weight = 292.47 Percent = 1.2E-6 Weight = 292.47 Percent = 1.2E-6 Weight = 291.24 Percent = 1.6E-6 Weight = 291.24 Percent = 1.6E-6 Weight = 290.01 Percent = 2.1E-6 Weight = 290.01 Percent = 2.1E-6 Weight = 288.78 Percent = 2.7E-6 Weight = 288.78 Percent = 2.7E-6 Weight = 287.55 Percent = 3.5E-6 Weight = 287.55 Percent = 3.5E-6 Weight = 286.33 Percent = 4.6E-6 Weight = 286.33 Percent = 4.6E-6 Weight = 285.1 Percent = 5.9E-6 Weight = 285.1 Percent = 5.9E-6 Weight = 283.87 Percent = 7.6E-6 Weight = 283.87 Percent = 7.6E-6 Weight = 282.64 Percent = 9.8E-6 Weight = 282.64 Percent = 9.8E-6 Weight = 281.41 Percent = 1.3E-5 Weight = 281.41 Percent = 1.3E-5 Weight = 280.18 Percent = 1.6E-5 Weight = 280.18 Percent = 1.6E-5 Weight = 278.95 Percent = 2.1E-5 Weight = 278.95 Percent = 2.1E-5 Weight = 277.72 Percent = 2.6E-5 Weight = 277.72 Percent = 2.6E-5 Weight = 276.49 Percent = 3.4E-5 Weight = 276.49 Percent = 3.4E-5 Weight = 275.26 Percent = 4.3E-5 Weight = 275.26 Percent = 4.3E-5 Weight = 274.03 Percent = 5.4E-5 Weight = 274.03 Percent = 5.4E-5 Weight = 272.8 Percent = 6.8E-5 Weight = 272.8 Percent = 6.8E-5 Weight = 271.57 Percent = 8.6E-5 Weight = 271.57 Percent = 8.6E-5 Weight = 270.34 Percent = .00011 Weight = 270.34 Percent = .00011 Weight = 269.11 Percent = .00014 Weight = 269.11 Percent = .00014 Weight = 267.88 Percent = .00017 Weight = 267.88 Percent = .00017 Weight = 266.65 Percent = .00021 Weight = 266.65 Percent = .00021 Weight = 265.42 Percent = .00027 Weight = 265.42 Percent = .00027 Weight = 264.19 Percent = .00033 Weight = 264.19 Percent = .00033 Weight = 262.96 Percent = .00041 Weight = 262.96 Percent = .00041 Weight = 261.73 Percent = .00051 Weight = 261.73 Percent = .00051 Weight = 260.5 Percent = .00063 Weight = 260.5 Percent = .00063 Weight = 259.27 Percent = .00078 Weight = 259.27 Percent = .00078 Weight = 258.04 Percent = .00096 Weight = 258.04 Percent = .00096 Weight = 256.81 Percent = 0.0012 Weight = 256.81 Percent = 0.0012 Weight = 255.58 Percent = 0.0015 Weight = 255.58 Percent = 0.0015 Weight = 254.35 Percent = 0.0018 Weight = 254.35 Percent = 0.0018 Weight = 253.12 Percent = 0.0022 Weight = 253.12 Percent = 0.0022 Weight = 251.89 Percent = 0.0026 Weight = 251.89 Percent = 0.0026 Weight = 250.66 Percent = 0.0032 Weight = 250.66 Percent = 0.0032 Weight = 249.43 Percent = 0.0039 Weight = 249.43 Percent = 0.0039 Weight = 248.21 Percent = 0.0047 Weight = 248.21 Percent = 0.0047 Weight = 246.98 Percent = 0.0057 Weight = 246.98 Percent = 0.0057 Weight = 245.75 Percent = 0.0069 Weight = 245.75 Percent = 0.0069 Weight = 244.52 Percent = 0.0083 Weight = 244.52 Percent = 0.0083 Weight = 243.29 Percent = 0.0099 Weight = 243.29 Percent = 0.0099 Weight = 242.06 Percent = 0.0119 Weight = 242.06 Percent = 0.0119 Weight = 240.83 Percent = 0.0142 Weight = 240.83 Percent = 0.0142 Weight = 239.6 Percent = 0.017 Weight = 239.6 Percent = 0.017 Weight = 238.37 Percent = 0.0202 Weight = 238.37 Percent = 0.0202 Weight = 237.14 Percent = 0.024 Weight = 237.14 Percent = 0.024 Weight = 235.91 Percent = 0.0284 Weight = 235.91 Percent = 0.0284 Weight = 234.68 Percent = 0.0335 Weight = 234.68 Percent = 0.0335 Weight = 233.45 Percent = 0.0396 Weight = 233.45 Percent = 0.0396 Weight = 232.22 Percent = 0.0465 Weight = 232.22 Percent = 0.0465 Weight = 230.99 Percent = 0.0547 Weight = 230.99 Percent = 0.0547 Weight = 229.76 Percent = 0.064 Weight = 229.76 Percent = 0.064 Weight = 228.53 Percent = 0.0749 Weight = 228.53 Percent = 0.0749 Weight = 227.3 Percent = 0.0873 Weight = 227.3 Percent = 0.0873 Weight = 226.07 Percent = 0.1016 Weight = 226.07 Percent = 0.1016 Weight = 224.84 Percent = 0.118 Weight = 224.84 Percent = 0.118 Weight = 223.61 Percent = 0.1368 Weight = 223.61 Percent = 0.1368 Weight = 222.38 Percent = 0.1581 Weight = 222.38 Percent = 0.1581 Weight = 221.15 Percent = 0.1825 Weight = 221.15 Percent = 0.1825 Weight = 219.92 Percent = 0.2101 Weight = 219.92 Percent = 0.2101 Weight = 218.69 Percent = 0.2413 Weight = 218.69 Percent = 0.2413 Weight = 217.46 Percent = 0.2766 Weight = 217.46 Percent = 0.2766 Weight = 216.23 Percent = 0.3163 Weight = 216.23 Percent = 0.3163 Weight = 215 Percent = 0.361 Weight = 215 Percent = 0.361 Weight = 213.77 Percent = 0.4111 Weight = 213.77 Percent = 0.4111 Weight = 212.54 Percent = 0.467 Weight = 212.54 Percent = 0.467 Weight = 211.32 Percent = 0.5295 Weight = 211.32 Percent = 0.5295 Weight = 210.09 Percent = 0.599 Weight = 210.09 Percent = 0.599 Weight = 208.86 Percent = 0.6762 Weight = 208.86 Percent = 0.6762 Weight = 207.63 Percent = 0.7616 Weight = 207.63 Percent = 0.7616 Weight = 206.4 Percent = 0.8559 Weight = 206.4 Percent = 0.8559 Weight = 205.17 Percent = 0.9598 Weight = 205.17 Percent = 0.9598 Weight = 203.94 Percent = 1.074 Weight = 203.94 Percent = 1.074 Weight = 202.71 Percent = 1.1991 Weight = 202.71 Percent = 1.1991 Weight = 201.48 Percent = 1.3359 Weight = 201.48 Percent = 1.3359 Weight = 200.25 Percent = 1.485 Weight = 200.25 Percent = 1.485 Weight = 199.02 Percent = 1.6472 Weight = 199.02 Percent = 1.6472 Weight = 197.79 Percent = 1.8231 Weight = 197.79 Percent = 1.8231 Weight = 196.56 Percent = 2.0133 Weight = 196.56 Percent = 2.0133 Weight = 195.33 Percent = 2.2186 Weight = 195.33 Percent = 2.2186 Weight = 194.1 Percent = 2.4394 Weight = 194.1 Percent = 2.4394 Weight = 192.87 Percent = 2.6763 Weight = 192.87 Percent = 2.6763 Weight = 191.64 Percent = 2.9299 Weight = 191.64 Percent = 2.9299 Weight = 190.41 Percent = 3.2004 Weight = 190.41 Percent = 3.2004 Weight = 189.18 Percent = 3.4883 Weight = 189.18 Percent = 3.4883 Weight = 187.95 Percent = 3.7938 Weight = 187.95 Percent = 3.7938 Weight = 186.72 Percent = 4.117 Weight = 186.72 Percent = 4.117 Weight = 185.49 Percent = 4.458 Weight = 185.49 Percent = 4.458 Weight = 184.26 Percent = 4.8167 Weight = 184.26 Percent = 4.8167 Weight = 183.03 Percent = 5.1928 Weight = 183.03 Percent = 5.1928 Weight = 181.8 Percent = 5.5861 Weight = 181.8 Percent = 5.5861 Weight = 180.57 Percent = 5.996 Weight = 180.57 Percent = 5.996 Weight = 179.34 Percent = 6.422 Weight = 179.34 Percent = 6.422 Weight = 178.11 Percent = 6.8632 Weight = 178.11 Percent = 6.8632 Weight = 175.65 Percent = 7.7873 Weight = 175.65 Percent = 7.7873 Weight = 164.59 Percent = 12.337 Weight = 164.59 Percent = 12.337 Weight = 162.13 Percent = 13.341 Weight = 162.13 Percent = 13.341 Weight = 159.67 Percent = 14.3 Weight = 159.67 Percent = 14.3 Weight = 158.44 Percent = 14.756 Weight = 158.44 Percent = 14.756 Weight = 157.21 Percent = 15.194 Weight = 157.21 Percent = 15.194 Weight = 155.98 Percent = 15.611 Weight = 155.98 Percent = 15.611 Weight = 154.75 Percent = 16.004 Weight = 154.75 Percent = 16.004 Weight = 153.52 Percent = 16.371 Weight = 153.52 Percent = 16.371 Weight = 152.29 Percent = 16.71 Weight = 152.29 Percent = 16.71 Weight = 151.06 Percent = 17.019 Weight = 151.06 Percent = 17.019 Weight = 149.83 Percent = 17.296 Weight = 149.83 Percent = 17.296 Weight = 148.6 Percent = 17.538 Weight = 148.6 Percent = 17.538 Weight = 147.37 Percent = 17.745 Weight = 147.37 Percent = 17.745 Weight = 146.14 Percent = 17.916 Weight = 146.14 Percent = 17.916 Weight = 144.91 Percent = 18.048 Weight = 144.91 Percent = 18.048 Weight = 143.68 Percent = 18.142 Weight = 143.68 Percent = 18.142 Weight = 142.45 Percent = 18.196 Weight = 142.45 Percent = 18.196 Weight = 141.39 Percent = 18.211 Weight = 141.39 Percent = 18.211 Weight = 141.22 Percent = 18.211 Weight = 141.22 Percent = 18.211 Weight = 139.99 Percent = 18.185 Weight = 139.99 Percent = 18.185 Weight = 138.76 Percent = 18.12 Weight = 138.76 Percent = 18.12 Weight = 137.53 Percent = 18.016 Weight = 137.53 Percent = 18.016 Weight = 136.3 Percent = 17.874 Weight = 136.3 Percent = 17.874 Weight = 135.08 Percent = 17.693 Weight = 135.08 Percent = 17.693 Weight = 133.85 Percent = 17.477 Weight = 133.85 Percent = 17.477 Weight = 132.62 Percent = 17.225 Weight = 132.62 Percent = 17.225 Weight = 131.39 Percent = 16.939 Weight = 131.39 Percent = 16.939 Weight = 130.16 Percent = 16.622 Weight = 130.16 Percent = 16.622 Weight = 128.93 Percent = 16.276 Weight = 128.93 Percent = 16.276 Weight = 127.7 Percent = 15.901 Weight = 127.7 Percent = 15.901 Weight = 126.47 Percent = 15.502 Weight = 126.47 Percent = 15.502 Weight = 125.24 Percent = 15.079 Weight = 125.24 Percent = 15.079 Weight = 124.01 Percent = 14.636 Weight = 124.01 Percent = 14.636 Weight = 122.78 Percent = 14.174 Weight = 122.78 Percent = 14.174 Weight = 121.55 Percent = 13.698 Weight = 121.55 Percent = 13.698 Weight = 112.94 Percent = 10.14 Weight = 112.94 Percent = 10.14 Weight = 109.25 Percent = 8.6262 Weight = 109.25 Percent = 8.6262 Weight = 106.79 Percent = 7.6603 Weight = 106.79 Percent = 7.6603 Weight = 104.33 Percent = 6.7434 Weight = 104.33 Percent = 6.7434 Weight = 103.1 Percent = 6.3062 Weight = 103.1 Percent = 6.3062 Weight = 101.87 Percent = 5.8844 Weight = 101.87 Percent = 5.8844 Weight = 100.64 Percent = 5.4789 Weight = 100.64 Percent = 5.4789 Weight = 99.415 Percent = 5.0902 Weight = 99.415 Percent = 5.0902 Weight = 98.185 Percent = 4.7187 Weight = 98.185 Percent = 4.7187 Weight = 96.955 Percent = 4.3647 Weight = 96.955 Percent = 4.3647 Weight = 95.726 Percent = 4.0285 Weight = 95.726 Percent = 4.0285 Weight = 94.496 Percent = 3.7101 Weight = 94.496 Percent = 3.7101 Weight = 93.266 Percent = 3.4093 Weight = 93.266 Percent = 3.4093 Weight = 92.037 Percent = 3.1261 Weight = 92.037 Percent = 3.1261 Weight = 90.807 Percent = 2.8602 Weight = 90.807 Percent = 2.8602 Weight = 89.577 Percent = 2.6111 Weight = 89.577 Percent = 2.6111 Weight = 88.348 Percent = 2.3786 Weight = 88.348 Percent = 2.3786 Weight = 87.118 Percent = 2.162 Weight = 87.118 Percent = 2.162 Weight = 85.888 Percent = 1.9608 Weight = 85.888 Percent = 1.9608 Weight = 84.659 Percent = 1.7745 Weight = 84.659 Percent = 1.7745 Weight = 83.429 Percent = 1.6023 Weight = 83.429 Percent = 1.6023 Weight = 82.199 Percent = 1.4437 Weight = 82.199 Percent = 1.4437 Weight = 80.97 Percent = 1.298 Weight = 80.97 Percent = 1.298 Weight = 79.74 Percent = 1.1644 Weight = 79.74 Percent = 1.1644 Weight = 78.51 Percent = 1.0423 Weight = 78.51 Percent = 1.0423 Weight = 77.281 Percent = 0.931 Weight = 77.281 Percent = 0.931 Weight = 76.051 Percent = 0.8297 Weight = 76.051 Percent = 0.8297 Weight = 74.821 Percent = 0.7378 Weight = 74.821 Percent = 0.7378 Weight = 73.592 Percent = 0.6547 Weight = 73.592 Percent = 0.6547 Weight = 72.362 Percent = 0.5796 Weight = 72.362 Percent = 0.5796 Weight = 71.132 Percent = 0.5121 Weight = 71.132 Percent = 0.5121 Weight = 69.903 Percent = 0.4514 Weight = 69.903 Percent = 0.4514 Weight = 68.673 Percent = 0.3971 Weight = 68.673 Percent = 0.3971 Weight = 67.443 Percent = 0.3485 Weight = 67.443 Percent = 0.3485 Weight = 66.214 Percent = 0.3052 Weight = 66.214 Percent = 0.3052 Weight = 64.984 Percent = 0.2667 Weight = 64.984 Percent = 0.2667 Weight = 63.754 Percent = 0.2325 Weight = 63.754 Percent = 0.2325 Weight = 62.525 Percent = 0.2023 Weight = 300 Percent = 0.0697 Weight = 300 Percent = 0.0697 Weight = 288 Percent = 0.0349 Weight = 288 Percent = 0.0349 Weight = 276 Percent = 0.1046 Weight = 276 Percent = 0.1046 Weight = 264 Percent = 0.0697 Weight = 264 Percent = 0.0697 Weight = 252 Percent = 0.0349 Weight = 252 Percent = 0.0349 Weight = 240 Percent = 0.244 Weight = 240 Percent = 0.244 Weight = 228 Percent = 0.488 Weight = 228 Percent = 0.488 Weight = 216 Percent = 0.8714 Weight = 216 Percent = 0.8714 Weight = 204 Percent = 1.3594 Weight = 204 Percent = 1.3594 Weight = 192 Percent = 2.5793 Weight = 192 Percent = 2.5793 Weight = 180 Percent = 5.298 Weight = 180 Percent = 5.298 Weight = 168 Percent = 7.3893 Weight = 168 Percent = 7.3893 Weight = 156 Percent = 13.245 Weight = 156 Percent = 13.245 Weight = 144 Percent = 18.473 Weight = 144 Percent = 18.473 Weight = 132 Percent = 21.575 Weight = 132 Percent = 21.575 Weight = 120 Percent = 17.079 Weight = 120 Percent = 17.079 Weight = 108 Percent = 8.5047 Weight = 108 Percent = 8.5047 Weight = 96 Percent = 2.161 Weight = 96 Percent = 2.161 Weight = 84 Percent = 0.3137 Weight = 84 Percent = 0.3137 Weight = 72 Percent = 0.1046 Weight = 72 Percent = 0.1046 Weight = 291.21 Percent = .00099 Weight = 289.83 Percent = 0.0019 Weight = 289.83 Percent = 0.0019 Weight = 288.45 Percent = 0.0034 Weight = 288.45 Percent = 0.0034 Weight = 287.06 Percent = 0.0059 Weight = 287.06 Percent = 0.0059 Weight = 285.68 Percent = 0.0095 Weight = 285.68 Percent = 0.0095 Weight = 284.3 Percent = 0.0145 Weight = 284.3 Percent = 0.0145 Weight = 282.91 Percent = 0.0209 Weight = 282.91 Percent = 0.0209 Weight = 281.53 Percent = 0.0285 Weight = 281.53 Percent = 0.0285 Weight = 278.77 Percent = 0.0449 Weight = 278.77 Percent = 0.0449 Weight = 277.38 Percent = 0.052 Weight = 277.38 Percent = 0.052 Weight = 276 Percent = 0.057 Weight = 276 Percent = 0.057 Weight = 274.62 Percent = 0.0595 Weight = 274.62 Percent = 0.0595 Weight = 273.23 Percent = 0.0594 Weight = 273.23 Percent = 0.0594 Weight = 271.85 Percent = 0.057 Weight = 271.85 Percent = 0.057 Weight = 270.47 Percent = 0.0535 Weight = 270.47 Percent = 0.0535 Weight = 269.09 Percent = 0.0502 Weight = 269.09 Percent = 0.0502 Weight = 267.7 Percent = 0.0483 Weight = 267.7 Percent = 0.0483 Weight = 266.32 Percent = 0.049 Weight = 266.32 Percent = 0.049 Weight = 264.94 Percent = 0.0529 Weight = 264.94 Percent = 0.0529 Weight = 263.55 Percent = 0.0601 Weight = 263.55 Percent = 0.0601 Weight = 262.17 Percent = 0.0703 Weight = 262.17 Percent = 0.0703 Weight = 260.79 Percent = 0.0829 Weight = 260.79 Percent = 0.0829 Weight = 259.41 Percent = 0.0973 Weight = 259.41 Percent = 0.0973 Weight = 258.02 Percent = 0.1132 Weight = 258.02 Percent = 0.1132 Weight = 256.64 Percent = 0.1311 Weight = 256.64 Percent = 0.1311 Weight = 255.26 Percent = 0.1518 Weight = 255.26 Percent = 0.1518 Weight = 253.88 Percent = 0.1766 Weight = 253.88 Percent = 0.1766 Weight = 252.49 Percent = 0.2069 Weight = 252.49 Percent = 0.2069 Weight = 251.11 Percent = 0.2437 Weight = 251.11 Percent = 0.2437 Weight = 249.73 Percent = 0.2872 Weight = 249.73 Percent = 0.2872 Weight = 248.34 Percent = 0.3366 Weight = 248.34 Percent = 0.3366 Weight = 244.2 Percent = 0.5014 Weight = 244.2 Percent = 0.5014 Weight = 242.81 Percent = 0.554 Weight = 242.81 Percent = 0.554 Weight = 241.43 Percent = 0.6024 Weight = 241.43 Percent = 0.6024 Weight = 240.05 Percent = 0.6459 Weight = 240.05 Percent = 0.6459 Weight = 238.66 Percent = 0.6855 Weight = 238.66 Percent = 0.6855 Weight = 237.28 Percent = 0.7236 Weight = 237.28 Percent = 0.7236 Weight = 235.9 Percent = 0.764 Weight = 235.9 Percent = 0.764 Weight = 234.52 Percent = 0.8113 Weight = 234.52 Percent = 0.8113 Weight = 233.13 Percent = 0.8702 Weight = 233.13 Percent = 0.8702 Weight = 231.75 Percent = 0.9442 Weight = 231.75 Percent = 0.9442 Weight = 230.37 Percent = 1.0346 Weight = 230.37 Percent = 1.0346 Weight = 228.98 Percent = 1.1402 Weight = 228.98 Percent = 1.1402 Weight = 222.07 Percent = 1.7558 Weight = 222.07 Percent = 1.7558 Weight = 220.69 Percent = 1.8846 Weight = 220.69 Percent = 1.8846 Weight = 219.3 Percent = 2.0239 Weight = 219.3 Percent = 2.0239 Weight = 217.92 Percent = 2.1813 Weight = 217.92 Percent = 2.1813 Weight = 216.54 Percent = 2.3631 Weight = 216.54 Percent = 2.3631 Weight = 215.16 Percent = 2.5728 Weight = 215.16 Percent = 2.5728 Weight = 213.77 Percent = 2.8104 Weight = 213.77 Percent = 2.8104 Weight = 212.39 Percent = 3.0722 Weight = 212.39 Percent = 3.0722 Weight = 211.01 Percent = 3.3521 Weight = 211.01 Percent = 3.3521 Weight = 209.63 Percent = 3.6439 Weight = 209.63 Percent = 3.6439 Weight = 206.86 Percent = 4.2486 Weight = 206.86 Percent = 4.2486 Weight = 205.48 Percent = 4.5646 Weight = 205.48 Percent = 4.5646 Weight = 204.09 Percent = 4.8998 Weight = 204.09 Percent = 4.8998 Weight = 202.71 Percent = 5.2654 Weight = 202.71 Percent = 5.2654 Weight = 201.33 Percent = 5.6723 Weight = 201.33 Percent = 5.6723 Weight = 199.95 Percent = 6.1271 Weight = 199.95 Percent = 6.1271 Weight = 198.56 Percent = 6.6287 Weight = 198.56 Percent = 6.6287 Weight = 194.41 Percent = 8.2785 Weight = 194.41 Percent = 8.2785 Weight = 193.03 Percent = 8.8113 Weight = 193.03 Percent = 8.8113 Weight = 191.65 Percent = 9.3111 Weight = 191.65 Percent = 9.3111 Weight = 186.12 Percent = 11.096 Weight = 186.12 Percent = 11.096 Weight = 180.59 Percent = 13.015 Weight = 180.59 Percent = 13.015 Weight = 179.2 Percent = 13.472 Weight = 179.2 Percent = 13.472 Weight = 177.82 Percent = 13.887 Weight = 177.82 Percent = 13.887 Weight = 176.44 Percent = 14.25 Weight = 176.44 Percent = 14.25 Weight = 175.05 Percent = 14.554 Weight = 175.05 Percent = 14.554 Weight = 173.67 Percent = 14.802 Weight = 173.67 Percent = 14.802 Weight = 172.29 Percent = 14.992 Weight = 172.29 Percent = 14.992 Weight = 170.91 Percent = 15.123 Weight = 170.91 Percent = 15.123 Weight = 169.52 Percent = 15.194 Weight = 169.52 Percent = 15.194 Weight = 168.14 Percent = 15.202 Weight = 168.14 Percent = 15.202 Weight = 166.76 Percent = 15.148 Weight = 166.76 Percent = 15.148 Weight = 165.38 Percent = 15.04 Weight = 165.38 Percent = 15.04 Weight = 163.99 Percent = 14.893 Weight = 163.99 Percent = 14.893 Weight = 161.23 Percent = 14.555 Weight = 161.23 Percent = 14.555 Weight = 159.84 Percent = 14.402 Weight = 159.84 Percent = 14.402 Weight = 158.46 Percent = 14.275 Weight = 158.46 Percent = 14.275 Weight = 157.08 Percent = 14.174 Weight = 157.08 Percent = 14.174 Weight = 155.7 Percent = 14.093 Weight = 155.7 Percent = 14.093 Weight = 154.31 Percent = 14.018 Weight = 154.31 Percent = 14.018 Weight = 152.93 Percent = 13.932 Weight = 152.93 Percent = 13.932 Weight = 151.55 Percent = 13.82 Weight = 151.55 Percent = 13.82 Weight = 150.16 Percent = 13.664 Weight = 150.16 Percent = 13.664 Weight = 148.78 Percent = 13.453 Weight = 148.78 Percent = 13.453 Weight = 147.4 Percent = 13.177 Weight = 147.4 Percent = 13.177 Weight = 146.02 Percent = 12.83 Weight = 146.02 Percent = 12.83 Weight = 144.63 Percent = 12.412 Weight = 144.63 Percent = 12.412 Weight = 143.25 Percent = 11.927 Weight = 143.25 Percent = 11.927 Weight = 141.87 Percent = 11.381 Weight = 141.87 Percent = 11.381 Weight = 140.48 Percent = 10.785 Weight = 140.48 Percent = 10.785 Weight = 132.19 Percent = 6.7541 Weight = 132.19 Percent = 6.7541 Weight = 130.8 Percent = 6.1004 Weight = 130.8 Percent = 6.1004 Weight = 129.42 Percent = 5.477 Weight = 129.42 Percent = 5.477 Weight = 128.04 Percent = 4.8924 Weight = 128.04 Percent = 4.8924 Weight = 126.66 Percent = 4.354 Weight = 126.66 Percent = 4.354 Weight = 125.27 Percent = 3.8674 Weight = 125.27 Percent = 3.8674 Weight = 123.89 Percent = 3.4358 Weight = 123.89 Percent = 3.4358 Weight = 122.51 Percent = 3.0593 Weight = 122.51 Percent = 3.0593 Weight = 121.13 Percent = 2.7343 Weight = 121.13 Percent = 2.7343 Weight = 119.74 Percent = 2.4535 Weight = 119.74 Percent = 2.4535 Weight = 118.36 Percent = 2.2069 Weight = 118.36 Percent = 2.2069 Weight = 116.98 Percent = 1.9832 Weight = 116.98 Percent = 1.9832 Weight = 115.59 Percent = 1.7719 Weight = 115.59 Percent = 1.7719 Weight = 111.45 Percent = 1.157 Weight = 111.45 Percent = 1.157 Weight = 110.06 Percent = 0.9603 Weight = 110.06 Percent = 0.9603 Weight = 108.68 Percent = 0.7762 Weight = 108.68 Percent = 0.7762 Weight = 107.3 Percent = 0.6107 Weight = 107.3 Percent = 0.6107 Weight = 105.91 Percent = 0.4683 Weight = 105.91 Percent = 0.4683 Weight = 104.53 Percent = 0.351 Weight = 104.53 Percent = 0.351 Weight = 103.15 Percent = 0.2584 Weight = 103.15 Percent = 0.2584 Weight = 101.77 Percent = 0.1879 Weight = 101.77 Percent = 0.1879 Weight = 100.38 Percent = 0.1359 Weight = 100.38 Percent = 0.1359 Weight = 99 Percent = 0.0982 Weight = 99 Percent = 0.0982 Weight = 97.617 Percent = 0.0711 Weight = 97.617 Percent = 0.0711 Weight = 96.234 Percent = 0.0515 Weight = 96.234 Percent = 0.0515 Weight = 94.852 Percent = 0.0371 Weight = 94.852 Percent = 0.0371 Weight = 93.469 Percent = 0.0264 Weight = 93.469 Percent = 0.0264 Weight = 92.086 Percent = 0.0183 Weight = 92.086 Percent = 0.0183 Weight = 90.703 Percent = 0.0123 Weight = 90.703 Percent = 0.0123 Weight = 89.32 Percent = 0.0079 Weight = 89.32 Percent = 0.0079 Weight = 87.938 Percent = 0.0049 Weight = 87.938 Percent = 0.0049 Weight = 86.555 Percent = 0.0029 Weight = 86.555 Percent = 0.0029 Weight = 85.172 Percent = 0.0016 Weight = 85.172 Percent = 0.0016 Weight = 83.789 Percent = .00084 Weight = 285 Percent = .00032 Weight = 284.02 Percent = .00039 Weight = 284.02 Percent = .00039 Weight = 283.05 Percent = .00046 Weight = 283.05 Percent = .00046 Weight = 282.07 Percent = .00055 Weight = 282.07 Percent = .00055 Weight = 281.09 Percent = .00065 Weight = 281.09 Percent = .00065 Weight = 280.12 Percent = .00078 Weight = 280.12 Percent = .00078 Weight = 279.14 Percent = .00092 Weight = 279.14 Percent = .00092 Weight = 278.16 Percent = 0.0011 Weight = 278.16 Percent = 0.0011 Weight = 277.19 Percent = 0.0013 Weight = 277.19 Percent = 0.0013 Weight = 276.21 Percent = 0.0015 Weight = 276.21 Percent = 0.0015 Weight = 275.23 Percent = 0.0018 Weight = 275.23 Percent = 0.0018 Weight = 274.26 Percent = 0.0021 Weight = 274.26 Percent = 0.0021 Weight = 273.28 Percent = 0.0025 Weight = 273.28 Percent = 0.0025 Weight = 272.3 Percent = 0.0029 Weight = 272.3 Percent = 0.0029 Weight = 271.32 Percent = 0.0034 Weight = 271.32 Percent = 0.0034 Weight = 270.35 Percent = 0.004 Weight = 270.35 Percent = 0.004 Weight = 269.37 Percent = 0.0047 Weight = 269.37 Percent = 0.0047 Weight = 268.39 Percent = 0.0055 Weight = 268.39 Percent = 0.0055 Weight = 267.42 Percent = 0.0064 Weight = 267.42 Percent = 0.0064 Weight = 266.44 Percent = 0.0075 Weight = 266.44 Percent = 0.0075 Weight = 265.46 Percent = 0.0087 Weight = 265.46 Percent = 0.0087 Weight = 264.49 Percent = 0.0101 Weight = 264.49 Percent = 0.0101 Weight = 263.51 Percent = 0.0116 Weight = 263.51 Percent = 0.0116 Weight = 262.53 Percent = 0.0135 Weight = 262.53 Percent = 0.0135 Weight = 261.56 Percent = 0.0156 Weight = 261.56 Percent = 0.0156 Weight = 260.58 Percent = 0.018 Weight = 260.58 Percent = 0.018 Weight = 259.6 Percent = 0.0207 Weight = 259.6 Percent = 0.0207 Weight = 258.63 Percent = 0.0238 Weight = 258.63 Percent = 0.0238 Weight = 257.65 Percent = 0.0273 Weight = 257.65 Percent = 0.0273 Weight = 256.67 Percent = 0.0314 Weight = 256.67 Percent = 0.0314 Weight = 255.7 Percent = 0.0359 Weight = 255.7 Percent = 0.0359 Weight = 254.72 Percent = 0.0411 Weight = 254.72 Percent = 0.0411 Weight = 253.74 Percent = 0.0469 Weight = 253.74 Percent = 0.0469 Weight = 252.77 Percent = 0.0534 Weight = 252.77 Percent = 0.0534 Weight = 251.79 Percent = 0.0608 Weight = 251.79 Percent = 0.0608 Weight = 250.81 Percent = 0.0691 Weight = 250.81 Percent = 0.0691 Weight = 249.84 Percent = 0.0784 Weight = 249.84 Percent = 0.0784 Weight = 248.86 Percent = 0.0889 Weight = 248.86 Percent = 0.0889 Weight = 247.88 Percent = 0.1006 Weight = 247.88 Percent = 0.1006 Weight = 246.9 Percent = 0.1136 Weight = 246.9 Percent = 0.1136 Weight = 245.93 Percent = 0.1282 Weight = 245.93 Percent = 0.1282 Weight = 244.95 Percent = 0.1444 Weight = 244.95 Percent = 0.1444 Weight = 243.97 Percent = 0.1624 Weight = 243.97 Percent = 0.1624 Weight = 243 Percent = 0.1824 Weight = 243 Percent = 0.1824 Weight = 242.02 Percent = 0.2046 Weight = 242.02 Percent = 0.2046 Weight = 241.04 Percent = 0.2291 Weight = 241.04 Percent = 0.2291 Weight = 240.07 Percent = 0.2562 Weight = 240.07 Percent = 0.2562 Weight = 239.09 Percent = 0.286 Weight = 239.09 Percent = 0.286 Weight = 238.11 Percent = 0.3188 Weight = 238.11 Percent = 0.3188 Weight = 237.14 Percent = 0.3548 Weight = 237.14 Percent = 0.3548 Weight = 236.16 Percent = 0.3944 Weight = 236.16 Percent = 0.3944 Weight = 235.18 Percent = 0.4377 Weight = 235.18 Percent = 0.4377 Weight = 234.21 Percent = 0.485 Weight = 234.21 Percent = 0.485 Weight = 233.23 Percent = 0.5366 Weight = 233.23 Percent = 0.5366 Weight = 232.25 Percent = 0.5929 Weight = 232.25 Percent = 0.5929 Weight = 231.28 Percent = 0.6541 Weight = 231.28 Percent = 0.6541 Weight = 230.3 Percent = 0.7205 Weight = 230.3 Percent = 0.7205 Weight = 229.32 Percent = 0.7925 Weight = 229.32 Percent = 0.7925 Weight = 228.35 Percent = 0.8703 Weight = 228.35 Percent = 0.8703 Weight = 227.37 Percent = 0.9544 Weight = 227.37 Percent = 0.9544 Weight = 226.39 Percent = 1.045 Weight = 226.39 Percent = 1.045 Weight = 225.42 Percent = 1.1426 Weight = 225.42 Percent = 1.1426 Weight = 224.44 Percent = 1.2474 Weight = 224.44 Percent = 1.2474 Weight = 223.46 Percent = 1.3598 Weight = 223.46 Percent = 1.3598 Weight = 222.48 Percent = 1.4801 Weight = 222.48 Percent = 1.4801 Weight = 221.51 Percent = 1.6086 Weight = 221.51 Percent = 1.6086 Weight = 220.53 Percent = 1.7457 Weight = 220.53 Percent = 1.7457 Weight = 219.55 Percent = 1.8916 Weight = 219.55 Percent = 1.8916 Weight = 218.58 Percent = 2.0467 Weight = 218.58 Percent = 2.0467 Weight = 217.6 Percent = 2.2112 Weight = 217.6 Percent = 2.2112 Weight = 216.62 Percent = 2.3854 Weight = 216.62 Percent = 2.3854 Weight = 215.65 Percent = 2.5694 Weight = 215.65 Percent = 2.5694 Weight = 214.67 Percent = 2.7636 Weight = 214.67 Percent = 2.7636 Weight = 213.69 Percent = 2.9679 Weight = 213.69 Percent = 2.9679 Weight = 212.72 Percent = 3.1826 Weight = 212.72 Percent = 3.1826 Weight = 211.74 Percent = 3.4078 Weight = 211.74 Percent = 3.4078 Weight = 210.76 Percent = 3.6435 Weight = 210.76 Percent = 3.6435 Weight = 209.79 Percent = 3.8896 Weight = 209.79 Percent = 3.8896 Weight = 208.81 Percent = 4.1462 Weight = 208.81 Percent = 4.1462 Weight = 207.83 Percent = 4.4132 Weight = 207.83 Percent = 4.4132 Weight = 206.86 Percent = 4.6903 Weight = 206.86 Percent = 4.6903 Weight = 205.88 Percent = 4.9774 Weight = 205.88 Percent = 4.9774 Weight = 204.9 Percent = 5.2742 Weight = 204.9 Percent = 5.2742 Weight = 203.93 Percent = 5.5803 Weight = 203.93 Percent = 5.5803 Weight = 201.97 Percent = 6.2191 Weight = 201.97 Percent = 6.2191 Weight = 200.02 Percent = 6.8897 Weight = 200.02 Percent = 6.8897 Weight = 198.06 Percent = 7.5872 Weight = 198.06 Percent = 7.5872 Weight = 192.2 Percent = 9.7766 Weight = 192.2 Percent = 9.7766 Weight = 188.3 Percent = 11.237 Weight = 188.3 Percent = 11.237 Weight = 186.34 Percent = 11.939 Weight = 186.34 Percent = 11.939 Weight = 184.39 Percent = 12.61 Weight = 184.39 Percent = 12.61 Weight = 183.41 Percent = 12.93 Weight = 183.41 Percent = 12.93 Weight = 182.44 Percent = 13.239 Weight = 182.44 Percent = 13.239 Weight = 181.46 Percent = 13.535 Weight = 181.46 Percent = 13.535 Weight = 180.48 Percent = 13.817 Weight = 180.48 Percent = 13.817 Weight = 179.51 Percent = 14.084 Weight = 179.51 Percent = 14.084 Weight = 178.53 Percent = 14.335 Weight = 178.53 Percent = 14.335 Weight = 177.55 Percent = 14.568 Weight = 177.55 Percent = 14.568 Weight = 176.58 Percent = 14.784 Weight = 176.58 Percent = 14.784 Weight = 175.6 Percent = 14.979 Weight = 175.6 Percent = 14.979 Weight = 174.62 Percent = 15.155 Weight = 174.62 Percent = 15.155 Weight = 173.65 Percent = 15.31 Weight = 173.65 Percent = 15.31 Weight = 172.67 Percent = 15.444 Weight = 172.67 Percent = 15.444 Weight = 171.69 Percent = 15.556 Weight = 171.69 Percent = 15.556 Weight = 170.71 Percent = 15.645 Weight = 170.71 Percent = 15.645 Weight = 169.74 Percent = 15.711 Weight = 169.74 Percent = 15.711 Weight = 168.76 Percent = 15.754 Weight = 168.76 Percent = 15.754 Weight = 167.78 Percent = 15.773 Weight = 167.78 Percent = 15.773 Weight = 167.47 Percent = 15.774 Weight = 167.47 Percent = 15.774 Weight = 166.81 Percent = 15.769 Weight = 166.81 Percent = 15.769 Weight = 165.83 Percent = 15.741 Weight = 165.83 Percent = 15.741 Weight = 164.85 Percent = 15.69 Weight = 164.85 Percent = 15.69 Weight = 163.88 Percent = 15.616 Weight = 163.88 Percent = 15.616 Weight = 162.9 Percent = 15.519 Weight = 162.9 Percent = 15.519 Weight = 161.92 Percent = 15.4 Weight = 161.92 Percent = 15.4 Weight = 160.95 Percent = 15.259 Weight = 160.95 Percent = 15.259 Weight = 159.97 Percent = 15.096 Weight = 159.97 Percent = 15.096 Weight = 158.99 Percent = 14.913 Weight = 158.99 Percent = 14.913 Weight = 158.02 Percent = 14.711 Weight = 158.02 Percent = 14.711 Weight = 157.04 Percent = 14.489 Weight = 157.04 Percent = 14.489 Weight = 156.06 Percent = 14.25 Weight = 156.06 Percent = 14.25 Weight = 155.09 Percent = 13.993 Weight = 155.09 Percent = 13.993 Weight = 154.11 Percent = 13.721 Weight = 154.11 Percent = 13.721 Weight = 153.13 Percent = 13.434 Weight = 153.13 Percent = 13.434 Weight = 152.16 Percent = 13.133 Weight = 152.16 Percent = 13.133 Weight = 151.18 Percent = 12.82 Weight = 151.18 Percent = 12.82 Weight = 149.23 Percent = 12.162 Weight = 149.23 Percent = 12.162 Weight = 139.46 Percent = 8.5431 Weight = 139.46 Percent = 8.5431 Weight = 136.53 Percent = 7.464 Weight = 136.53 Percent = 7.464 Weight = 134.57 Percent = 6.7707 Weight = 134.57 Percent = 6.7707 Weight = 132.62 Percent = 6.1053 Weight = 132.62 Percent = 6.1053 Weight = 130.67 Percent = 5.4725 Weight = 130.67 Percent = 5.4725 Weight = 129.69 Percent = 5.1696 Weight = 129.69 Percent = 5.1696 Weight = 128.71 Percent = 4.8762 Weight = 128.71 Percent = 4.8762 Weight = 127.74 Percent = 4.5925 Weight = 127.74 Percent = 4.5925 Weight = 126.76 Percent = 4.3189 Weight = 126.76 Percent = 4.3189 Weight = 125.78 Percent = 4.0556 Weight = 125.78 Percent = 4.0556 Weight = 124.81 Percent = 3.8026 Weight = 124.81 Percent = 3.8026 Weight = 123.83 Percent = 3.5601 Weight = 123.83 Percent = 3.5601 Weight = 122.85 Percent = 3.3281 Weight = 122.85 Percent = 3.3281 Weight = 121.87 Percent = 3.1066 Weight = 121.87 Percent = 3.1066 Weight = 120.9 Percent = 2.8955 Weight = 120.9 Percent = 2.8955 Weight = 119.92 Percent = 2.6947 Weight = 119.92 Percent = 2.6947 Weight = 118.94 Percent = 2.5041 Weight = 118.94 Percent = 2.5041 Weight = 117.97 Percent = 2.3235 Weight = 117.97 Percent = 2.3235 Weight = 116.99 Percent = 2.1528 Weight = 116.99 Percent = 2.1528 Weight = 116.01 Percent = 1.9916 Weight = 116.01 Percent = 1.9916 Weight = 115.04 Percent = 1.8397 Weight = 115.04 Percent = 1.8397 Weight = 114.06 Percent = 1.6969 Weight = 114.06 Percent = 1.6969 Weight = 113.08 Percent = 1.5628 Weight = 113.08 Percent = 1.5628 Weight = 112.11 Percent = 1.4372 Weight = 112.11 Percent = 1.4372 Weight = 111.13 Percent = 1.3197 Weight = 111.13 Percent = 1.3197 Weight = 110.15 Percent = 1.21 Weight = 110.15 Percent = 1.21 Weight = 109.18 Percent = 1.1078 Weight = 109.18 Percent = 1.1078 Weight = 108.2 Percent = 1.0127 Weight = 108.2 Percent = 1.0127 Weight = 107.22 Percent = 0.9243 Weight = 107.22 Percent = 0.9243 Weight = 106.25 Percent = 0.8425 Weight = 106.25 Percent = 0.8425 Weight = 105.27 Percent = 0.7667 Weight = 105.27 Percent = 0.7667 Weight = 104.29 Percent = 0.6967 Weight = 104.29 Percent = 0.6967 Weight = 103.32 Percent = 0.6322 Weight = 103.32 Percent = 0.6322 Weight = 102.34 Percent = 0.5727 Weight = 102.34 Percent = 0.5727 Weight = 101.36 Percent = 0.5181 Weight = 101.36 Percent = 0.5181 Weight = 100.39 Percent = 0.468 Weight = 100.39 Percent = 0.468 Weight = 99.408 Percent = 0.4221 Weight = 99.408 Percent = 0.4221 Weight = 98.432 Percent = 0.3802 Weight = 98.432 Percent = 0.3802 Weight = 97.455 Percent = 0.3419 Weight = 97.455 Percent = 0.3419 Weight = 96.478 Percent = 0.307 Weight = 96.478 Percent = 0.307 Weight = 95.501 Percent = 0.2752 Weight = 95.501 Percent = 0.2752 Weight = 94.524 Percent = 0.2464 Weight = 94.524 Percent = 0.2464 Weight = 93.548 Percent = 0.2203 Weight = 93.548 Percent = 0.2203 Weight = 92.571 Percent = 0.1966 Weight = 92.571 Percent = 0.1966 Weight = 91.594 Percent = 0.1752 Weight = 280 Percent = 0.0428 Weight = 280 Percent = 0.0428 Weight = 270 Percent = 0.0428 Weight = 270 Percent = 0.0428 Weight = 260 Percent = 0.1285 Weight = 260 Percent = 0.1285 Weight = 250 Percent = 0.2142 Weight = 250 Percent = 0.2142 Weight = 240 Percent = 0.7712 Weight = 240 Percent = 0.7712 Weight = 230 Percent = 0.9426 Weight = 230 Percent = 0.9426 Weight = 220 Percent = 1.8423 Weight = 220 Percent = 1.8423 Weight = 210 Percent = 3.599 Weight = 210 Percent = 3.599 Weight = 200 Percent = 5.8698 Weight = 200 Percent = 5.8698 Weight = 190 Percent = 10.197 Weight = 190 Percent = 10.197 Weight = 180 Percent = 14.053 Weight = 180 Percent = 14.053 Weight = 170 Percent = 15.424 Weight = 170 Percent = 15.424 Weight = 160 Percent = 14.139 Weight = 160 Percent = 14.139 Weight = 150 Percent = 13.967 Weight = 150 Percent = 13.967 Weight = 140 Percent = 10.583 Weight = 140 Percent = 10.583 Weight = 130 Percent = 5.1414 Weight = 130 Percent = 5.1414 Weight = 120 Percent = 2.2708 Weight = 120 Percent = 2.2708 Weight = 110 Percent = 0.7284 Weight = 110 Percent = 0.7284 Weight = 100 Percent = 0.0428 Weight = 100 Percent = 0.0428 Sex = Male Weight = 235 Sex = Male Weight = 235 Sex = Male Weight = 236 Sex = Male Weight = 236 Sex = Male Weight = 236 Sex = Male Weight = 237 Sex = Male Weight = 237 Sex = Male Weight = 238 Sex = Male Weight = 238 Sex = Male Weight = 239 Sex = Male Weight = 239 Sex = Male Weight = 239 Sex = Male Weight = 240 Sex = Male Weight = 241 Sex = Male Weight = 243 Sex = Male Weight = 244 Sex = Male Weight = 244 Sex = Male Weight = 244 Sex = Male Weight = 245 Sex = Male Weight = 245 Sex = Male Weight = 246 Sex = Male Weight = 247 Sex = Male Weight = 250 Sex = Male Weight = 255 Sex = Male Weight = 256 Sex = Male Weight = 260 Sex = Male Weight = 273 Sex = Male Weight = 276 Sex = Female Weight = 201 Sex = Female Weight = 202 Sex = Female Weight = 202 Sex = Female Weight = 202 Sex = Female Weight = 202 Sex = Female Weight = 203 Sex = Female Weight = 203 Sex = Female Weight = 203 Sex = Female Weight = 203 Sex = Female Weight = 203 Sex = Female Weight = 203 Sex = Female Weight = 203 Sex = Female Weight = 204 Sex = Female Weight = 205 Sex = Female Weight = 207 Sex = Female Weight = 207 Sex = Female Weight = 208 Sex = Female Weight = 208 Sex = Female Weight = 208 Sex = Female Weight = 208 Sex = Female Weight = 208 Sex = Female Weight = 209 Sex = Female Weight = 209 Sex = Female Weight = 209 Sex = Female Weight = 209 Sex = Female Weight = 210 Sex = Female Weight = 210 Sex = Female Weight = 210 Sex = Female Weight = 210 Sex = Female Weight = 210 Sex = Female Weight = 210 Sex = Female Weight = 211 Sex = Female Weight = 211 Sex = Female Weight = 211 Sex = Female Weight = 212 Sex = Female Weight = 213 Sex = Female Weight = 214 Sex = Female Weight = 215 Sex = Female Weight = 215 Sex = Female Weight = 216 Sex = Female Weight = 216 Sex = Female Weight = 216 Sex = Female Weight = 216 Sex = Female Weight = 217 Sex = Female Weight = 217 Sex = Female Weight = 218 Sex = Female Weight = 219 Sex = Female Weight = 219 Sex = Female Weight = 221 Sex = Female Weight = 221 Sex = Female Weight = 222 Sex = Female Weight = 222 Sex = Female Weight = 224 Sex = Female Weight = 225 Sex = Female Weight = 226 Sex = Female Weight = 227 Sex = Female Weight = 228 Sex = Female Weight = 229 Sex = Female Weight = 229 Sex = Female Weight = 230 Sex = Female Weight = 230 Sex = Female Weight = 231 Sex = Female Weight = 232 Sex = Female Weight = 232 Sex = Female Weight = 235 Sex = Female Weight = 235 Sex = Female Weight = 236 Sex = Female Weight = 238 Sex = Female Weight = 239 Sex = Female Weight = 241 Sex = Female Weight = 242 Sex = Female Weight = 250 Sex = Female Weight = 261 Sex = Female Weight = 269 Sex = Female Weight = 271 Sex = Female Weight = 275 Sex = Female Weight = 281 Sex = Female Weight = 293 Sex = Female Weight = 300 Sex = Female Weight = 300 Sex = Female Weight = 72 Sex = Female Weight = 71 Sex = Female Weight = 67 Sex = Male Data Minimum = 99 Minimum Whisker = 99 First Quartile = 149 Median = 167 Third Quartile = 183 Maximum Whisker = 234 Data Maximum = 276 Mean = 167.47 Standard Deviation = 25.291 Number of Observations = 2334 Sum of Weight = . Sex = Male Data Minimum = 99 Minimum Whisker = 99 First Quartile = 149 Median = 167 Third Quartile = 183 Maximum Whisker = 234 Data Maximum = 276 Mean = 167.47 Standard Deviation = 25.291 Number of Observations = 2334 Sum of Weight = . Sex = Male Data Minimum = 99 Minimum Whisker = 99 First Quartile = 149 Median = 167 Third Quartile = 183 Maximum Whisker = 234 Data Maximum = 276 Mean = 167.47 Standard Deviation = 25.291 Number of Observations = 2334 Sum of Weight = . Sex = Male Data Minimum = 99 Minimum Whisker = 99 First Quartile = 149 Median = 167 Third Quartile = 183 Maximum Whisker = 234 Data Maximum = 276 Mean = 167.47 Standard Deviation = 25.291 Number of Observations = 2334 Sum of Weight = . Sex = Male Data Minimum = 99 Minimum Whisker = 99 First Quartile = 149 Median = 167 Third Quartile = 183 Maximum Whisker = 234 Data Maximum = 276 Mean = 167.47 Standard Deviation = 25.291 Number of Observations = 2334 Sum of Weight = . Sex = Male Data Minimum = 99 Minimum Whisker = 99 First Quartile = 149 Median = 167 Third Quartile = 183 Maximum Whisker = 234 Data Maximum = 276 Mean = 167.47 Standard Deviation = 25.291 Number of Observations = 2334 Sum of Weight = . Sex = Male Data Minimum = 99 Minimum Whisker = 99 First Quartile = 149 Median = 167 Third Quartile = 183 Maximum Whisker = 234 Data Maximum = 276 Mean = 167.47 Standard Deviation = 25.291 Number of Observations = 2334 Sum of Weight = . Sex = Male Data Minimum = 99 Minimum Whisker = 99 First Quartile = 149 Median = 167 Third Quartile = 183 Maximum Whisker = 234 Data Maximum = 276 Mean = 167.47 Standard Deviation = 25.291 Number of Observations = 2334 Sum of Weight = . Sex = Female Data Minimum = 67 Minimum Whisker = 82 First Quartile = 123 Median = 138 Third Quartile = 154 Maximum Whisker = 200 Data Maximum = 300 Mean = 141.39 Standard Deviation = 26.288 Number of Observations = 2869 Sum of Weight = . Sex = Female Data Minimum = 67 Minimum Whisker = 82 First Quartile = 123 Median = 138 Third Quartile = 154 Maximum Whisker = 200 Data Maximum = 300 Mean = 141.39 Standard Deviation = 26.288 Number of Observations = 2869 Sum of Weight = . Sex = Female Data Minimum = 67 Minimum Whisker = 82 First Quartile = 123 Median = 138 Third Quartile = 154 Maximum Whisker = 200 Data Maximum = 300 Mean = 141.39 Standard Deviation = 26.288 Number of Observations = 2869 Sum of Weight = . Sex = Female Data Minimum = 67 Minimum Whisker = 82 First Quartile = 123 Median = 138 Third Quartile = 154 Maximum Whisker = 200 Data Maximum = 300 Mean = 141.39 Standard Deviation = 26.288 Number of Observations = 2869 Sum of Weight = . Sex = Female Data Minimum = 67 Minimum Whisker = 82 First Quartile = 123 Median = 138 Third Quartile = 154 Maximum Whisker = 200 Data Maximum = 300 Mean = 141.39 Standard Deviation = 26.288 Number of Observations = 2869 Sum of Weight = . Sex = Female Data Minimum = 67 Minimum Whisker = 82 First Quartile = 123 Median = 138 Third Quartile = 154 Maximum Whisker = 200 Data Maximum = 300 Mean = 141.39 Standard Deviation = 26.288 Number of Observations = 2869 Sum of Weight = . Sex = Female Data Minimum = 67 Minimum Whisker = 82 First Quartile = 123 Median = 138 Third Quartile = 154 Maximum Whisker = 200 Data Maximum = 300 Mean = 141.39 Standard Deviation = 26.288 Number of Observations = 2869 Sum of Weight = . Sex = Female Data Minimum = 67 Minimum Whisker = 82 First Quartile = 123 Median = 138 Third Quartile = 154 Maximum Whisker = 200 Data Maximum = 300 Mean = 141.39 Standard Deviation = 26.288 Number of Observations = 2869 Sum of Weight = .
Summary Panel for Weight

Q-Q Plots

Slope = 26.288 Y = 141.39 Slope = 25.291 Y = 167.47
Q-Q Plots for Weight

Nonparametric Two-sample Tests on Heart / Weight Data by Sex

The Npar1way Procedure

Variable Weight

Wilcoxon Analysis

Scores

Wilcoxon Scores (Rank Sums) for Variable Weight
Classified by Variable Sex
Sex N Sum of
Scores		 Expected
Under H0		 Std Dev
Under H0		 Mean
Score
Average scores were used for ties.
Female 2869 5594004.0 7465138.0 53884.9799 1949.80969
Male 2334 7944202.0 6073068.0 53884.9799 3403.68552

Two-Sample Test

Wilcoxon Two-Sample Test
Statistic Z Pr > Z Pr > |Z| t Approximation
Pr > Z Pr > |Z|
Z includes a continuity correction of 0.5.
7944202 34.7246 <.0001 <.0001 <.0001 <.0001

Kruskal-Wallis Test

Kruskal-Wallis Test
Chi-Square DF Pr > ChiSq
1205.7974 1 <.0001

Box Plot

Sex = Male Data Minimum = 54 Minimum Whisker = 54 First Quartile = 2521 Median = 3628.5 Third Quartile = 4431 Maximum Whisker = 5199 Data Maximum = 5199 Mean = 3403.7 Standard Deviation = 1225.4 Number of Observations = 2334 Sum of Weight = . Sex = Male Data Minimum = 54 Minimum Whisker = 54 First Quartile = 2521 Median = 3628.5 Third Quartile = 4431 Maximum Whisker = 5199 Data Maximum = 5199 Mean = 3403.7 Standard Deviation = 1225.4 Number of Observations = 2334 Sum of Weight = . Sex = Male Data Minimum = 54 Minimum Whisker = 54 First Quartile = 2521 Median = 3628.5 Third Quartile = 4431 Maximum Whisker = 5199 Data Maximum = 5199 Mean = 3403.7 Standard Deviation = 1225.4 Number of Observations = 2334 Sum of Weight = . Sex = Male Data Minimum = 54 Minimum Whisker = 54 First Quartile = 2521 Median = 3628.5 Third Quartile = 4431 Maximum Whisker = 5199 Data Maximum = 5199 Mean = 3403.7 Standard Deviation = 1225.4 Number of Observations = 2334 Sum of Weight = . Sex = Male Data Minimum = 54 Minimum Whisker = 54 First Quartile = 2521 Median = 3628.5 Third Quartile = 4431 Maximum Whisker = 5199 Data Maximum = 5199 Mean = 3403.7 Standard Deviation = 1225.4 Number of Observations = 2334 Sum of Weight = . Sex = Male Data Minimum = 54 Minimum Whisker = 54 First Quartile = 2521 Median = 3628.5 Third Quartile = 4431 Maximum Whisker = 5199 Data Maximum = 5199 Mean = 3403.7 Standard Deviation = 1225.4 Number of Observations = 2334 Sum of Weight = . Sex = Male Data Minimum = 54 Minimum Whisker = 54 First Quartile = 2521 Median = 3628.5 Third Quartile = 4431 Maximum Whisker = 5199 Data Maximum = 5199 Mean = 3403.7 Standard Deviation = 1225.4 Number of Observations = 2334 Sum of Weight = . Sex = Male Data Minimum = 54 Minimum Whisker = 54 First Quartile = 2521 Median = 3628.5 Third Quartile = 4431 Maximum Whisker = 5199 Data Maximum = 5199 Mean = 3403.7 Standard Deviation = 1225.4 Number of Observations = 2334 Sum of Weight = . Sex = Female Data Minimum = 1 Minimum Whisker = 1 First Quartile = 755.5 Median = 1735 Third Quartile = 2880 Maximum Whisker = 5202.5 Data Maximum = 5202.5 Mean = 1949.8 Standard Deviation = 1386.4 Number of Observations = 2869 Sum of Weight = . Sex = Female Data Minimum = 1 Minimum Whisker = 1 First Quartile = 755.5 Median = 1735 Third Quartile = 2880 Maximum Whisker = 5202.5 Data Maximum = 5202.5 Mean = 1949.8 Standard Deviation = 1386.4 Number of Observations = 2869 Sum of Weight = . Sex = Female Data Minimum = 1 Minimum Whisker = 1 First Quartile = 755.5 Median = 1735 Third Quartile = 2880 Maximum Whisker = 5202.5 Data Maximum = 5202.5 Mean = 1949.8 Standard Deviation = 1386.4 Number of Observations = 2869 Sum of Weight = . Sex = Female Data Minimum = 1 Minimum Whisker = 1 First Quartile = 755.5 Median = 1735 Third Quartile = 2880 Maximum Whisker = 5202.5 Data Maximum = 5202.5 Mean = 1949.8 Standard Deviation = 1386.4 Number of Observations = 2869 Sum of Weight = . Sex = Female Data Minimum = 1 Minimum Whisker = 1 First Quartile = 755.5 Median = 1735 Third Quartile = 2880 Maximum Whisker = 5202.5 Data Maximum = 5202.5 Mean = 1949.8 Standard Deviation = 1386.4 Number of Observations = 2869 Sum of Weight = . Sex = Female Data Minimum = 1 Minimum Whisker = 1 First Quartile = 755.5 Median = 1735 Third Quartile = 2880 Maximum Whisker = 5202.5 Data Maximum = 5202.5 Mean = 1949.8 Standard Deviation = 1386.4 Number of Observations = 2869 Sum of Weight = . Sex = Female Data Minimum = 1 Minimum Whisker = 1 First Quartile = 755.5 Median = 1735 Third Quartile = 2880 Maximum Whisker = 5202.5 Data Maximum = 5202.5 Mean = 1949.8 Standard Deviation = 1386.4 Number of Observations = 2869 Sum of Weight = . Sex = Female Data Minimum = 1 Minimum Whisker = 1 First Quartile = 755.5 Median = 1735 Third Quartile = 2880 Maximum Whisker = 5202.5 Data Maximum = 5202.5 Mean = 1949.8 Standard Deviation = 1386.4 Number of Observations = 2869 Sum of Weight = .
Box Plot of Wilcoxon Scores for Weight Classified by Sex
  • “The three tests for normality, for both values of Sex, show p-values less than .05, leading us to reject the null hypothesis that the distribution of weight for females and males is normally distributed. Look at the histogram and Q-Q plots to determine if parametric tests are appropriate.”
  • “There are two different confidence limits listed and two t- and p-values in the table; one set of values is computed assuming that the two groups have equal variance; the other set of values is computed assuming unequal variance. The most common strategy to choose Which set of values is to examine the F test, which tests the equality of variances for the groups. (The null hypothesis is that the variances are equal; the alternative hypothesis is that they are not equal.) If the p-value for this test is less than .05, you choose the t- and p- values under the assumption of unequal variances (labeled Satterthwaite); if the p-value is greater than .05 (in this case it is .0503), you use the values based on equal variances (labeled Pooled) which has t-value of -36.20 and p-value of <.0001. Based on the test of homogeneity of variance p-value of .0503, we use the pooled values in the table. We reject the null hypothesis that the populations from which you took the female and male weight samples have equal means, and conclude that the female mean was less than the male mean.”
  • *(Nonparametric Two-sample Tests performed on same data for optional reference.)

Nonparametric Two-sample Tests.

SAS Code, click to expand

SAS Code:

#  (&path1 and biostats libname previously defined)
/* Nonparametric Two-sample Tests - generated code - start */

/* Test for normality */
title1 "Performing Normality Tests on Pike vs. Roach Fish";
proc univariate data=sashelp.fish normal mu0=0;
    ods select TestsForNormality;
    where (Species EQ "Pike") OR (Species EQ "Roach");
    class Species;
    var Weight;
run;

/* t test */
title1 "Unpaired t Test on Pike vs. Roach Fish";
proc ttest data=sashelp.fish sides=2 h0=0 plots(only showh0)=(summaryPlot 
        qqplot);
    where (Species EQ "Pike") OR (Species EQ "Roach");
    class Species;
    var Weight;
run;

/* Nonparametric test */
title1 "Nonparametric Two-sample Tests on Pike vs. Roach Fish";
proc npar1way data=sashelp.fish wilcoxon plots=wilcoxonplot;
    where (Species EQ "Pike") OR (Species EQ "Roach");
    class Species;
    var Weight;
run;
title1;

/* "We see smaller sample sizes for the two fish species (n=20 for Roach and n=17 for Pike) compared to our previous example.  The tests for normality reject the null hypothesis that these weights for Pike come from a population that is normally distributed, and the histograms show a distribution that is not symmetric or normal.  Time to use nonparametric tests."  */ 

/* "The Wilcoxon rank sum test shows the sum of ranks for the two fish species.  If the null hypothesis is true, you would expect the sum of ranks to be about the same for both groups, which they are not.  This is also reflected on the histograms which show Roach fish being lighter than Pike fish.  There are two p-values shown in the Wilcoxon Two-Sample Test section: a z-test (with a correction for continuity) for larger samples; and a t approximation sometimes used for smaller samples (such as this example).  both p-values are tiny (<.0001) which implies that Roach fish are lighter than Pike fish." */

/* Nonparametric Two-sample Tests - generated code - end */

SAS Output

Results: biostats_by_ex_SAScode.sas

Results: biostats_by_ex_SAScode.sas

Performing Normality Tests on Pike vs. Roach Fish

Variable: Weight

Species = Pike

The Univariate Procedure

Weight

Species = Pike

Tests For Normality

Tests for Normality
Test Statistic p Value
Shapiro-Wilk W 0.821287 Pr < W 0.0040
Kolmogorov-Smirnov D 0.267641 Pr > D <0.0100
Cramer-von Mises W-Sq 0.218639 Pr > W-Sq <0.0050
Anderson-Darling A-Sq 1.255384 Pr > A-Sq <0.0050

Performing Normality Tests on Pike vs. Roach Fish

Variable: Weight

Species = Roach

Species = Roach

Tests For Normality

Tests for Normality
Test Statistic p Value
Shapiro-Wilk W 0.932277 Pr < W 0.1708
Kolmogorov-Smirnov D 0.176514 Pr > D 0.0986
Cramer-von Mises W-Sq 0.102833 Pr > W-Sq 0.0968
Anderson-Darling A-Sq 0.572359 Pr > A-Sq 0.1243

The Ttest Procedure

Weight

Unpaired t Test on Pike vs. Roach Fish

Variable: Weight

 

 

Statistics

Species Method N Mean Std Dev Std Err Minimum Maximum
Pike   17 718.7 494.1 119.8 200.0 1650.0
Roach   20 152.1 88.8289 19.8627 0 390.0
Diff (1-2) Pooled   566.7 340.5 112.3    
Diff (1-2) Satterthwaite   566.7   121.5    

Confidence Limits

Species Method Mean 95% CL Mean Std Dev 95% CL Std Dev
Pike   718.7 464.6 972.8 494.1 368.0 752.0
Roach   152.1 110.5 193.6 88.8289 67.5535 129.7
Diff (1-2) Pooled 566.7 338.7 794.7 340.5 276.1 444.1
Diff (1-2) Satterthwaite 566.7 310.2 823.1      

T-Tests

Method Variances DF t Value Pr > |t|
Pooled Equal 35 5.05 <.0001
Satterthwaite Unequal 16.88 4.66 0.0002

Equality of Variances

Equality of Variances
Method Num DF Den DF F Value Pr > F
Folded F 16 19 30.95 <.0001

Summary Panel

Weight = 2329.7 Percent = 0.2165 Weight = 2318.4 Percent = 0.2418 Weight = 2318.4 Percent = 0.2418 Weight = 2307 Percent = 0.2696 Weight = 2307 Percent = 0.2696 Weight = 2295.7 Percent = 0.3001 Weight = 2295.7 Percent = 0.3001 Weight = 2284.4 Percent = 0.3335 Weight = 2284.4 Percent = 0.3335 Weight = 2273 Percent = 0.37 Weight = 2273 Percent = 0.37 Weight = 2261.7 Percent = 0.4097 Weight = 2261.7 Percent = 0.4097 Weight = 2250.4 Percent = 0.453 Weight = 2250.4 Percent = 0.453 Weight = 2239.1 Percent = 0.4999 Weight = 2239.1 Percent = 0.4999 Weight = 2227.7 Percent = 0.5508 Weight = 2227.7 Percent = 0.5508 Weight = 2216.4 Percent = 0.6058 Weight = 2216.4 Percent = 0.6058 Weight = 2205.1 Percent = 0.6652 Weight = 2205.1 Percent = 0.6652 Weight = 2193.8 Percent = 0.7292 Weight = 2193.8 Percent = 0.7292 Weight = 2182.4 Percent = 0.7979 Weight = 2182.4 Percent = 0.7979 Weight = 2171.1 Percent = 0.8717 Weight = 2171.1 Percent = 0.8717 Weight = 2159.8 Percent = 0.9506 Weight = 2159.8 Percent = 0.9506 Weight = 2148.4 Percent = 1.035 Weight = 2148.4 Percent = 1.035 Weight = 2137.1 Percent = 1.1249 Weight = 2137.1 Percent = 1.1249 Weight = 2125.8 Percent = 1.2205 Weight = 2125.8 Percent = 1.2205 Weight = 2114.5 Percent = 1.322 Weight = 2114.5 Percent = 1.322 Weight = 2103.1 Percent = 1.4296 Weight = 2103.1 Percent = 1.4296 Weight = 2091.8 Percent = 1.5433 Weight = 2091.8 Percent = 1.5433 Weight = 2080.5 Percent = 1.6633 Weight = 2080.5 Percent = 1.6633 Weight = 2069.1 Percent = 1.7895 Weight = 2069.1 Percent = 1.7895 Weight = 2057.8 Percent = 1.9222 Weight = 2057.8 Percent = 1.9222 Weight = 2046.5 Percent = 2.0611 Weight = 2046.5 Percent = 2.0611 Weight = 2035.2 Percent = 2.2065 Weight = 2035.2 Percent = 2.2065 Weight = 2023.8 Percent = 2.3581 Weight = 2023.8 Percent = 2.3581 Weight = 2012.5 Percent = 2.516 Weight = 2012.5 Percent = 2.516 Weight = 2001.2 Percent = 2.6799 Weight = 2001.2 Percent = 2.6799 Weight = 1989.8 Percent = 2.8498 Weight = 1989.8 Percent = 2.8498 Weight = 1978.5 Percent = 3.0255 Weight = 1978.5 Percent = 3.0255 Weight = 1967.2 Percent = 3.2067 Weight = 1967.2 Percent = 3.2067 Weight = 1944.5 Percent = 3.5845 Weight = 1944.5 Percent = 3.5845 Weight = 1921.9 Percent = 3.9807 Weight = 1921.9 Percent = 3.9807 Weight = 1819.9 Percent = 5.8907 Weight = 1819.9 Percent = 5.8907 Weight = 1785.9 Percent = 6.5248 Weight = 1785.9 Percent = 6.5248 Weight = 1763.3 Percent = 6.9317 Weight = 1763.3 Percent = 6.9317 Weight = 1740.6 Percent = 7.3197 Weight = 1740.6 Percent = 7.3197 Weight = 1729.3 Percent = 7.5051 Weight = 1729.3 Percent = 7.5051 Weight = 1718 Percent = 7.6839 Weight = 1718 Percent = 7.6839 Weight = 1706.6 Percent = 7.8555 Weight = 1706.6 Percent = 7.8555 Weight = 1695.3 Percent = 8.0195 Weight = 1695.3 Percent = 8.0195 Weight = 1684 Percent = 8.1754 Weight = 1684 Percent = 8.1754 Weight = 1672.7 Percent = 8.3226 Weight = 1672.7 Percent = 8.3226 Weight = 1661.3 Percent = 8.4608 Weight = 1661.3 Percent = 8.4608 Weight = 1650 Percent = 8.5897 Weight = 1650 Percent = 8.5897 Weight = 1638.7 Percent = 8.7089 Weight = 1638.7 Percent = 8.7089 Weight = 1627.3 Percent = 8.8182 Weight = 1627.3 Percent = 8.8182 Weight = 1616 Percent = 8.9174 Weight = 1616 Percent = 8.9174 Weight = 1604.7 Percent = 9.0063 Weight = 1604.7 Percent = 9.0063 Weight = 1593.4 Percent = 9.085 Weight = 1593.4 Percent = 9.085 Weight = 1582 Percent = 9.1534 Weight = 1582 Percent = 9.1534 Weight = 1570.7 Percent = 9.2114 Weight = 1570.7 Percent = 9.2114 Weight = 1559.4 Percent = 9.2594 Weight = 1559.4 Percent = 9.2594 Weight = 1548 Percent = 9.2973 Weight = 1548 Percent = 9.2973 Weight = 1536.7 Percent = 9.3254 Weight = 1536.7 Percent = 9.3254 Weight = 1525.4 Percent = 9.3441 Weight = 1525.4 Percent = 9.3441 Weight = 1514.1 Percent = 9.3536 Weight = 1514.1 Percent = 9.3536 Weight = 1502.7 Percent = 9.3543 Weight = 1502.7 Percent = 9.3543 Weight = 1491.4 Percent = 9.3467 Weight = 1491.4 Percent = 9.3467 Weight = 1480.1 Percent = 9.3313 Weight = 1480.1 Percent = 9.3313 Weight = 1468.8 Percent = 9.3084 Weight = 1468.8 Percent = 9.3084 Weight = 1457.4 Percent = 9.2788 Weight = 1457.4 Percent = 9.2788 Weight = 1446.1 Percent = 9.243 Weight = 1446.1 Percent = 9.243 Weight = 1434.8 Percent = 9.2016 Weight = 1434.8 Percent = 9.2016 Weight = 1423.4 Percent = 9.1553 Weight = 1423.4 Percent = 9.1553 Weight = 1412.1 Percent = 9.1048 Weight = 1412.1 Percent = 9.1048 Weight = 1400.8 Percent = 9.0506 Weight = 1400.8 Percent = 9.0506 Weight = 1389.5 Percent = 8.9937 Weight = 1389.5 Percent = 8.9937 Weight = 1344.1 Percent = 8.7516 Weight = 1344.1 Percent = 8.7516 Weight = 1321.5 Percent = 8.6323 Weight = 1321.5 Percent = 8.6323 Weight = 1310.2 Percent = 8.5756 Weight = 1310.2 Percent = 8.5756 Weight = 1298.8 Percent = 8.5218 Weight = 1298.8 Percent = 8.5218 Weight = 1287.5 Percent = 8.4715 Weight = 1287.5 Percent = 8.4715 Weight = 1276.2 Percent = 8.4256 Weight = 1276.2 Percent = 8.4256 Weight = 1264.8 Percent = 8.3845 Weight = 1264.8 Percent = 8.3845 Weight = 1253.5 Percent = 8.3491 Weight = 1253.5 Percent = 8.3491 Weight = 1242.2 Percent = 8.3198 Weight = 1242.2 Percent = 8.3198 Weight = 1230.9 Percent = 8.2974 Weight = 1230.9 Percent = 8.2974 Weight = 1219.5 Percent = 8.2823 Weight = 1219.5 Percent = 8.2823 Weight = 1208.2 Percent = 8.2752 Weight = 1208.2 Percent = 8.2752 Weight = 1196.9 Percent = 8.2766 Weight = 1196.9 Percent = 8.2766 Weight = 1185.5 Percent = 8.287 Weight = 1185.5 Percent = 8.287 Weight = 1174.2 Percent = 8.3071 Weight = 1174.2 Percent = 8.3071 Weight = 1162.9 Percent = 8.3371 Weight = 1162.9 Percent = 8.3371 Weight = 1151.6 Percent = 8.3777 Weight = 1151.6 Percent = 8.3777 Weight = 1140.2 Percent = 8.4292 Weight = 1140.2 Percent = 8.4292 Weight = 1128.9 Percent = 8.4921 Weight = 1128.9 Percent = 8.4921 Weight = 1117.6 Percent = 8.5668 Weight = 1117.6 Percent = 8.5668 Weight = 1106.3 Percent = 8.6537 Weight = 1106.3 Percent = 8.6537 Weight = 1094.9 Percent = 8.7532 Weight = 1094.9 Percent = 8.7532 Weight = 1083.6 Percent = 8.8656 Weight = 1083.6 Percent = 8.8656 Weight = 1072.3 Percent = 8.9913 Weight = 1072.3 Percent = 8.9913 Weight = 1060.9 Percent = 9.1305 Weight = 1060.9 Percent = 9.1305 Weight = 1049.6 Percent = 9.2836 Weight = 1049.6 Percent = 9.2836 Weight = 1038.3 Percent = 9.4508 Weight = 1038.3 Percent = 9.4508 Weight = 1027 Percent = 9.6323 Weight = 1027 Percent = 9.6323 Weight = 1015.6 Percent = 9.8283 Weight = 1015.6 Percent = 9.8283 Weight = 1004.3 Percent = 10.039 Weight = 1004.3 Percent = 10.039 Weight = 992.97 Percent = 10.265 Weight = 992.97 Percent = 10.265 Weight = 981.64 Percent = 10.505 Weight = 981.64 Percent = 10.505 Weight = 970.31 Percent = 10.761 Weight = 970.31 Percent = 10.761 Weight = 958.98 Percent = 11.032 Weight = 958.98 Percent = 11.032 Weight = 947.66 Percent = 11.318 Weight = 947.66 Percent = 11.318 Weight = 936.33 Percent = 11.619 Weight = 936.33 Percent = 11.619 Weight = 925 Percent = 11.934 Weight = 925 Percent = 11.934 Weight = 913.67 Percent = 12.265 Weight = 913.67 Percent = 12.265 Weight = 902.34 Percent = 12.61 Weight = 902.34 Percent = 12.61 Weight = 891.02 Percent = 12.969 Weight = 891.02 Percent = 12.969 Weight = 879.69 Percent = 13.343 Weight = 879.69 Percent = 13.343 Weight = 868.36 Percent = 13.729 Weight = 868.36 Percent = 13.729 Weight = 857.03 Percent = 14.129 Weight = 857.03 Percent = 14.129 Weight = 834.38 Percent = 14.966 Weight = 834.38 Percent = 14.966 Weight = 811.72 Percent = 15.848 Weight = 811.72 Percent = 15.848 Weight = 789.06 Percent = 16.768 Weight = 789.06 Percent = 16.768 Weight = 698.44 Percent = 20.659 Weight = 698.44 Percent = 20.659 Weight = 664.45 Percent = 22.108 Weight = 664.45 Percent = 22.108 Weight = 641.8 Percent = 23.038 Weight = 641.8 Percent = 23.038 Weight = 619.14 Percent = 23.923 Weight = 619.14 Percent = 23.923 Weight = 607.81 Percent = 24.344 Weight = 607.81 Percent = 24.344 Weight = 596.48 Percent = 24.748 Weight = 596.48 Percent = 24.748 Weight = 585.16 Percent = 25.134 Weight = 585.16 Percent = 25.134 Weight = 573.83 Percent = 25.5 Weight = 573.83 Percent = 25.5 Weight = 562.5 Percent = 25.845 Weight = 562.5 Percent = 25.845 Weight = 551.17 Percent = 26.167 Weight = 551.17 Percent = 26.167 Weight = 539.84 Percent = 26.464 Weight = 539.84 Percent = 26.464 Weight = 528.52 Percent = 26.735 Weight = 528.52 Percent = 26.735 Weight = 517.19 Percent = 26.978 Weight = 517.19 Percent = 26.978 Weight = 505.86 Percent = 27.193 Weight = 505.86 Percent = 27.193 Weight = 494.53 Percent = 27.378 Weight = 494.53 Percent = 27.378 Weight = 483.2 Percent = 27.532 Weight = 483.2 Percent = 27.532 Weight = 471.88 Percent = 27.655 Weight = 471.88 Percent = 27.655 Weight = 460.55 Percent = 27.744 Weight = 460.55 Percent = 27.744 Weight = 449.22 Percent = 27.8 Weight = 449.22 Percent = 27.8 Weight = 437.89 Percent = 27.823 Weight = 437.89 Percent = 27.823 Weight = 426.56 Percent = 27.81 Weight = 426.56 Percent = 27.81 Weight = 415.23 Percent = 27.764 Weight = 415.23 Percent = 27.764 Weight = 403.91 Percent = 27.682 Weight = 403.91 Percent = 27.682 Weight = 392.58 Percent = 27.566 Weight = 392.58 Percent = 27.566 Weight = 381.25 Percent = 27.415 Weight = 381.25 Percent = 27.415 Weight = 369.92 Percent = 27.23 Weight = 369.92 Percent = 27.23 Weight = 358.59 Percent = 27.011 Weight = 358.59 Percent = 27.011 Weight = 347.27 Percent = 26.759 Weight = 347.27 Percent = 26.759 Weight = 335.94 Percent = 26.474 Weight = 335.94 Percent = 26.474 Weight = 324.61 Percent = 26.158 Weight = 324.61 Percent = 26.158 Weight = 313.28 Percent = 25.812 Weight = 313.28 Percent = 25.812 Weight = 301.95 Percent = 25.436 Weight = 301.95 Percent = 25.436 Weight = 290.63 Percent = 25.031 Weight = 290.63 Percent = 25.031 Weight = 279.3 Percent = 24.601 Weight = 279.3 Percent = 24.601 Weight = 267.97 Percent = 24.144 Weight = 267.97 Percent = 24.144 Weight = 256.64 Percent = 23.664 Weight = 256.64 Percent = 23.664 Weight = 245.31 Percent = 23.162 Weight = 245.31 Percent = 23.162 Weight = 233.98 Percent = 22.639 Weight = 233.98 Percent = 22.639 Weight = 222.66 Percent = 22.098 Weight = 222.66 Percent = 22.098 Weight = 211.33 Percent = 21.539 Weight = 211.33 Percent = 21.539 Weight = 75.391 Percent = 14.194 Weight = 75.391 Percent = 14.194 Weight = 41.406 Percent = 12.383 Weight = 41.406 Percent = 12.383 Weight = 18.75 Percent = 11.223 Weight = 18.75 Percent = 11.223 Weight = -3.906 Percent = 10.113 Weight = -3.906 Percent = 10.113 Weight = -26.56 Percent = 9.0585 Weight = -26.56 Percent = 9.0585 Weight = -37.89 Percent = 8.5543 Weight = -37.89 Percent = 8.5543 Weight = -49.22 Percent = 8.0662 Weight = -49.22 Percent = 8.0662 Weight = -60.55 Percent = 7.5946 Weight = -60.55 Percent = 7.5946 Weight = -71.88 Percent = 7.1399 Weight = -71.88 Percent = 7.1399 Weight = -83.2 Percent = 6.7023 Weight = -83.2 Percent = 6.7023 Weight = -94.53 Percent = 6.2821 Weight = -94.53 Percent = 6.2821 Weight = -105.9 Percent = 5.8795 Weight = -105.9 Percent = 5.8795 Weight = -117.2 Percent = 5.4943 Weight = -117.2 Percent = 5.4943 Weight = -128.5 Percent = 5.1266 Weight = -128.5 Percent = 5.1266 Weight = -139.8 Percent = 4.7762 Weight = -139.8 Percent = 4.7762 Weight = -151.2 Percent = 4.4431 Weight = -151.2 Percent = 4.4431 Weight = -162.5 Percent = 4.1269 Weight = -162.5 Percent = 4.1269 Weight = -173.8 Percent = 3.8273 Weight = -173.8 Percent = 3.8273 Weight = -185.2 Percent = 3.5441 Weight = -185.2 Percent = 3.5441 Weight = -196.5 Percent = 3.2768 Weight = -196.5 Percent = 3.2768 Weight = -207.8 Percent = 3.025 Weight = -207.8 Percent = 3.025 Weight = -219.1 Percent = 2.7883 Weight = -219.1 Percent = 2.7883 Weight = -230.5 Percent = 2.5661 Weight = -230.5 Percent = 2.5661 Weight = -241.8 Percent = 2.358 Weight = -241.8 Percent = 2.358 Weight = -253.1 Percent = 2.1634 Weight = -253.1 Percent = 2.1634 Weight = -264.5 Percent = 1.9818 Weight = -264.5 Percent = 1.9818 Weight = -275.8 Percent = 1.8126 Weight = -275.8 Percent = 1.8126 Weight = -287.1 Percent = 1.6552 Weight = -287.1 Percent = 1.6552 Weight = -298.4 Percent = 1.5092 Weight = -298.4 Percent = 1.5092 Weight = -309.8 Percent = 1.3739 Weight = -309.8 Percent = 1.3739 Weight = -321.1 Percent = 1.2488 Weight = -321.1 Percent = 1.2488 Weight = -332.4 Percent = 1.1333 Weight = -332.4 Percent = 1.1333 Weight = -343.8 Percent = 1.0268 Weight = -343.8 Percent = 1.0268 Weight = -355.1 Percent = 0.9289 Weight = -355.1 Percent = 0.9289 Weight = -366.4 Percent = 0.839 Weight = -366.4 Percent = 0.839 Weight = -377.7 Percent = 0.7566 Weight = -377.7 Percent = 0.7566 Weight = -389.1 Percent = 0.6813 Weight = -389.1 Percent = 0.6813 Weight = -400.4 Percent = 0.6124 Weight = -400.4 Percent = 0.6124 Weight = -411.7 Percent = 0.5496 Weight = -411.7 Percent = 0.5496 Weight = -423 Percent = 0.4925 Weight = -423 Percent = 0.4925 Weight = -434.4 Percent = 0.4407 Weight = -434.4 Percent = 0.4407 Weight = -445.7 Percent = 0.3936 Weight = -445.7 Percent = 0.3936 Weight = -457 Percent = 0.351 Weight = -457 Percent = 0.351 Weight = -468.4 Percent = 0.3125 Weight = -468.4 Percent = 0.3125 Weight = -479.7 Percent = 0.2778 Weight = 2201.1 Percent = 0.2691 Weight = 2186.2 Percent = 0.2945 Weight = 2186.2 Percent = 0.2945 Weight = 2171.2 Percent = 0.3221 Weight = 2171.2 Percent = 0.3221 Weight = 2156.2 Percent = 0.352 Weight = 2156.2 Percent = 0.352 Weight = 2141.2 Percent = 0.3842 Weight = 2141.2 Percent = 0.3842 Weight = 2126.3 Percent = 0.4191 Weight = 2126.3 Percent = 0.4191 Weight = 2111.3 Percent = 0.4566 Weight = 2111.3 Percent = 0.4566 Weight = 2096.3 Percent = 0.4971 Weight = 2096.3 Percent = 0.4971 Weight = 2081.3 Percent = 0.5407 Weight = 2081.3 Percent = 0.5407 Weight = 2066.4 Percent = 0.5875 Weight = 2066.4 Percent = 0.5875 Weight = 2051.4 Percent = 0.6379 Weight = 2051.4 Percent = 0.6379 Weight = 2036.4 Percent = 0.6919 Weight = 2036.4 Percent = 0.6919 Weight = 2021.4 Percent = 0.7498 Weight = 2021.4 Percent = 0.7498 Weight = 2006.5 Percent = 0.8117 Weight = 2006.5 Percent = 0.8117 Weight = 1991.5 Percent = 0.878 Weight = 1991.5 Percent = 0.878 Weight = 1976.5 Percent = 0.9489 Weight = 1976.5 Percent = 0.9489 Weight = 1961.5 Percent = 1.0245 Weight = 1961.5 Percent = 1.0245 Weight = 1946.6 Percent = 1.1051 Weight = 1946.6 Percent = 1.1051 Weight = 1931.6 Percent = 1.191 Weight = 1931.6 Percent = 1.191 Weight = 1916.6 Percent = 1.2824 Weight = 1916.6 Percent = 1.2824 Weight = 1901.6 Percent = 1.3795 Weight = 1901.6 Percent = 1.3795 Weight = 1886.7 Percent = 1.4826 Weight = 1886.7 Percent = 1.4826 Weight = 1871.7 Percent = 1.592 Weight = 1871.7 Percent = 1.592 Weight = 1856.7 Percent = 1.7078 Weight = 1856.7 Percent = 1.7078 Weight = 1841.8 Percent = 1.8304 Weight = 1841.8 Percent = 1.8304 Weight = 1826.8 Percent = 1.96 Weight = 1826.8 Percent = 1.96 Weight = 1811.8 Percent = 2.0969 Weight = 1811.8 Percent = 2.0969 Weight = 1796.8 Percent = 2.2412 Weight = 1796.8 Percent = 2.2412 Weight = 1781.9 Percent = 2.3933 Weight = 1781.9 Percent = 2.3933 Weight = 1766.9 Percent = 2.5534 Weight = 1766.9 Percent = 2.5534 Weight = 1751.9 Percent = 2.7217 Weight = 1751.9 Percent = 2.7217 Weight = 1736.9 Percent = 2.8984 Weight = 1736.9 Percent = 2.8984 Weight = 1722 Percent = 3.0837 Weight = 1722 Percent = 3.0837 Weight = 1707 Percent = 3.2779 Weight = 1707 Percent = 3.2779 Weight = 1692 Percent = 3.4811 Weight = 1692 Percent = 3.4811 Weight = 1677 Percent = 3.6935 Weight = 1677 Percent = 3.6935 Weight = 1662.1 Percent = 3.9153 Weight = 1662.1 Percent = 3.9153 Weight = 1647.1 Percent = 4.1465 Weight = 1647.1 Percent = 4.1465 Weight = 1632.1 Percent = 4.3874 Weight = 1632.1 Percent = 4.3874 Weight = 1617.1 Percent = 4.6381 Weight = 1617.1 Percent = 4.6381 Weight = 1602.2 Percent = 4.8985 Weight = 1602.2 Percent = 4.8985 Weight = 1587.2 Percent = 5.1689 Weight = 1587.2 Percent = 5.1689 Weight = 1572.2 Percent = 5.4491 Weight = 1572.2 Percent = 5.4491 Weight = 1557.2 Percent = 5.7393 Weight = 1557.2 Percent = 5.7393 Weight = 1542.3 Percent = 6.0394 Weight = 1542.3 Percent = 6.0394 Weight = 1527.3 Percent = 6.3493 Weight = 1527.3 Percent = 6.3493 Weight = 1497.4 Percent = 6.9984 Weight = 1497.4 Percent = 6.9984 Weight = 1467.4 Percent = 7.6856 Weight = 1467.4 Percent = 7.6856 Weight = 1437.5 Percent = 8.4093 Weight = 1437.5 Percent = 8.4093 Weight = 1407.5 Percent = 9.1675 Weight = 1407.5 Percent = 9.1675 Weight = 1377.6 Percent = 9.9573 Weight = 1377.6 Percent = 9.9573 Weight = 1153 Percent = 16.462 Weight = 1153 Percent = 16.462 Weight = 1108 Percent = 17.758 Weight = 1108 Percent = 17.758 Weight = 1078.1 Percent = 18.592 Weight = 1078.1 Percent = 18.592 Weight = 1048.1 Percent = 19.394 Weight = 1048.1 Percent = 19.394 Weight = 1018.2 Percent = 20.157 Weight = 1018.2 Percent = 20.157 Weight = 1003.2 Percent = 20.521 Weight = 1003.2 Percent = 20.521 Weight = 988.24 Percent = 20.873 Weight = 988.24 Percent = 20.873 Weight = 973.26 Percent = 21.211 Weight = 973.26 Percent = 21.211 Weight = 958.29 Percent = 21.534 Weight = 958.29 Percent = 21.534 Weight = 943.32 Percent = 21.843 Weight = 943.32 Percent = 21.843 Weight = 928.34 Percent = 22.136 Weight = 928.34 Percent = 22.136 Weight = 913.37 Percent = 22.412 Weight = 913.37 Percent = 22.412 Weight = 898.39 Percent = 22.671 Weight = 898.39 Percent = 22.671 Weight = 883.42 Percent = 22.911 Weight = 883.42 Percent = 22.911 Weight = 868.45 Percent = 23.133 Weight = 868.45 Percent = 23.133 Weight = 853.47 Percent = 23.336 Weight = 853.47 Percent = 23.336 Weight = 838.5 Percent = 23.519 Weight = 838.5 Percent = 23.519 Weight = 823.52 Percent = 23.682 Weight = 823.52 Percent = 23.682 Weight = 808.55 Percent = 23.823 Weight = 808.55 Percent = 23.823 Weight = 793.58 Percent = 23.944 Weight = 793.58 Percent = 23.944 Weight = 778.6 Percent = 24.043 Weight = 778.6 Percent = 24.043 Weight = 763.63 Percent = 24.12 Weight = 763.63 Percent = 24.12 Weight = 748.65 Percent = 24.176 Weight = 748.65 Percent = 24.176 Weight = 733.68 Percent = 24.209 Weight = 733.68 Percent = 24.209 Weight = 718.71 Percent = 24.22 Weight = 718.71 Percent = 24.22 Weight = 703.73 Percent = 24.209 Weight = 703.73 Percent = 24.209 Weight = 688.76 Percent = 24.176 Weight = 688.76 Percent = 24.176 Weight = 673.78 Percent = 24.12 Weight = 673.78 Percent = 24.12 Weight = 658.81 Percent = 24.043 Weight = 658.81 Percent = 24.043 Weight = 643.84 Percent = 23.944 Weight = 643.84 Percent = 23.944 Weight = 628.86 Percent = 23.823 Weight = 628.86 Percent = 23.823 Weight = 613.89 Percent = 23.682 Weight = 613.89 Percent = 23.682 Weight = 598.91 Percent = 23.519 Weight = 598.91 Percent = 23.519 Weight = 583.94 Percent = 23.336 Weight = 583.94 Percent = 23.336 Weight = 568.97 Percent = 23.133 Weight = 568.97 Percent = 23.133 Weight = 553.99 Percent = 22.911 Weight = 553.99 Percent = 22.911 Weight = 539.02 Percent = 22.671 Weight = 539.02 Percent = 22.671 Weight = 524.04 Percent = 22.412 Weight = 524.04 Percent = 22.412 Weight = 509.07 Percent = 22.136 Weight = 509.07 Percent = 22.136 Weight = 494.1 Percent = 21.843 Weight = 494.1 Percent = 21.843 Weight = 479.12 Percent = 21.534 Weight = 479.12 Percent = 21.534 Weight = 464.15 Percent = 21.211 Weight = 464.15 Percent = 21.211 Weight = 449.17 Percent = 20.873 Weight = 449.17 Percent = 20.873 Weight = 434.2 Percent = 20.521 Weight = 434.2 Percent = 20.521 Weight = 419.23 Percent = 20.157 Weight = 419.23 Percent = 20.157 Weight = 389.28 Percent = 19.394 Weight = 389.28 Percent = 19.394 Weight = 359.33 Percent = 18.592 Weight = 359.33 Percent = 18.592 Weight = 179.64 Percent = 13.358 Weight = 179.64 Percent = 13.358 Weight = 119.75 Percent = 11.618 Weight = 119.75 Percent = 11.618 Weight = 74.825 Percent = 10.363 Weight = 74.825 Percent = 10.363 Weight = 44.878 Percent = 9.5586 Weight = 44.878 Percent = 9.5586 Weight = 14.93 Percent = 8.7843 Weight = 14.93 Percent = 8.7843 Weight = -15.02 Percent = 8.043 Weight = -15.02 Percent = 8.043 Weight = -44.97 Percent = 7.3374 Weight = -44.97 Percent = 7.3374 Weight = -74.91 Percent = 6.6691 Weight = -74.91 Percent = 6.6691 Weight = -89.89 Percent = 6.3493 Weight = -89.89 Percent = 6.3493 Weight = -104.9 Percent = 6.0394 Weight = -104.9 Percent = 6.0394 Weight = -119.8 Percent = 5.7393 Weight = -119.8 Percent = 5.7393 Weight = -134.8 Percent = 5.4491 Weight = -134.8 Percent = 5.4491 Weight = -149.8 Percent = 5.1689 Weight = -149.8 Percent = 5.1689 Weight = -164.8 Percent = 4.8985 Weight = -164.8 Percent = 4.8985 Weight = -179.7 Percent = 4.6381 Weight = -179.7 Percent = 4.6381 Weight = -194.7 Percent = 4.3874 Weight = -194.7 Percent = 4.3874 Weight = -209.7 Percent = 4.1465 Weight = -209.7 Percent = 4.1465 Weight = -224.7 Percent = 3.9153 Weight = -224.7 Percent = 3.9153 Weight = -239.6 Percent = 3.6935 Weight = -239.6 Percent = 3.6935 Weight = -254.6 Percent = 3.4811 Weight = -254.6 Percent = 3.4811 Weight = -269.6 Percent = 3.2779 Weight = -269.6 Percent = 3.2779 Weight = -284.5 Percent = 3.0837 Weight = -284.5 Percent = 3.0837 Weight = -299.5 Percent = 2.8984 Weight = -299.5 Percent = 2.8984 Weight = -314.5 Percent = 2.7217 Weight = -314.5 Percent = 2.7217 Weight = -329.5 Percent = 2.5534 Weight = -329.5 Percent = 2.5534 Weight = -344.4 Percent = 2.3933 Weight = -344.4 Percent = 2.3933 Weight = -359.4 Percent = 2.2412 Weight = -359.4 Percent = 2.2412 Weight = -374.4 Percent = 2.0969 Weight = -374.4 Percent = 2.0969 Weight = -389.4 Percent = 1.96 Weight = -389.4 Percent = 1.96 Weight = -404.3 Percent = 1.8304 Weight = -404.3 Percent = 1.8304 Weight = -419.3 Percent = 1.7078 Weight = -419.3 Percent = 1.7078 Weight = -434.3 Percent = 1.592 Weight = -434.3 Percent = 1.592 Weight = -449.3 Percent = 1.4826 Weight = -449.3 Percent = 1.4826 Weight = -464.2 Percent = 1.3795 Weight = -464.2 Percent = 1.3795 Weight = -479.2 Percent = 1.2824 Weight = -479.2 Percent = 1.2824 Weight = -494.2 Percent = 1.191 Weight = -494.2 Percent = 1.191 Weight = -509.2 Percent = 1.1051 Weight = -509.2 Percent = 1.1051 Weight = -524.1 Percent = 1.0245 Weight = -524.1 Percent = 1.0245 Weight = -539.1 Percent = 0.9489 Weight = -539.1 Percent = 0.9489 Weight = -554.1 Percent = 0.878 Weight = -554.1 Percent = 0.878 Weight = -569.1 Percent = 0.8117 Weight = -569.1 Percent = 0.8117 Weight = -584 Percent = 0.7498 Weight = -584 Percent = 0.7498 Weight = -599 Percent = 0.6919 Weight = -599 Percent = 0.6919 Weight = -614 Percent = 0.6379 Weight = -614 Percent = 0.6379 Weight = -629 Percent = 0.5875 Weight = -629 Percent = 0.5875 Weight = -643.9 Percent = 0.5407 Weight = -643.9 Percent = 0.5407 Weight = -658.9 Percent = 0.4971 Weight = -658.9 Percent = 0.4971 Weight = -673.9 Percent = 0.4566 Weight = -673.9 Percent = 0.4566 Weight = -688.8 Percent = 0.4191 Weight = -688.8 Percent = 0.4191 Weight = -703.8 Percent = 0.3842 Weight = -703.8 Percent = 0.3842 Weight = -718.8 Percent = 0.352 Weight = -718.8 Percent = 0.352 Weight = -733.8 Percent = 0.3221 Weight = -733.8 Percent = 0.3221 Weight = -748.7 Percent = 0.2945 Weight = -748.7 Percent = 0.2945 Weight = -763.7 Percent = 0.2691 Weight = 1650 Percent = 17.647 Weight = 1650 Percent = 17.647 Weight = 1350 Percent = 5.8824 Weight = 1350 Percent = 5.8824 Weight = 1050 Percent = 5.8824 Weight = 1050 Percent = 5.8824 Weight = 750 Percent = 5.8824 Weight = 750 Percent = 5.8824 Weight = 450 Percent = 58.824 Weight = 450 Percent = 58.824 Weight = 150 Percent = 5.8824 Weight = 150 Percent = 5.8824 Weight = 472.27 Percent = 0.2087 Weight = 469.22 Percent = 0.2625 Weight = 469.22 Percent = 0.2625 Weight = 466.17 Percent = 0.3271 Weight = 466.17 Percent = 0.3271 Weight = 463.13 Percent = 0.4043 Weight = 463.13 Percent = 0.4043 Weight = 460.08 Percent = 0.4953 Weight = 460.08 Percent = 0.4953 Weight = 457.03 Percent = 0.6016 Weight = 457.03 Percent = 0.6016 Weight = 453.98 Percent = 0.7244 Weight = 453.98 Percent = 0.7244 Weight = 450.94 Percent = 0.8648 Weight = 450.94 Percent = 0.8648 Weight = 447.89 Percent = 1.0235 Weight = 447.89 Percent = 1.0235 Weight = 444.84 Percent = 1.2009 Weight = 444.84 Percent = 1.2009 Weight = 441.8 Percent = 1.397 Weight = 441.8 Percent = 1.397 Weight = 438.75 Percent = 1.6111 Weight = 438.75 Percent = 1.6111 Weight = 435.7 Percent = 1.842 Weight = 435.7 Percent = 1.842 Weight = 432.66 Percent = 2.088 Weight = 432.66 Percent = 2.088 Weight = 417.42 Percent = 3.4337 Weight = 417.42 Percent = 3.4337 Weight = 414.38 Percent = 3.6964 Weight = 414.38 Percent = 3.6964 Weight = 411.33 Percent = 3.9453 Weight = 411.33 Percent = 3.9453 Weight = 408.28 Percent = 4.1753 Weight = 408.28 Percent = 4.1753 Weight = 405.23 Percent = 4.3814 Weight = 405.23 Percent = 4.3814 Weight = 402.19 Percent = 4.5591 Weight = 402.19 Percent = 4.5591 Weight = 399.14 Percent = 4.7045 Weight = 399.14 Percent = 4.7045 Weight = 396.09 Percent = 4.8147 Weight = 396.09 Percent = 4.8147 Weight = 393.05 Percent = 4.8877 Weight = 393.05 Percent = 4.8877 Weight = 390 Percent = 4.9225 Weight = 390 Percent = 4.9225 Weight = 386.95 Percent = 4.9195 Weight = 386.95 Percent = 4.9195 Weight = 383.91 Percent = 4.8802 Weight = 383.91 Percent = 4.8802 Weight = 380.86 Percent = 4.8074 Weight = 380.86 Percent = 4.8074 Weight = 377.81 Percent = 4.7051 Weight = 377.81 Percent = 4.7051 Weight = 374.77 Percent = 4.5785 Weight = 374.77 Percent = 4.5785 Weight = 362.58 Percent = 3.9591 Weight = 362.58 Percent = 3.9591 Weight = 359.53 Percent = 3.8134 Weight = 359.53 Percent = 3.8134 Weight = 356.48 Percent = 3.6867 Weight = 356.48 Percent = 3.6867 Weight = 353.44 Percent = 3.5864 Weight = 353.44 Percent = 3.5864 Weight = 350.39 Percent = 3.5193 Weight = 350.39 Percent = 3.5193 Weight = 347.34 Percent = 3.4912 Weight = 347.34 Percent = 3.4912 Weight = 344.3 Percent = 3.5071 Weight = 344.3 Percent = 3.5071 Weight = 341.25 Percent = 3.5708 Weight = 341.25 Percent = 3.5708 Weight = 338.2 Percent = 3.6849 Weight = 338.2 Percent = 3.6849 Weight = 335.16 Percent = 3.8503 Weight = 335.16 Percent = 3.8503 Weight = 332.11 Percent = 4.0669 Weight = 332.11 Percent = 4.0669 Weight = 329.06 Percent = 4.3326 Weight = 329.06 Percent = 4.3326 Weight = 326.02 Percent = 4.6443 Weight = 326.02 Percent = 4.6443 Weight = 322.97 Percent = 4.9971 Weight = 322.97 Percent = 4.9971 Weight = 319.92 Percent = 5.3849 Weight = 319.92 Percent = 5.3849 Weight = 304.69 Percent = 7.562 Weight = 304.69 Percent = 7.562 Weight = 301.64 Percent = 7.9789 Weight = 301.64 Percent = 7.9789 Weight = 298.59 Percent = 8.3673 Weight = 298.59 Percent = 8.3673 Weight = 295.55 Percent = 8.7185 Weight = 295.55 Percent = 8.7185 Weight = 292.5 Percent = 9.025 Weight = 292.5 Percent = 9.025 Weight = 289.45 Percent = 9.2808 Weight = 289.45 Percent = 9.2808 Weight = 286.41 Percent = 9.4817 Weight = 286.41 Percent = 9.4817 Weight = 283.36 Percent = 9.6253 Weight = 283.36 Percent = 9.6253 Weight = 280.31 Percent = 9.7115 Weight = 280.31 Percent = 9.7115 Weight = 277.27 Percent = 9.7423 Weight = 277.27 Percent = 9.7423 Weight = 274.22 Percent = 9.722 Weight = 274.22 Percent = 9.722 Weight = 271.17 Percent = 9.6572 Weight = 271.17 Percent = 9.6572 Weight = 268.13 Percent = 9.5566 Weight = 268.13 Percent = 9.5566 Weight = 265.08 Percent = 9.4308 Weight = 265.08 Percent = 9.4308 Weight = 258.98 Percent = 9.1544 Weight = 258.98 Percent = 9.1544 Weight = 255.94 Percent = 9.0321 Weight = 255.94 Percent = 9.0321 Weight = 252.89 Percent = 8.9408 Weight = 252.89 Percent = 8.9408 Weight = 249.84 Percent = 8.896 Weight = 249.84 Percent = 8.896 Weight = 246.8 Percent = 8.9134 Weight = 246.8 Percent = 8.9134 Weight = 243.75 Percent = 9.008 Weight = 243.75 Percent = 9.008 Weight = 240.7 Percent = 9.1941 Weight = 240.7 Percent = 9.1941 Weight = 237.66 Percent = 9.4846 Weight = 237.66 Percent = 9.4846 Weight = 234.61 Percent = 9.8913 Weight = 234.61 Percent = 9.8913 Weight = 231.56 Percent = 10.424 Weight = 231.56 Percent = 10.424 Weight = 228.52 Percent = 11.09 Weight = 228.52 Percent = 11.09 Weight = 225.47 Percent = 11.895 Weight = 225.47 Percent = 11.895 Weight = 222.42 Percent = 12.843 Weight = 222.42 Percent = 12.843 Weight = 219.38 Percent = 13.934 Weight = 219.38 Percent = 13.934 Weight = 216.33 Percent = 15.165 Weight = 216.33 Percent = 15.165 Weight = 213.28 Percent = 16.534 Weight = 213.28 Percent = 16.534 Weight = 210.23 Percent = 18.031 Weight = 210.23 Percent = 18.031 Weight = 207.19 Percent = 19.647 Weight = 207.19 Percent = 19.647 Weight = 204.14 Percent = 21.369 Weight = 204.14 Percent = 21.369 Weight = 201.09 Percent = 23.182 Weight = 201.09 Percent = 23.182 Weight = 198.05 Percent = 25.067 Weight = 198.05 Percent = 25.067 Weight = 188.91 Percent = 30.952 Weight = 188.91 Percent = 30.952 Weight = 182.81 Percent = 34.831 Weight = 182.81 Percent = 34.831 Weight = 179.77 Percent = 36.684 Weight = 179.77 Percent = 36.684 Weight = 176.72 Percent = 38.446 Weight = 176.72 Percent = 38.446 Weight = 173.67 Percent = 40.095 Weight = 173.67 Percent = 40.095 Weight = 170.63 Percent = 41.609 Weight = 170.63 Percent = 41.609 Weight = 167.58 Percent = 42.969 Weight = 167.58 Percent = 42.969 Weight = 164.53 Percent = 44.16 Weight = 164.53 Percent = 44.16 Weight = 161.48 Percent = 45.168 Weight = 161.48 Percent = 45.168 Weight = 158.44 Percent = 45.985 Weight = 158.44 Percent = 45.985 Weight = 155.39 Percent = 46.605 Weight = 155.39 Percent = 46.605 Weight = 152.34 Percent = 47.027 Weight = 152.34 Percent = 47.027 Weight = 149.3 Percent = 47.253 Weight = 149.3 Percent = 47.253 Weight = 146.25 Percent = 47.289 Weight = 146.25 Percent = 47.289 Weight = 143.2 Percent = 47.143 Weight = 143.2 Percent = 47.143 Weight = 140.16 Percent = 46.829 Weight = 140.16 Percent = 46.829 Weight = 137.11 Percent = 46.359 Weight = 137.11 Percent = 46.359 Weight = 134.06 Percent = 45.751 Weight = 134.06 Percent = 45.751 Weight = 131.02 Percent = 45.021 Weight = 131.02 Percent = 45.021 Weight = 127.97 Percent = 44.188 Weight = 127.97 Percent = 44.188 Weight = 124.92 Percent = 43.269 Weight = 124.92 Percent = 43.269 Weight = 121.88 Percent = 42.282 Weight = 121.88 Percent = 42.282 Weight = 118.83 Percent = 41.242 Weight = 118.83 Percent = 41.242 Weight = 103.59 Percent = 35.726 Weight = 103.59 Percent = 35.726 Weight = 94.453 Percent = 32.464 Weight = 94.453 Percent = 32.464 Weight = 88.359 Percent = 30.369 Weight = 88.359 Percent = 30.369 Weight = 79.219 Percent = 27.34 Weight = 79.219 Percent = 27.34 Weight = 70.078 Percent = 24.422 Weight = 70.078 Percent = 24.422 Weight = 60.938 Percent = 21.61 Weight = 60.938 Percent = 21.61 Weight = 54.844 Percent = 19.81 Weight = 54.844 Percent = 19.81 Weight = 48.75 Percent = 18.093 Weight = 48.75 Percent = 18.093 Weight = 45.703 Percent = 17.271 Weight = 45.703 Percent = 17.271 Weight = 42.656 Percent = 16.477 Weight = 42.656 Percent = 16.477 Weight = 39.609 Percent = 15.713 Weight = 39.609 Percent = 15.713 Weight = 36.563 Percent = 14.979 Weight = 36.563 Percent = 14.979 Weight = 33.516 Percent = 14.277 Weight = 33.516 Percent = 14.277 Weight = 30.469 Percent = 13.606 Weight = 30.469 Percent = 13.606 Weight = 27.422 Percent = 12.965 Weight = 27.422 Percent = 12.965 Weight = 24.375 Percent = 12.353 Weight = 24.375 Percent = 12.353 Weight = 21.328 Percent = 11.768 Weight = 21.328 Percent = 11.768 Weight = 18.281 Percent = 11.206 Weight = 18.281 Percent = 11.206 Weight = 15.234 Percent = 10.666 Weight = 15.234 Percent = 10.666 Weight = 9.1406 Percent = 9.6368 Weight = 9.1406 Percent = 9.6368 Weight = 3.0469 Percent = 8.6561 Weight = 3.0469 Percent = 8.6561 Weight = -9.141 Percent = 6.7722 Weight = -9.141 Percent = 6.7722 Weight = -18.28 Percent = 5.4093 Weight = -18.28 Percent = 5.4093 Weight = -24.38 Percent = 4.5403 Weight = -24.38 Percent = 4.5403 Weight = -27.42 Percent = 4.1238 Weight = -27.42 Percent = 4.1238 Weight = -30.47 Percent = 3.7227 Weight = -30.47 Percent = 3.7227 Weight = -33.52 Percent = 3.339 Weight = -33.52 Percent = 3.339 Weight = -36.56 Percent = 2.9751 Weight = -36.56 Percent = 2.9751 Weight = -39.61 Percent = 2.6327 Weight = -39.61 Percent = 2.6327 Weight = -42.66 Percent = 2.3133 Weight = -42.66 Percent = 2.3133 Weight = -45.7 Percent = 2.018 Weight = -45.7 Percent = 2.018 Weight = -48.75 Percent = 1.7474 Weight = -48.75 Percent = 1.7474 Weight = -51.8 Percent = 1.5018 Weight = -51.8 Percent = 1.5018 Weight = -54.84 Percent = 1.2808 Weight = -54.84 Percent = 1.2808 Weight = -57.89 Percent = 1.0839 Weight = -57.89 Percent = 1.0839 Weight = -60.94 Percent = 0.9101 Weight = -60.94 Percent = 0.9101 Weight = -63.98 Percent = 0.7582 Weight = -63.98 Percent = 0.7582 Weight = -67.03 Percent = 0.6265 Weight = -67.03 Percent = 0.6265 Weight = -70.08 Percent = 0.5135 Weight = -70.08 Percent = 0.5135 Weight = -73.13 Percent = 0.4175 Weight = -73.13 Percent = 0.4175 Weight = -76.17 Percent = 0.3367 Weight = -76.17 Percent = 0.3367 Weight = -79.22 Percent = 0.2693 Weight = -79.22 Percent = 0.2693 Weight = -82.27 Percent = 0.2136 Weight = 418.54 Percent = 0.3991 Weight = 415.84 Percent = 0.4369 Weight = 415.84 Percent = 0.4369 Weight = 413.15 Percent = 0.4778 Weight = 413.15 Percent = 0.4778 Weight = 410.46 Percent = 0.5221 Weight = 410.46 Percent = 0.5221 Weight = 407.77 Percent = 0.57 Weight = 407.77 Percent = 0.57 Weight = 405.08 Percent = 0.6216 Weight = 405.08 Percent = 0.6216 Weight = 402.39 Percent = 0.6774 Weight = 402.39 Percent = 0.6774 Weight = 399.69 Percent = 0.7374 Weight = 399.69 Percent = 0.7374 Weight = 397 Percent = 0.8021 Weight = 397 Percent = 0.8021 Weight = 394.31 Percent = 0.8716 Weight = 394.31 Percent = 0.8716 Weight = 391.62 Percent = 0.9462 Weight = 391.62 Percent = 0.9462 Weight = 388.93 Percent = 1.0263 Weight = 388.93 Percent = 1.0263 Weight = 386.24 Percent = 1.1122 Weight = 386.24 Percent = 1.1122 Weight = 383.54 Percent = 1.2041 Weight = 383.54 Percent = 1.2041 Weight = 380.85 Percent = 1.3025 Weight = 380.85 Percent = 1.3025 Weight = 378.16 Percent = 1.4076 Weight = 378.16 Percent = 1.4076 Weight = 375.47 Percent = 1.5198 Weight = 375.47 Percent = 1.5198 Weight = 372.78 Percent = 1.6394 Weight = 372.78 Percent = 1.6394 Weight = 370.08 Percent = 1.7668 Weight = 370.08 Percent = 1.7668 Weight = 367.39 Percent = 1.9023 Weight = 367.39 Percent = 1.9023 Weight = 364.7 Percent = 2.0464 Weight = 364.7 Percent = 2.0464 Weight = 362.01 Percent = 2.1993 Weight = 362.01 Percent = 2.1993 Weight = 359.32 Percent = 2.3616 Weight = 359.32 Percent = 2.3616 Weight = 356.63 Percent = 2.5334 Weight = 356.63 Percent = 2.5334 Weight = 353.93 Percent = 2.7153 Weight = 353.93 Percent = 2.7153 Weight = 351.24 Percent = 2.9076 Weight = 351.24 Percent = 2.9076 Weight = 348.55 Percent = 3.1106 Weight = 348.55 Percent = 3.1106 Weight = 345.86 Percent = 3.3247 Weight = 345.86 Percent = 3.3247 Weight = 343.17 Percent = 3.5503 Weight = 343.17 Percent = 3.5503 Weight = 340.47 Percent = 3.7878 Weight = 340.47 Percent = 3.7878 Weight = 337.78 Percent = 4.0374 Weight = 337.78 Percent = 4.0374 Weight = 335.09 Percent = 4.2995 Weight = 335.09 Percent = 4.2995 Weight = 332.4 Percent = 4.5744 Weight = 332.4 Percent = 4.5744 Weight = 329.71 Percent = 4.8625 Weight = 329.71 Percent = 4.8625 Weight = 327.02 Percent = 5.1639 Weight = 327.02 Percent = 5.1639 Weight = 324.32 Percent = 5.479 Weight = 324.32 Percent = 5.479 Weight = 321.63 Percent = 5.808 Weight = 321.63 Percent = 5.808 Weight = 318.94 Percent = 6.1511 Weight = 318.94 Percent = 6.1511 Weight = 316.25 Percent = 6.5084 Weight = 316.25 Percent = 6.5084 Weight = 313.56 Percent = 6.8802 Weight = 313.56 Percent = 6.8802 Weight = 310.87 Percent = 7.2666 Weight = 310.87 Percent = 7.2666 Weight = 308.17 Percent = 7.6676 Weight = 308.17 Percent = 7.6676 Weight = 305.48 Percent = 8.0834 Weight = 305.48 Percent = 8.0834 Weight = 302.79 Percent = 8.5138 Weight = 302.79 Percent = 8.5138 Weight = 300.1 Percent = 8.959 Weight = 300.1 Percent = 8.959 Weight = 297.41 Percent = 9.4188 Weight = 297.41 Percent = 9.4188 Weight = 292.02 Percent = 10.382 Weight = 292.02 Percent = 10.382 Weight = 286.64 Percent = 11.401 Weight = 286.64 Percent = 11.401 Weight = 281.26 Percent = 12.475 Weight = 281.26 Percent = 12.475 Weight = 275.87 Percent = 13.599 Weight = 275.87 Percent = 13.599 Weight = 270.49 Percent = 14.771 Weight = 270.49 Percent = 14.771 Weight = 230.11 Percent = 24.42 Weight = 230.11 Percent = 24.42 Weight = 222.04 Percent = 26.342 Weight = 222.04 Percent = 26.342 Weight = 216.65 Percent = 27.58 Weight = 216.65 Percent = 27.58 Weight = 211.27 Percent = 28.77 Weight = 211.27 Percent = 28.77 Weight = 205.89 Percent = 29.901 Weight = 205.89 Percent = 29.901 Weight = 203.19 Percent = 30.441 Weight = 203.19 Percent = 30.441 Weight = 200.5 Percent = 30.963 Weight = 200.5 Percent = 30.963 Weight = 197.81 Percent = 31.464 Weight = 197.81 Percent = 31.464 Weight = 195.12 Percent = 31.945 Weight = 195.12 Percent = 31.945 Weight = 192.43 Percent = 32.403 Weight = 192.43 Percent = 32.403 Weight = 189.73 Percent = 32.837 Weight = 189.73 Percent = 32.837 Weight = 187.04 Percent = 33.247 Weight = 187.04 Percent = 33.247 Weight = 184.35 Percent = 33.63 Weight = 184.35 Percent = 33.63 Weight = 181.66 Percent = 33.987 Weight = 181.66 Percent = 33.987 Weight = 178.97 Percent = 34.317 Weight = 178.97 Percent = 34.317 Weight = 176.28 Percent = 34.617 Weight = 176.28 Percent = 34.617 Weight = 173.58 Percent = 34.889 Weight = 173.58 Percent = 34.889 Weight = 170.89 Percent = 35.13 Weight = 170.89 Percent = 35.13 Weight = 168.2 Percent = 35.34 Weight = 168.2 Percent = 35.34 Weight = 165.51 Percent = 35.519 Weight = 165.51 Percent = 35.519 Weight = 162.82 Percent = 35.666 Weight = 162.82 Percent = 35.666 Weight = 160.13 Percent = 35.781 Weight = 160.13 Percent = 35.781 Weight = 157.43 Percent = 35.863 Weight = 157.43 Percent = 35.863 Weight = 154.74 Percent = 35.913 Weight = 154.74 Percent = 35.913 Weight = 152.05 Percent = 35.929 Weight = 152.05 Percent = 35.929 Weight = 149.36 Percent = 35.913 Weight = 149.36 Percent = 35.913 Weight = 146.67 Percent = 35.863 Weight = 146.67 Percent = 35.863 Weight = 143.97 Percent = 35.781 Weight = 143.97 Percent = 35.781 Weight = 141.28 Percent = 35.666 Weight = 141.28 Percent = 35.666 Weight = 138.59 Percent = 35.519 Weight = 138.59 Percent = 35.519 Weight = 135.9 Percent = 35.34 Weight = 135.9 Percent = 35.34 Weight = 133.21 Percent = 35.13 Weight = 133.21 Percent = 35.13 Weight = 130.52 Percent = 34.889 Weight = 130.52 Percent = 34.889 Weight = 127.82 Percent = 34.617 Weight = 127.82 Percent = 34.617 Weight = 125.13 Percent = 34.317 Weight = 125.13 Percent = 34.317 Weight = 122.44 Percent = 33.987 Weight = 122.44 Percent = 33.987 Weight = 119.75 Percent = 33.63 Weight = 119.75 Percent = 33.63 Weight = 117.06 Percent = 33.247 Weight = 117.06 Percent = 33.247 Weight = 114.37 Percent = 32.837 Weight = 114.37 Percent = 32.837 Weight = 111.67 Percent = 32.403 Weight = 111.67 Percent = 32.403 Weight = 108.98 Percent = 31.945 Weight = 108.98 Percent = 31.945 Weight = 106.29 Percent = 31.464 Weight = 106.29 Percent = 31.464 Weight = 103.6 Percent = 30.963 Weight = 103.6 Percent = 30.963 Weight = 100.91 Percent = 30.441 Weight = 100.91 Percent = 30.441 Weight = 98.214 Percent = 29.901 Weight = 98.214 Percent = 29.901 Weight = 92.831 Percent = 28.77 Weight = 92.831 Percent = 28.77 Weight = 87.447 Percent = 27.58 Weight = 87.447 Percent = 27.58 Weight = 55.146 Percent = 19.816 Weight = 55.146 Percent = 19.816 Weight = 44.379 Percent = 17.235 Weight = 44.379 Percent = 17.235 Weight = 36.303 Percent = 15.373 Weight = 36.303 Percent = 15.373 Weight = 30.92 Percent = 14.179 Weight = 30.92 Percent = 14.179 Weight = 25.536 Percent = 13.031 Weight = 25.536 Percent = 13.031 Weight = 20.153 Percent = 11.931 Weight = 20.153 Percent = 11.931 Weight = 14.769 Percent = 10.884 Weight = 14.769 Percent = 10.884 Weight = 9.3854 Percent = 9.893 Weight = 9.3854 Percent = 9.893 Weight = 6.6936 Percent = 9.4188 Weight = 6.6936 Percent = 9.4188 Weight = 4.0018 Percent = 8.959 Weight = 4.0018 Percent = 8.959 Weight = 1.31 Percent = 8.5138 Weight = 1.31 Percent = 8.5138 Weight = -1.382 Percent = 8.0834 Weight = -1.382 Percent = 8.0834 Weight = -4.074 Percent = 7.6676 Weight = -4.074 Percent = 7.6676 Weight = -6.765 Percent = 7.2666 Weight = -6.765 Percent = 7.2666 Weight = -9.457 Percent = 6.8802 Weight = -9.457 Percent = 6.8802 Weight = -12.15 Percent = 6.5084 Weight = -12.15 Percent = 6.5084 Weight = -14.84 Percent = 6.1511 Weight = -14.84 Percent = 6.1511 Weight = -17.53 Percent = 5.808 Weight = -17.53 Percent = 5.808 Weight = -20.22 Percent = 5.479 Weight = -20.22 Percent = 5.479 Weight = -22.92 Percent = 5.1639 Weight = -22.92 Percent = 5.1639 Weight = -25.61 Percent = 4.8625 Weight = -25.61 Percent = 4.8625 Weight = -28.3 Percent = 4.5744 Weight = -28.3 Percent = 4.5744 Weight = -30.99 Percent = 4.2995 Weight = -30.99 Percent = 4.2995 Weight = -33.68 Percent = 4.0374 Weight = -33.68 Percent = 4.0374 Weight = -36.37 Percent = 3.7878 Weight = -36.37 Percent = 3.7878 Weight = -39.07 Percent = 3.5503 Weight = -39.07 Percent = 3.5503 Weight = -41.76 Percent = 3.3247 Weight = -41.76 Percent = 3.3247 Weight = -44.45 Percent = 3.1106 Weight = -44.45 Percent = 3.1106 Weight = -47.14 Percent = 2.9076 Weight = -47.14 Percent = 2.9076 Weight = -49.83 Percent = 2.7153 Weight = -49.83 Percent = 2.7153 Weight = -52.53 Percent = 2.5334 Weight = -52.53 Percent = 2.5334 Weight = -55.22 Percent = 2.3616 Weight = -55.22 Percent = 2.3616 Weight = -57.91 Percent = 2.1993 Weight = -57.91 Percent = 2.1993 Weight = -60.6 Percent = 2.0464 Weight = -60.6 Percent = 2.0464 Weight = -63.29 Percent = 1.9023 Weight = -63.29 Percent = 1.9023 Weight = -65.98 Percent = 1.7668 Weight = -65.98 Percent = 1.7668 Weight = -68.68 Percent = 1.6394 Weight = -68.68 Percent = 1.6394 Weight = -71.37 Percent = 1.5198 Weight = -71.37 Percent = 1.5198 Weight = -74.06 Percent = 1.4076 Weight = -74.06 Percent = 1.4076 Weight = -76.75 Percent = 1.3025 Weight = -76.75 Percent = 1.3025 Weight = -79.44 Percent = 1.2041 Weight = -79.44 Percent = 1.2041 Weight = -82.14 Percent = 1.1122 Weight = -82.14 Percent = 1.1122 Weight = -84.83 Percent = 1.0263 Weight = -84.83 Percent = 1.0263 Weight = -87.52 Percent = 0.9462 Weight = -87.52 Percent = 0.9462 Weight = -90.21 Percent = 0.8716 Weight = -90.21 Percent = 0.8716 Weight = -92.9 Percent = 0.8021 Weight = -92.9 Percent = 0.8021 Weight = -95.59 Percent = 0.7374 Weight = -95.59 Percent = 0.7374 Weight = -98.29 Percent = 0.6774 Weight = -98.29 Percent = 0.6774 Weight = -101 Percent = 0.6216 Weight = -101 Percent = 0.6216 Weight = -103.7 Percent = 0.57 Weight = -103.7 Percent = 0.57 Weight = -106.4 Percent = 0.5221 Weight = -106.4 Percent = 0.5221 Weight = -109.1 Percent = 0.4778 Weight = -109.1 Percent = 0.4778 Weight = -111.7 Percent = 0.4369 Weight = -111.7 Percent = 0.4369 Weight = -114.4 Percent = 0.3991 Weight = 360 Percent = 5 Weight = 360 Percent = 5 Weight = 280 Percent = 10 Weight = 280 Percent = 10 Weight = 200 Percent = 30 Weight = 200 Percent = 30 Weight = 120 Percent = 35 Weight = 120 Percent = 35 Weight = 40 Percent = 20 Weight = 40 Percent = 20 Species = Roach Weight = 290 Species = Roach Weight = 390 Species = Roach Data Minimum = 0 Minimum Whisker = 0 First Quartile = 98.5 Median = 147.5 Third Quartile = 174.5 Maximum Whisker = 272 Data Maximum = 390 Mean = 152.05 Standard Deviation = 88.829 Number of Observations = 20 Sum of Weight = . Species = Roach Data Minimum = 0 Minimum Whisker = 0 First Quartile = 98.5 Median = 147.5 Third Quartile = 174.5 Maximum Whisker = 272 Data Maximum = 390 Mean = 152.05 Standard Deviation = 88.829 Number of Observations = 20 Sum of Weight = . Species = Roach Data Minimum = 0 Minimum Whisker = 0 First Quartile = 98.5 Median = 147.5 Third Quartile = 174.5 Maximum Whisker = 272 Data Maximum = 390 Mean = 152.05 Standard Deviation = 88.829 Number of Observations = 20 Sum of Weight = . Species = Roach Data Minimum = 0 Minimum Whisker = 0 First Quartile = 98.5 Median = 147.5 Third Quartile = 174.5 Maximum Whisker = 272 Data Maximum = 390 Mean = 152.05 Standard Deviation = 88.829 Number of Observations = 20 Sum of Weight = . Species = Roach Data Minimum = 0 Minimum Whisker = 0 First Quartile = 98.5 Median = 147.5 Third Quartile = 174.5 Maximum Whisker = 272 Data Maximum = 390 Mean = 152.05 Standard Deviation = 88.829 Number of Observations = 20 Sum of Weight = . Species = Roach Data Minimum = 0 Minimum Whisker = 0 First Quartile = 98.5 Median = 147.5 Third Quartile = 174.5 Maximum Whisker = 272 Data Maximum = 390 Mean = 152.05 Standard Deviation = 88.829 Number of Observations = 20 Sum of Weight = . Species = Roach Data Minimum = 0 Minimum Whisker = 0 First Quartile = 98.5 Median = 147.5 Third Quartile = 174.5 Maximum Whisker = 272 Data Maximum = 390 Mean = 152.05 Standard Deviation = 88.829 Number of Observations = 20 Sum of Weight = . Species = Roach Data Minimum = 0 Minimum Whisker = 0 First Quartile = 98.5 Median = 147.5 Third Quartile = 174.5 Maximum Whisker = 272 Data Maximum = 390 Mean = 152.05 Standard Deviation = 88.829 Number of Observations = 20 Sum of Weight = . Species = Pike Data Minimum = 200 Minimum Whisker = 200 First Quartile = 345 Median = 510 Third Quartile = 950 Maximum Whisker = 1650 Data Maximum = 1650 Mean = 718.71 Standard Deviation = 494.14 Number of Observations = 17 Sum of Weight = . Species = Pike Data Minimum = 200 Minimum Whisker = 200 First Quartile = 345 Median = 510 Third Quartile = 950 Maximum Whisker = 1650 Data Maximum = 1650 Mean = 718.71 Standard Deviation = 494.14 Number of Observations = 17 Sum of Weight = . Species = Pike Data Minimum = 200 Minimum Whisker = 200 First Quartile = 345 Median = 510 Third Quartile = 950 Maximum Whisker = 1650 Data Maximum = 1650 Mean = 718.71 Standard Deviation = 494.14 Number of Observations = 17 Sum of Weight = . Species = Pike Data Minimum = 200 Minimum Whisker = 200 First Quartile = 345 Median = 510 Third Quartile = 950 Maximum Whisker = 1650 Data Maximum = 1650 Mean = 718.71 Standard Deviation = 494.14 Number of Observations = 17 Sum of Weight = . Species = Pike Data Minimum = 200 Minimum Whisker = 200 First Quartile = 345 Median = 510 Third Quartile = 950 Maximum Whisker = 1650 Data Maximum = 1650 Mean = 718.71 Standard Deviation = 494.14 Number of Observations = 17 Sum of Weight = . Species = Pike Data Minimum = 200 Minimum Whisker = 200 First Quartile = 345 Median = 510 Third Quartile = 950 Maximum Whisker = 1650 Data Maximum = 1650 Mean = 718.71 Standard Deviation = 494.14 Number of Observations = 17 Sum of Weight = . Species = Pike Data Minimum = 200 Minimum Whisker = 200 First Quartile = 345 Median = 510 Third Quartile = 950 Maximum Whisker = 1650 Data Maximum = 1650 Mean = 718.71 Standard Deviation = 494.14 Number of Observations = 17 Sum of Weight = . Species = Pike Data Minimum = 200 Minimum Whisker = 200 First Quartile = 345 Median = 510 Third Quartile = 950 Maximum Whisker = 1650 Data Maximum = 1650 Mean = 718.71 Standard Deviation = 494.14 Number of Observations = 17 Sum of Weight = .
Summary Panel for Weight

Q-Q Plots

Quantile = 1.7962 Weight = 1650 Quantile = 1.3153 Weight = 1600 Quantile = 1.0272 Weight = 1550 Quantile = 0.8059 Weight = 1250 Quantile = 0.6185 Weight = 950 Quantile = 0.4507 Weight = 770 Quantile = 0.2948 Weight = 567 Quantile = 0.1458 Weight = 540 Quantile = 0 Weight = 510 Quantile = -0.146 Weight = 500 Quantile = -0.295 Weight = 456 Quantile = -0.451 Weight = 430 Quantile = -0.619 Weight = 345 Quantile = -0.806 Weight = 300 Quantile = -1.027 Weight = 300 Quantile = -1.315 Weight = 300 Quantile = -1.796 Weight = 200 Slope = 494.14 Y = 718.71 Quantile = 1.8682 Weight = 390 Quantile = 1.4034 Weight = 290 Quantile = 1.1281 Weight = 272 Quantile = 0.9191 Weight = 200 Quantile = 0.7441 Weight = 180 Quantile = 0.5895 Weight = 169 Quantile = 0.4478 Weight = 161 Quantile = 0.3146 Weight = 160 Quantile = 0.1868 Weight = 160 Quantile = 0.0619 Weight = 150 Quantile = -0.062 Weight = 145 Quantile = -0.187 Weight = 140 Quantile = -0.315 Weight = 120 Quantile = -0.448 Weight = 120 Quantile = -0.589 Weight = 110 Quantile = -0.744 Weight = 87 Quantile = -0.919 Weight = 78 Quantile = -1.128 Weight = 69 Quantile = -1.403 Weight = 40 Quantile = -1.868 Weight = 0 Slope = 88.829 Y = 152.05
Q-Q Plots for Weight

Nonparametric Two-sample Tests on Pike vs. Roach Fish

The Npar1way Procedure

Variable Weight

Wilcoxon Analysis

Scores

Wilcoxon Scores (Rank Sums) for Variable Weight
Classified by Variable Species
Species N Sum of
Scores		 Expected
Under H0		 Std Dev
Under H0		 Mean
Score
Average scores were used for ties.
Roach 20 217.50 380.0 32.798983 10.875000
Pike 17 485.50 323.0 32.798983 28.558824

Two-Sample Test

Wilcoxon Two-Sample Test
Statistic Z Pr > Z Pr > |Z| t Approximation
Pr > Z Pr > |Z|
Z includes a continuity correction of 0.5.
485.5000 4.9392 <.0001 <.0001 <.0001 <.0001

Kruskal-Wallis Test

Kruskal-Wallis Test
Chi-Square DF Pr > ChiSq
24.5463 1 <.0001

Box Plot

Species = Pike Data Minimum = 17.5 Minimum Whisker = 17.5 First Quartile = 24 Median = 29 Third Quartile = 33 Maximum Whisker = 37 Data Maximum = 37 Mean = 28.559 Standard Deviation = 5.6951 Number of Observations = 17 Sum of Weight = . Species = Pike Data Minimum = 17.5 Minimum Whisker = 17.5 First Quartile = 24 Median = 29 Third Quartile = 33 Maximum Whisker = 37 Data Maximum = 37 Mean = 28.559 Standard Deviation = 5.6951 Number of Observations = 17 Sum of Weight = . Species = Pike Data Minimum = 17.5 Minimum Whisker = 17.5 First Quartile = 24 Median = 29 Third Quartile = 33 Maximum Whisker = 37 Data Maximum = 37 Mean = 28.559 Standard Deviation = 5.6951 Number of Observations = 17 Sum of Weight = . Species = Pike Data Minimum = 17.5 Minimum Whisker = 17.5 First Quartile = 24 Median = 29 Third Quartile = 33 Maximum Whisker = 37 Data Maximum = 37 Mean = 28.559 Standard Deviation = 5.6951 Number of Observations = 17 Sum of Weight = . Species = Pike Data Minimum = 17.5 Minimum Whisker = 17.5 First Quartile = 24 Median = 29 Third Quartile = 33 Maximum Whisker = 37 Data Maximum = 37 Mean = 28.559 Standard Deviation = 5.6951 Number of Observations = 17 Sum of Weight = . Species = Pike Data Minimum = 17.5 Minimum Whisker = 17.5 First Quartile = 24 Median = 29 Third Quartile = 33 Maximum Whisker = 37 Data Maximum = 37 Mean = 28.559 Standard Deviation = 5.6951 Number of Observations = 17 Sum of Weight = . Species = Pike Data Minimum = 17.5 Minimum Whisker = 17.5 First Quartile = 24 Median = 29 Third Quartile = 33 Maximum Whisker = 37 Data Maximum = 37 Mean = 28.559 Standard Deviation = 5.6951 Number of Observations = 17 Sum of Weight = . Species = Pike Data Minimum = 17.5 Minimum Whisker = 17.5 First Quartile = 24 Median = 29 Third Quartile = 33 Maximum Whisker = 37 Data Maximum = 37 Mean = 28.559 Standard Deviation = 5.6951 Number of Observations = 17 Sum of Weight = . Species = Roach Data Minimum = 1 Minimum Whisker = 1 First Quartile = 5.5 Median = 10.5 Third Quartile = 15.5 Maximum Whisker = 25 Data Maximum = 25 Mean = 10.875 Standard Deviation = 6.5772 Number of Observations = 20 Sum of Weight = . Species = Roach Data Minimum = 1 Minimum Whisker = 1 First Quartile = 5.5 Median = 10.5 Third Quartile = 15.5 Maximum Whisker = 25 Data Maximum = 25 Mean = 10.875 Standard Deviation = 6.5772 Number of Observations = 20 Sum of Weight = . Species = Roach Data Minimum = 1 Minimum Whisker = 1 First Quartile = 5.5 Median = 10.5 Third Quartile = 15.5 Maximum Whisker = 25 Data Maximum = 25 Mean = 10.875 Standard Deviation = 6.5772 Number of Observations = 20 Sum of Weight = . Species = Roach Data Minimum = 1 Minimum Whisker = 1 First Quartile = 5.5 Median = 10.5 Third Quartile = 15.5 Maximum Whisker = 25 Data Maximum = 25 Mean = 10.875 Standard Deviation = 6.5772 Number of Observations = 20 Sum of Weight = . Species = Roach Data Minimum = 1 Minimum Whisker = 1 First Quartile = 5.5 Median = 10.5 Third Quartile = 15.5 Maximum Whisker = 25 Data Maximum = 25 Mean = 10.875 Standard Deviation = 6.5772 Number of Observations = 20 Sum of Weight = . Species = Roach Data Minimum = 1 Minimum Whisker = 1 First Quartile = 5.5 Median = 10.5 Third Quartile = 15.5 Maximum Whisker = 25 Data Maximum = 25 Mean = 10.875 Standard Deviation = 6.5772 Number of Observations = 20 Sum of Weight = . Species = Roach Data Minimum = 1 Minimum Whisker = 1 First Quartile = 5.5 Median = 10.5 Third Quartile = 15.5 Maximum Whisker = 25 Data Maximum = 25 Mean = 10.875 Standard Deviation = 6.5772 Number of Observations = 20 Sum of Weight = . Species = Roach Data Minimum = 1 Minimum Whisker = 1 First Quartile = 5.5 Median = 10.5 Third Quartile = 15.5 Maximum Whisker = 25 Data Maximum = 25 Mean = 10.875 Standard Deviation = 6.5772 Number of Observations = 20 Sum of Weight = .
Box Plot of Wilcoxon Scores for Weight Classified by Species
  • “We see smaller sample sizes for the two fish species (n=20 for Roach and n=17 for Pike) compared to our previous example. The tests for normality reject the null hypothesis that these weights for Pike come from a population that is normally distributed, and the histograms show a distribution that is not symmetric or normal. Time to use nonparametric tests.”
  • “The Wilcoxon rank sum test shows the sum of ranks for the two fish species. If the null hypothesis is true, you would expect the sum of ranks to be about the same for both groups, which they are not. This is also reflected on the histograms which show Roach fish being lighter than Pike fish. There are two p-values shown in the Wilcoxon Two-Sample Test section: a z-test (with a correction for continuity) for larger samples; and a t approximation sometimes used for smaller samples (such as this example). both p-values are tiny (<.0001) which implies that Roach fish are lighter than Pike fish.”

Paired t Test.

SAS Code, click to expand

SAS Code:

#  (&path1 and biostats libname previously defined)
/* Paired t Test - generated code - start */

ods noproctitle;
ods graphics / imagemap=on;

data Work._Paired_diffs_;
    set work.yoga;
    _Difference_=Before - After;
    label _Difference_="Difference: Before - After";
run;

/* Test for normality */
title1 "Normality Tests on Yoga data";
proc univariate data=Work._Paired_diffs_ normal mu0=0;
    ods select TestsForNormality;
    var _Difference_;
run;

/* t test */
title1 "Paired t Test on Yoga data";
proc ttest data=work.yoga sides=2 h0=0 plots(showh0);
    paired Before*After;
run;

/* Nonparametric test */
title1 "Nonparametric Two-sample Tests on Yoga data";
proc univariate data=work._paired_diffs_ mu0=0;
    ods select TestsForLocation;
    var _Difference_;
run;

/* Clean up */
proc delete data=work._paired_diffs_;
run;

/* Data taken from a small study designed to show if a half hour of yoga can lower a subject's heart rate. Before and After heart rates for 10 participants were measured. */

/* "All tests for normality are not significant, but due to the tiny sample size (n=10) you should not interpret this as difference scores being normally distributed.  You need to look at the histogram or Q-Q plot to decide if you should be using a nonparametric test.  The t table shows a mean difference is 4.222 with t-value of 3.74 and p-value of .0057.  Because the mean difference is positive (computed as before - after), we conclude that yoga helped reduce heart rate." */

/* "When in doubt, rerun analysis using nonparametric tests such as the Sign test and the Wilcoxon Signed Rank test.  Both show a significant difference at the .05 level." */

/* "Do not simply look at the pvalues from the normality tests. Doing so often results in incorrect decisions. When sample sizes are large, the tests for normality are often significant. When sample sizes are small, they are rarely significant. And, it is with small samples that deviations from normality are most important." */

title1;

/* Paired t Test - generated code - end */

SAS Output

Results: biostats_by_ex_SAScode.sas

Results: biostats_by_ex_SAScode.sas

Normality Tests on Yoga data

Variable: _Difference_ (Difference: Before - After)

The Univariate Procedure

_Difference_

Tests For Normality

Tests for Normality
Test Statistic p Value
Shapiro-Wilk W 0.952338 Pr < W 0.7157
Kolmogorov-Smirnov D 0.162908 Pr > D >0.1500
Cramer-von Mises W-Sq 0.027145 Pr > W-Sq >0.2500
Anderson-Darling A-Sq 0.209771 Pr > A-Sq >0.2500

The Ttest Procedure

Before - After

Paired t Test on Yoga data

Difference: Before - After

 

 

Statistics

N Mean Std Dev Std Err Minimum Maximum
9 4.2222 3.3830 1.1277 0 10.0000

Confidence Limits

Mean 95% CL Mean Std Dev 95% CL Std Dev
4.2222 1.6218 6.8226 3.3830 2.2850 6.4810

T-Tests

DF t Value Pr > |t|
8 3.74 0.0057

Summary Panel

Before - After = 16.328 Percent = 0.2551 Before - After = 16.25 Percent = 0.2761 Before - After = 16.25 Percent = 0.2761 Before - After = 16.172 Percent = 0.2987 Before - After = 16.172 Percent = 0.2987 Before - After = 16.094 Percent = 0.3227 Before - After = 16.094 Percent = 0.3227 Before - After = 16.016 Percent = 0.3485 Before - After = 16.016 Percent = 0.3485 Before - After = 15.938 Percent = 0.3759 Before - After = 15.938 Percent = 0.3759 Before - After = 15.859 Percent = 0.4051 Before - After = 15.859 Percent = 0.4051 Before - After = 15.781 Percent = 0.4363 Before - After = 15.781 Percent = 0.4363 Before - After = 15.703 Percent = 0.4694 Before - After = 15.703 Percent = 0.4694 Before - After = 15.625 Percent = 0.5046 Before - After = 15.625 Percent = 0.5046 Before - After = 15.547 Percent = 0.5419 Before - After = 15.547 Percent = 0.5419 Before - After = 15.469 Percent = 0.5816 Before - After = 15.469 Percent = 0.5816 Before - After = 15.391 Percent = 0.6235 Before - After = 15.391 Percent = 0.6235 Before - After = 15.313 Percent = 0.6679 Before - After = 15.313 Percent = 0.6679 Before - After = 15.234 Percent = 0.7149 Before - After = 15.234 Percent = 0.7149 Before - After = 15.156 Percent = 0.7645 Before - After = 15.156 Percent = 0.7645 Before - After = 15.078 Percent = 0.8169 Before - After = 15.078 Percent = 0.8169 Before - After = 15 Percent = 0.8721 Before - After = 15 Percent = 0.8721 Before - After = 14.922 Percent = 0.9302 Before - After = 14.922 Percent = 0.9302 Before - After = 14.844 Percent = 0.9913 Before - After = 14.844 Percent = 0.9913 Before - After = 14.766 Percent = 1.0556 Before - After = 14.766 Percent = 1.0556 Before - After = 14.688 Percent = 1.1231 Before - After = 14.688 Percent = 1.1231 Before - After = 14.609 Percent = 1.1939 Before - After = 14.609 Percent = 1.1939 Before - After = 14.531 Percent = 1.2681 Before - After = 14.531 Percent = 1.2681 Before - After = 14.453 Percent = 1.3458 Before - After = 14.453 Percent = 1.3458 Before - After = 14.375 Percent = 1.4271 Before - After = 14.375 Percent = 1.4271 Before - After = 14.297 Percent = 1.512 Before - After = 14.297 Percent = 1.512 Before - After = 14.219 Percent = 1.6007 Before - After = 14.219 Percent = 1.6007 Before - After = 14.141 Percent = 1.6931 Before - After = 14.141 Percent = 1.6931 Before - After = 14.063 Percent = 1.7895 Before - After = 14.063 Percent = 1.7895 Before - After = 13.984 Percent = 1.8898 Before - After = 13.984 Percent = 1.8898 Before - After = 13.906 Percent = 1.9941 Before - After = 13.906 Percent = 1.9941 Before - After = 13.828 Percent = 2.1024 Before - After = 13.828 Percent = 2.1024 Before - After = 13.75 Percent = 2.2149 Before - After = 13.75 Percent = 2.2149 Before - After = 13.672 Percent = 2.3315 Before - After = 13.672 Percent = 2.3315 Before - After = 13.594 Percent = 2.4523 Before - After = 13.594 Percent = 2.4523 Before - After = 13.516 Percent = 2.5773 Before - After = 13.516 Percent = 2.5773 Before - After = 13.438 Percent = 2.7066 Before - After = 13.438 Percent = 2.7066 Before - After = 13.359 Percent = 2.8401 Before - After = 13.359 Percent = 2.8401 Before - After = 13.281 Percent = 2.978 Before - After = 13.281 Percent = 2.978 Before - After = 13.203 Percent = 3.1201 Before - After = 13.203 Percent = 3.1201 Before - After = 13.047 Percent = 3.4171 Before - After = 13.047 Percent = 3.4171 Before - After = 12.891 Percent = 3.7312 Before - After = 12.891 Percent = 3.7312 Before - After = 12.734 Percent = 4.062 Before - After = 12.734 Percent = 4.062 Before - After = 12.578 Percent = 4.4093 Before - After = 12.578 Percent = 4.4093 Before - After = 12.422 Percent = 4.7725 Before - After = 12.422 Percent = 4.7725 Before - After = 12.266 Percent = 5.1511 Before - After = 12.266 Percent = 5.1511 Before - After = 12.109 Percent = 5.5444 Before - After = 12.109 Percent = 5.5444 Before - After = 11.953 Percent = 5.9516 Before - After = 11.953 Percent = 5.9516 Before - After = 11.719 Percent = 6.5864 Before - After = 11.719 Percent = 6.5864 Before - After = 11.484 Percent = 7.2471 Before - After = 11.484 Percent = 7.2471 Before - After = 11.25 Percent = 7.9303 Before - After = 11.25 Percent = 7.9303 Before - After = 9.375 Percent = 13.79 Before - After = 9.375 Percent = 13.79 Before - After = 8.3594 Percent = 16.966 Before - After = 8.3594 Percent = 16.966 Before - After = 7.6563 Percent = 19.102 Before - After = 7.6563 Percent = 19.102 Before - After = 7.1875 Percent = 20.484 Before - After = 7.1875 Percent = 20.484 Before - After = 6.7969 Percent = 21.6 Before - After = 6.7969 Percent = 21.6 Before - After = 6.4844 Percent = 22.462 Before - After = 6.4844 Percent = 22.462 Before - After = 6.25 Percent = 23.085 Before - After = 6.25 Percent = 23.085 Before - After = 6.0156 Percent = 23.685 Before - After = 6.0156 Percent = 23.685 Before - After = 5.8594 Percent = 24.071 Before - After = 5.8594 Percent = 24.071 Before - After = 5.7031 Percent = 24.443 Before - After = 5.7031 Percent = 24.443 Before - After = 5.5469 Percent = 24.802 Before - After = 5.5469 Percent = 24.802 Before - After = 5.3906 Percent = 25.145 Before - After = 5.3906 Percent = 25.145 Before - After = 5.2344 Percent = 25.472 Before - After = 5.2344 Percent = 25.472 Before - After = 5.0781 Percent = 25.782 Before - After = 5.0781 Percent = 25.782 Before - After = 5 Percent = 25.93 Before - After = 5 Percent = 25.93 Before - After = 4.9219 Percent = 26.073 Before - After = 4.9219 Percent = 26.073 Before - After = 4.8438 Percent = 26.212 Before - After = 4.8438 Percent = 26.212 Before - After = 4.7656 Percent = 26.345 Before - After = 4.7656 Percent = 26.345 Before - After = 4.6875 Percent = 26.473 Before - After = 4.6875 Percent = 26.473 Before - After = 4.6094 Percent = 26.596 Before - After = 4.6094 Percent = 26.596 Before - After = 4.5313 Percent = 26.713 Before - After = 4.5313 Percent = 26.713 Before - After = 4.4531 Percent = 26.825 Before - After = 4.4531 Percent = 26.825 Before - After = 4.375 Percent = 26.931 Before - After = 4.375 Percent = 26.931 Before - After = 4.2969 Percent = 27.031 Before - After = 4.2969 Percent = 27.031 Before - After = 4.2188 Percent = 27.126 Before - After = 4.2188 Percent = 27.126 Before - After = 4.1406 Percent = 27.214 Before - After = 4.1406 Percent = 27.214 Before - After = 4.0625 Percent = 27.296 Before - After = 4.0625 Percent = 27.296 Before - After = 3.9844 Percent = 27.371 Before - After = 3.9844 Percent = 27.371 Before - After = 3.9063 Percent = 27.44 Before - After = 3.9063 Percent = 27.44 Before - After = 3.8281 Percent = 27.502 Before - After = 3.8281 Percent = 27.502 Before - After = 3.75 Percent = 27.558 Before - After = 3.75 Percent = 27.558 Before - After = 3.6719 Percent = 27.607 Before - After = 3.6719 Percent = 27.607 Before - After = 3.5938 Percent = 27.648 Before - After = 3.5938 Percent = 27.648 Before - After = 3.5156 Percent = 27.682 Before - After = 3.5156 Percent = 27.682 Before - After = 3.4375 Percent = 27.709 Before - After = 3.4375 Percent = 27.709 Before - After = 3.3594 Percent = 27.729 Before - After = 3.3594 Percent = 27.729 Before - After = 3.2813 Percent = 27.741 Before - After = 3.2813 Percent = 27.741 Before - After = 3.2031 Percent = 27.745 Before - After = 3.2031 Percent = 27.745 Before - After = 3.125 Percent = 27.741 Before - After = 3.125 Percent = 27.741 Before - After = 3.0469 Percent = 27.729 Before - After = 3.0469 Percent = 27.729 Before - After = 2.9688 Percent = 27.709 Before - After = 2.9688 Percent = 27.709 Before - After = 2.8906 Percent = 27.681 Before - After = 2.8906 Percent = 27.681 Before - After = 2.8125 Percent = 27.645 Before - After = 2.8125 Percent = 27.645 Before - After = 2.7344 Percent = 27.599 Before - After = 2.7344 Percent = 27.599 Before - After = 2.6563 Percent = 27.545 Before - After = 2.6563 Percent = 27.545 Before - After = 2.5781 Percent = 27.483 Before - After = 2.5781 Percent = 27.483 Before - After = 2.5 Percent = 27.411 Before - After = 2.5 Percent = 27.411 Before - After = 2.4219 Percent = 27.33 Before - After = 2.4219 Percent = 27.33 Before - After = 2.3438 Percent = 27.241 Before - After = 2.3438 Percent = 27.241 Before - After = 2.2656 Percent = 27.142 Before - After = 2.2656 Percent = 27.142 Before - After = 2.1875 Percent = 27.033 Before - After = 2.1875 Percent = 27.033 Before - After = 2.1094 Percent = 26.915 Before - After = 2.1094 Percent = 26.915 Before - After = 2.0313 Percent = 26.788 Before - After = 2.0313 Percent = 26.788 Before - After = 1.9531 Percent = 26.651 Before - After = 1.9531 Percent = 26.651 Before - After = 1.875 Percent = 26.504 Before - After = 1.875 Percent = 26.504 Before - After = 1.7969 Percent = 26.348 Before - After = 1.7969 Percent = 26.348 Before - After = 1.7188 Percent = 26.182 Before - After = 1.7188 Percent = 26.182 Before - After = 1.6406 Percent = 26.006 Before - After = 1.6406 Percent = 26.006 Before - After = 1.5625 Percent = 25.82 Before - After = 1.5625 Percent = 25.82 Before - After = 1.4844 Percent = 25.624 Before - After = 1.4844 Percent = 25.624 Before - After = 1.4063 Percent = 25.419 Before - After = 1.4063 Percent = 25.419 Before - After = 1.3281 Percent = 25.204 Before - After = 1.3281 Percent = 25.204 Before - After = 1.25 Percent = 24.98 Before - After = 1.25 Percent = 24.98 Before - After = 1.1719 Percent = 24.745 Before - After = 1.1719 Percent = 24.745 Before - After = 1.0938 Percent = 24.502 Before - After = 1.0938 Percent = 24.502 Before - After = 1.0156 Percent = 24.249 Before - After = 1.0156 Percent = 24.249 Before - After = 0.9375 Percent = 23.986 Before - After = 0.9375 Percent = 23.986 Before - After = 0.8594 Percent = 23.715 Before - After = 0.8594 Percent = 23.715 Before - After = 0.7813 Percent = 23.434 Before - After = 0.7813 Percent = 23.434 Before - After = 0.7031 Percent = 23.145 Before - After = 0.7031 Percent = 23.145 Before - After = 0.5469 Percent = 22.541 Before - After = 0.5469 Percent = 22.541 Before - After = 0.3906 Percent = 21.904 Before - After = 0.3906 Percent = 21.904 Before - After = 0.2344 Percent = 21.237 Before - After = 0.2344 Percent = 21.237 Before - After = 0.0781 Percent = 20.543 Before - After = 0.0781 Percent = 20.543 Before - After = -1.484 Percent = 12.778 Before - After = -1.484 Percent = 12.778 Before - After = -1.797 Percent = 11.233 Before - After = -1.797 Percent = 11.233 Before - After = -2.031 Percent = 10.118 Before - After = -2.031 Percent = 10.118 Before - After = -2.188 Percent = 9.3998 Before - After = -2.188 Percent = 9.3998 Before - After = -2.344 Percent = 8.7054 Before - After = -2.344 Percent = 8.7054 Before - After = -2.5 Percent = 8.0369 Before - After = -2.5 Percent = 8.0369 Before - After = -2.656 Percent = 7.396 Before - After = -2.656 Percent = 7.396 Before - After = -2.813 Percent = 6.7842 Before - After = -2.813 Percent = 6.7842 Before - After = -2.969 Percent = 6.2028 Before - After = -2.969 Percent = 6.2028 Before - After = -3.125 Percent = 5.6527 Before - After = -3.125 Percent = 5.6527 Before - After = -3.203 Percent = 5.3895 Before - After = -3.203 Percent = 5.3895 Before - After = -3.281 Percent = 5.1343 Before - After = -3.281 Percent = 5.1343 Before - After = -3.359 Percent = 4.8872 Before - After = -3.359 Percent = 4.8872 Before - After = -3.438 Percent = 4.648 Before - After = -3.438 Percent = 4.648 Before - After = -3.516 Percent = 4.4168 Before - After = -3.516 Percent = 4.4168 Before - After = -3.594 Percent = 4.1936 Before - After = -3.594 Percent = 4.1936 Before - After = -3.672 Percent = 3.9784 Before - After = -3.672 Percent = 3.9784 Before - After = -3.75 Percent = 3.771 Before - After = -3.75 Percent = 3.771 Before - After = -3.828 Percent = 3.5714 Before - After = -3.828 Percent = 3.5714 Before - After = -3.906 Percent = 3.3794 Before - After = -3.906 Percent = 3.3794 Before - After = -3.984 Percent = 3.1951 Before - After = -3.984 Percent = 3.1951 Before - After = -4.063 Percent = 3.0182 Before - After = -4.063 Percent = 3.0182 Before - After = -4.141 Percent = 2.8487 Before - After = -4.141 Percent = 2.8487 Before - After = -4.219 Percent = 2.6864 Before - After = -4.219 Percent = 2.6864 Before - After = -4.297 Percent = 2.5312 Before - After = -4.297 Percent = 2.5312 Before - After = -4.375 Percent = 2.3828 Before - After = -4.375 Percent = 2.3828 Before - After = -4.453 Percent = 2.2413 Before - After = -4.453 Percent = 2.2413 Before - After = -4.531 Percent = 2.1063 Before - After = -4.531 Percent = 2.1063 Before - After = -4.609 Percent = 1.9777 Before - After = -4.609 Percent = 1.9777 Before - After = -4.688 Percent = 1.8554 Before - After = -4.688 Percent = 1.8554 Before - After = -4.766 Percent = 1.7391 Before - After = -4.766 Percent = 1.7391 Before - After = -4.844 Percent = 1.6287 Before - After = -4.844 Percent = 1.6287 Before - After = -4.922 Percent = 1.5239 Before - After = -4.922 Percent = 1.5239 Before - After = -5 Percent = 1.4247 Before - After = -5 Percent = 1.4247 Before - After = -5.078 Percent = 1.3307 Before - After = -5.078 Percent = 1.3307 Before - After = -5.156 Percent = 1.2419 Before - After = -5.156 Percent = 1.2419 Before - After = -5.234 Percent = 1.1579 Before - After = -5.234 Percent = 1.1579 Before - After = -5.313 Percent = 1.0787 Before - After = -5.313 Percent = 1.0787 Before - After = -5.391 Percent = 1.0041 Before - After = -5.391 Percent = 1.0041 Before - After = -5.469 Percent = 0.9337 Before - After = -5.469 Percent = 0.9337 Before - After = -5.547 Percent = 0.8675 Before - After = -5.547 Percent = 0.8675 Before - After = -5.625 Percent = 0.8053 Before - After = -5.625 Percent = 0.8053 Before - After = -5.703 Percent = 0.7469 Before - After = -5.703 Percent = 0.7469 Before - After = -5.781 Percent = 0.6922 Before - After = -5.781 Percent = 0.6922 Before - After = -5.859 Percent = 0.6408 Before - After = -5.859 Percent = 0.6408 Before - After = -5.938 Percent = 0.5928 Before - After = -5.938 Percent = 0.5928 Before - After = -6.016 Percent = 0.5478 Before - After = -6.016 Percent = 0.5478 Before - After = -6.094 Percent = 0.5058 Before - After = -6.094 Percent = 0.5058 Before - After = -6.172 Percent = 0.4667 Before - After = -6.172 Percent = 0.4667 Before - After = -6.25 Percent = 0.4301 Before - After = -6.25 Percent = 0.4301 Before - After = -6.328 Percent = 0.3961 Before - After = 14.371 Percent = 0.393 Before - After = 14.269 Percent = 0.4302 Before - After = 14.269 Percent = 0.4302 Before - After = 14.166 Percent = 0.4705 Before - After = 14.166 Percent = 0.4705 Before - After = 14.064 Percent = 0.5141 Before - After = 14.064 Percent = 0.5141 Before - After = 13.961 Percent = 0.5612 Before - After = 13.961 Percent = 0.5612 Before - After = 13.859 Percent = 0.6121 Before - After = 13.859 Percent = 0.6121 Before - After = 13.756 Percent = 0.667 Before - After = 13.756 Percent = 0.667 Before - After = 13.654 Percent = 0.7261 Before - After = 13.654 Percent = 0.7261 Before - After = 13.551 Percent = 0.7898 Before - After = 13.551 Percent = 0.7898 Before - After = 13.448 Percent = 0.8582 Before - After = 13.448 Percent = 0.8582 Before - After = 13.346 Percent = 0.9317 Before - After = 13.346 Percent = 0.9317 Before - After = 13.243 Percent = 1.0106 Before - After = 13.243 Percent = 1.0106 Before - After = 13.141 Percent = 1.0951 Before - After = 13.141 Percent = 1.0951 Before - After = 13.038 Percent = 1.1857 Before - After = 13.038 Percent = 1.1857 Before - After = 12.936 Percent = 1.2825 Before - After = 12.936 Percent = 1.2825 Before - After = 12.833 Percent = 1.386 Before - After = 12.833 Percent = 1.386 Before - After = 12.731 Percent = 1.4965 Before - After = 12.731 Percent = 1.4965 Before - After = 12.628 Percent = 1.6142 Before - After = 12.628 Percent = 1.6142 Before - After = 12.526 Percent = 1.7397 Before - After = 12.526 Percent = 1.7397 Before - After = 12.423 Percent = 1.8731 Before - After = 12.423 Percent = 1.8731 Before - After = 12.321 Percent = 2.015 Before - After = 12.321 Percent = 2.015 Before - After = 12.218 Percent = 2.1656 Before - After = 12.218 Percent = 2.1656 Before - After = 12.116 Percent = 2.3253 Before - After = 12.116 Percent = 2.3253 Before - After = 12.013 Percent = 2.4946 Before - After = 12.013 Percent = 2.4946 Before - After = 11.911 Percent = 2.6737 Before - After = 11.911 Percent = 2.6737 Before - After = 11.808 Percent = 2.863 Before - After = 11.808 Percent = 2.863 Before - After = 11.706 Percent = 3.0629 Before - After = 11.706 Percent = 3.0629 Before - After = 11.603 Percent = 3.2737 Before - After = 11.603 Percent = 3.2737 Before - After = 11.501 Percent = 3.4959 Before - After = 11.501 Percent = 3.4959 Before - After = 11.398 Percent = 3.7297 Before - After = 11.398 Percent = 3.7297 Before - After = 11.296 Percent = 3.9755 Before - After = 11.296 Percent = 3.9755 Before - After = 11.193 Percent = 4.2336 Before - After = 11.193 Percent = 4.2336 Before - After = 11.091 Percent = 4.5043 Before - After = 11.091 Percent = 4.5043 Before - After = 10.988 Percent = 4.7879 Before - After = 10.988 Percent = 4.7879 Before - After = 10.886 Percent = 5.0847 Before - After = 10.886 Percent = 5.0847 Before - After = 10.783 Percent = 5.395 Before - After = 10.783 Percent = 5.395 Before - After = 10.681 Percent = 5.7189 Before - After = 10.681 Percent = 5.7189 Before - After = 10.578 Percent = 6.0567 Before - After = 10.578 Percent = 6.0567 Before - After = 10.476 Percent = 6.4086 Before - After = 10.476 Percent = 6.4086 Before - After = 10.373 Percent = 6.7747 Before - After = 10.373 Percent = 6.7747 Before - After = 10.271 Percent = 7.1552 Before - After = 10.271 Percent = 7.1552 Before - After = 10.168 Percent = 7.5501 Before - After = 10.168 Percent = 7.5501 Before - After = 10.066 Percent = 7.9594 Before - After = 10.066 Percent = 7.9594 Before - After = 9.963 Percent = 8.3833 Before - After = 9.963 Percent = 8.3833 Before - After = 9.8605 Percent = 8.8216 Before - After = 9.8605 Percent = 8.8216 Before - After = 9.758 Percent = 9.2743 Before - After = 9.758 Percent = 9.2743 Before - After = 9.553 Percent = 10.222 Before - After = 9.553 Percent = 10.222 Before - After = 9.3479 Percent = 11.226 Before - After = 9.3479 Percent = 11.226 Before - After = 9.1429 Percent = 12.283 Before - After = 9.1429 Percent = 12.283 Before - After = 8.9379 Percent = 13.391 Before - After = 8.9379 Percent = 13.391 Before - After = 8.7328 Percent = 14.544 Before - After = 8.7328 Percent = 14.544 Before - After = 7.1951 Percent = 24.046 Before - After = 7.1951 Percent = 24.046 Before - After = 6.8876 Percent = 25.938 Before - After = 6.8876 Percent = 25.938 Before - After = 6.6826 Percent = 27.157 Before - After = 6.6826 Percent = 27.157 Before - After = 6.4775 Percent = 28.329 Before - After = 6.4775 Percent = 28.329 Before - After = 6.2725 Percent = 29.442 Before - After = 6.2725 Percent = 29.442 Before - After = 6.17 Percent = 29.974 Before - After = 6.17 Percent = 29.974 Before - After = 6.0675 Percent = 30.488 Before - After = 6.0675 Percent = 30.488 Before - After = 5.965 Percent = 30.982 Before - After = 5.965 Percent = 30.982 Before - After = 5.8624 Percent = 31.455 Before - After = 5.8624 Percent = 31.455 Before - After = 5.7599 Percent = 31.906 Before - After = 5.7599 Percent = 31.906 Before - After = 5.6574 Percent = 32.333 Before - After = 5.6574 Percent = 32.333 Before - After = 5.5549 Percent = 32.737 Before - After = 5.5549 Percent = 32.737 Before - After = 5.4524 Percent = 33.115 Before - After = 5.4524 Percent = 33.115 Before - After = 5.3499 Percent = 33.466 Before - After = 5.3499 Percent = 33.466 Before - After = 5.2474 Percent = 33.79 Before - After = 5.2474 Percent = 33.79 Before - After = 5.1448 Percent = 34.087 Before - After = 5.1448 Percent = 34.087 Before - After = 5.0423 Percent = 34.354 Before - After = 5.0423 Percent = 34.354 Before - After = 4.9398 Percent = 34.591 Before - After = 4.9398 Percent = 34.591 Before - After = 4.8373 Percent = 34.798 Before - After = 4.8373 Percent = 34.798 Before - After = 4.7348 Percent = 34.974 Before - After = 4.7348 Percent = 34.974 Before - After = 4.6323 Percent = 35.119 Before - After = 4.6323 Percent = 35.119 Before - After = 4.5298 Percent = 35.232 Before - After = 4.5298 Percent = 35.232 Before - After = 4.4273 Percent = 35.313 Before - After = 4.4273 Percent = 35.313 Before - After = 4.3247 Percent = 35.362 Before - After = 4.3247 Percent = 35.362 Before - After = 4.2222 Percent = 35.378 Before - After = 4.2222 Percent = 35.378 Before - After = 4.1197 Percent = 35.362 Before - After = 4.1197 Percent = 35.362 Before - After = 4.0172 Percent = 35.313 Before - After = 4.0172 Percent = 35.313 Before - After = 3.9147 Percent = 35.232 Before - After = 3.9147 Percent = 35.232 Before - After = 3.8122 Percent = 35.119 Before - After = 3.8122 Percent = 35.119 Before - After = 3.7097 Percent = 34.974 Before - After = 3.7097 Percent = 34.974 Before - After = 3.6071 Percent = 34.798 Before - After = 3.6071 Percent = 34.798 Before - After = 3.5046 Percent = 34.591 Before - After = 3.5046 Percent = 34.591 Before - After = 3.4021 Percent = 34.354 Before - After = 3.4021 Percent = 34.354 Before - After = 3.2996 Percent = 34.087 Before - After = 3.2996 Percent = 34.087 Before - After = 3.1971 Percent = 33.79 Before - After = 3.1971 Percent = 33.79 Before - After = 3.0946 Percent = 33.466 Before - After = 3.0946 Percent = 33.466 Before - After = 2.9921 Percent = 33.115 Before - After = 2.9921 Percent = 33.115 Before - After = 2.8895 Percent = 32.737 Before - After = 2.8895 Percent = 32.737 Before - After = 2.787 Percent = 32.333 Before - After = 2.787 Percent = 32.333 Before - After = 2.6845 Percent = 31.906 Before - After = 2.6845 Percent = 31.906 Before - After = 2.582 Percent = 31.455 Before - After = 2.582 Percent = 31.455 Before - After = 2.4795 Percent = 30.982 Before - After = 2.4795 Percent = 30.982 Before - After = 2.377 Percent = 30.488 Before - After = 2.377 Percent = 30.488 Before - After = 2.2745 Percent = 29.974 Before - After = 2.2745 Percent = 29.974 Before - After = 2.1719 Percent = 29.442 Before - After = 2.1719 Percent = 29.442 Before - After = 1.9669 Percent = 28.329 Before - After = 1.9669 Percent = 28.329 Before - After = 1.7619 Percent = 27.157 Before - After = 1.7619 Percent = 27.157 Before - After = 0.5317 Percent = 19.512 Before - After = 0.5317 Percent = 19.512 Before - After = 0.1217 Percent = 16.97 Before - After = 0.1217 Percent = 16.97 Before - After = -0.186 Percent = 15.137 Before - After = -0.186 Percent = 15.137 Before - After = -0.391 Percent = 13.962 Before - After = -0.391 Percent = 13.962 Before - After = -0.596 Percent = 12.831 Before - After = -0.596 Percent = 12.831 Before - After = -0.801 Percent = 11.748 Before - After = -0.801 Percent = 11.748 Before - After = -1.006 Percent = 10.717 Before - After = -1.006 Percent = 10.717 Before - After = -1.211 Percent = 9.7413 Before - After = -1.211 Percent = 9.7413 Before - After = -1.314 Percent = 9.2743 Before - After = -1.314 Percent = 9.2743 Before - After = -1.416 Percent = 8.8216 Before - After = -1.416 Percent = 8.8216 Before - After = -1.519 Percent = 8.3833 Before - After = -1.519 Percent = 8.3833 Before - After = -1.621 Percent = 7.9594 Before - After = -1.621 Percent = 7.9594 Before - After = -1.724 Percent = 7.5501 Before - After = -1.724 Percent = 7.5501 Before - After = -1.826 Percent = 7.1552 Before - After = -1.826 Percent = 7.1552 Before - After = -1.929 Percent = 6.7747 Before - After = -1.929 Percent = 6.7747 Before - After = -2.031 Percent = 6.4086 Before - After = -2.031 Percent = 6.4086 Before - After = -2.134 Percent = 6.0567 Before - After = -2.134 Percent = 6.0567 Before - After = -2.236 Percent = 5.7189 Before - After = -2.236 Percent = 5.7189 Before - After = -2.339 Percent = 5.395 Before - After = -2.339 Percent = 5.395 Before - After = -2.441 Percent = 5.0847 Before - After = -2.441 Percent = 5.0847 Before - After = -2.544 Percent = 4.7879 Before - After = -2.544 Percent = 4.7879 Before - After = -2.646 Percent = 4.5043 Before - After = -2.646 Percent = 4.5043 Before - After = -2.749 Percent = 4.2336 Before - After = -2.749 Percent = 4.2336 Before - After = -2.851 Percent = 3.9755 Before - After = -2.851 Percent = 3.9755 Before - After = -2.954 Percent = 3.7297 Before - After = -2.954 Percent = 3.7297 Before - After = -3.056 Percent = 3.4959 Before - After = -3.056 Percent = 3.4959 Before - After = -3.159 Percent = 3.2737 Before - After = -3.159 Percent = 3.2737 Before - After = -3.261 Percent = 3.0629 Before - After = -3.261 Percent = 3.0629 Before - After = -3.364 Percent = 2.863 Before - After = -3.364 Percent = 2.863 Before - After = -3.466 Percent = 2.6737 Before - After = -3.466 Percent = 2.6737 Before - After = -3.569 Percent = 2.4946 Before - After = -3.569 Percent = 2.4946 Before - After = -3.671 Percent = 2.3253 Before - After = -3.671 Percent = 2.3253 Before - After = -3.774 Percent = 2.1656 Before - After = -3.774 Percent = 2.1656 Before - After = -3.876 Percent = 2.015 Before - After = -3.876 Percent = 2.015 Before - After = -3.979 Percent = 1.8731 Before - After = -3.979 Percent = 1.8731 Before - After = -4.081 Percent = 1.7397 Before - After = -4.081 Percent = 1.7397 Before - After = -4.184 Percent = 1.6142 Before - After = -4.184 Percent = 1.6142 Before - After = -4.286 Percent = 1.4965 Before - After = -4.286 Percent = 1.4965 Before - After = -4.389 Percent = 1.386 Before - After = -4.389 Percent = 1.386 Before - After = -4.491 Percent = 1.2825 Before - After = -4.491 Percent = 1.2825 Before - After = -4.594 Percent = 1.1857 Before - After = -4.594 Percent = 1.1857 Before - After = -4.697 Percent = 1.0951 Before - After = -4.697 Percent = 1.0951 Before - After = -4.799 Percent = 1.0106 Before - After = -4.799 Percent = 1.0106 Before - After = -4.902 Percent = 0.9317 Before - After = -4.902 Percent = 0.9317 Before - After = -5.004 Percent = 0.8582 Before - After = -5.004 Percent = 0.8582 Before - After = -5.107 Percent = 0.7898 Before - After = -5.107 Percent = 0.7898 Before - After = -5.209 Percent = 0.7261 Before - After = -5.209 Percent = 0.7261 Before - After = -5.312 Percent = 0.667 Before - After = -5.312 Percent = 0.667 Before - After = -5.414 Percent = 0.6121 Before - After = -5.414 Percent = 0.6121 Before - After = -5.517 Percent = 0.5612 Before - After = -5.517 Percent = 0.5612 Before - After = -5.619 Percent = 0.5141 Before - After = -5.619 Percent = 0.5141 Before - After = -5.722 Percent = 0.4705 Before - After = -5.722 Percent = 0.4705 Before - After = -5.824 Percent = 0.4302 Before - After = -5.824 Percent = 0.4302 Before - After = -5.927 Percent = 0.393 Before - After = 9 Percent = 22.222 Before - After = 9 Percent = 22.222 Before - After = 6 Percent = 22.222 Before - After = 6 Percent = 22.222 Before - After = 3 Percent = 22.222 Before - After = 3 Percent = 22.222 Before - After = 0 Percent = 33.333 Before - After = 0 Percent = 33.333 Data Minimum = 0 Minimum Whisker = 0 First Quartile = 1 Median = 4 Third Quartile = 6 Maximum Whisker = 10 Data Maximum = 10 Mean = 4.2222 Standard Deviation = 3.383 Number of Observations = 9 Sum of Weight = . Data Minimum = 0 Minimum Whisker = 0 First Quartile = 1 Median = 4 Third Quartile = 6 Maximum Whisker = 10 Data Maximum = 10 Mean = 4.2222 Standard Deviation = 3.383 Number of Observations = 9 Sum of Weight = . Data Minimum = 0 Minimum Whisker = 0 First Quartile = 1 Median = 4 Third Quartile = 6 Maximum Whisker = 10 Data Maximum = 10 Mean = 4.2222 Standard Deviation = 3.383 Number of Observations = 9 Sum of Weight = . Data Minimum = 0 Minimum Whisker = 0 First Quartile = 1 Median = 4 Third Quartile = 6 Maximum Whisker = 10 Data Maximum = 10 Mean = 4.2222 Standard Deviation = 3.383 Number of Observations = 9 Sum of Weight = . Data Minimum = 0 Minimum Whisker = 0 First Quartile = 1 Median = 4 Third Quartile = 6 Maximum Whisker = 10 Data Maximum = 10 Mean = 4.2222 Standard Deviation = 3.383 Number of Observations = 9 Sum of Weight = . Data Minimum = 0 Minimum Whisker = 0 First Quartile = 1 Median = 4 Third Quartile = 6 Maximum Whisker = 10 Data Maximum = 10 Mean = 4.2222 Standard Deviation = 3.383 Number of Observations = 9 Sum of Weight = . Data Minimum = 0 Minimum Whisker = 0 First Quartile = 1 Median = 4 Third Quartile = 6 Maximum Whisker = 10 Data Maximum = 10 Mean = 4.2222 Standard Deviation = 3.383 Number of Observations = 9 Sum of Weight = . Data Minimum = 0 Minimum Whisker = 0 First Quartile = 1 Median = 4 Third Quartile = 6 Maximum Whisker = 10 Data Maximum = 10 Mean = 4.2222 Standard Deviation = 3.383 Number of Observations = 9 Sum of Weight = . Null Value = 0 Lower Confidence Limit = 1.6218 Upper Confidence Limit = 6.8226 Lower Confidence Limit = 1.6218 Upper Confidence Limit = 6.8226 Lower Confidence Limit = 1.6218 Upper Confidence Limit = 6.8226 Lower Confidence Limit = 1.6218 Upper Confidence Limit = 6.8226 Lower Confidence Limit = 1.6218 Upper Confidence Limit = 6.8226 Lower Confidence Limit = 1.6218 Upper Confidence Limit = 6.8226 Lower Confidence Limit = 1.6218 Upper Confidence Limit = 6.8226 Lower Confidence Limit = 1.6218 Upper Confidence Limit = 6.8226 Lower Confidence Limit = 1.6218 Upper Confidence Limit = 6.8226
Summary Panel for Difference of Before and After

Profiles Plot

Variable = After Before Or After Mean = 69.778 Variable = Before Before Or After Mean = 74 Variable = After Before Or After = 72 Observation = 9 Variable = Before Before Or After = 77 Observation = 9 Variable = After Before Or After = 76 Observation = 8 Variable = Before Before Or After = 77 Observation = 8 Variable = After Before Or After = 61 Observation = 7 Variable = Before Before Or After = 69 Observation = 7 Variable = After Before Or After = 77 Observation = 6 Variable = Before Before Or After = 80 Observation = 6 Variable = After Before Or After = 73 Observation = 5 Variable = Before Before Or After = 83 Observation = 5 Variable = After Before Or After = 57 Observation = 4 Variable = Before Before Or After = 58 Observation = 4 Variable = After Before Or After = 70 Observation = 3 Variable = Before Before Or After = 76 Observation = 3 Variable = After Before Or After = 68 Observation = 2 Variable = Before Before Or After = 68 Observation = 2 Variable = After Before Or After = 74 Observation = 1 Variable = Before Before Or After = 78 Observation = 1
Profiles Plot for Before and After

Agreement Plot

Slope = 1 Y = 0 Before Mean = 74 After Mean = 69.778 Before = 77 After = 72 Observation = 9 Before = 77 After = 76 Observation = 8 Before = 69 After = 61 Observation = 7 Before = 80 After = 77 Observation = 6 Before = 83 After = 73 Observation = 5 Before = 58 After = 57 Observation = 4 Before = 76 After = 70 Observation = 3 Before = 68 After = 68 Observation = 2 Before = 78 After = 74 Observation = 1
Agreement Plot for Before and After

Q-Q Plot

Quantile = 1.4942 Difference = 10 Quantile = 0.932 Difference = 8 Quantile = 0.5716 Difference = 6 Quantile = 0.2744 Difference = 5 Quantile = 0 Difference = 4 Quantile = -0.274 Difference = 3 Quantile = -0.572 Difference = 1 Quantile = -0.932 Difference = 1 Quantile = -1.494 Difference = 0 Slope = 3.383 Y = 4.2222
Q-Q Plot for Difference of Before and After

Nonparametric Two-sample Tests on Yoga data

Variable: _Difference_ (Difference: Before - After)

The Univariate Procedure

_Difference_

Tests For Location

Tests for Location: Mu0=0
Test Statistic p Value
Student's t t 3.744251 Pr > |t| 0.0057
Sign M 4 Pr >= |M| 0.0078
Signed Rank S 18 Pr >= |S| 0.0078
  • “Data taken from a small study designed to show if a half hour of yoga can lower a subject’s heart rate. Before and After heart rates for 10 participants were measured.”
  • “All tests for normality are not significant, but due to the tiny sample size (n=10) you should not interpret this as difference scores being normally distributed. You need to look at the histogram or Q-Q plot to decide if you should be using a nonparametric test. The t table shows a mean difference is 4.222 with t-value of 3.74 and p-value of .0057. Because the mean difference is positive (computed as before - after), we conclude that yoga helped reduce heart rate.”
  • “When in doubt, rerun analysis using nonparametric tests such as the Sign test and the Wilcoxon Signed Rank test. Both show a significant difference at the .05 level.”
  • “Do not simply look at the p-values from the normality tests. Doing so often results in incorrect decisions. When sample sizes are large, the tests for normality are often significant. When sample sizes are small, they are rarely significant. And, it is with small samples that deviations from normality are most important.”

Chapter 8: Comparing More Than Two Means (ANOVA)

Performing a One-Way Analysis of Variance.

SAS Code, click to expand

SAS Code:

#  (&path1 and biostats libname previously defined)
/*** Chapter 8: Comparing More Than Two Means (ANOVA) ***/

/* Performing a One-Way Analysis of Variance - generated code - start */

ods noproctitle;
ods graphics / imagemap=on;

title1 "One-Way Analysis of Variance - tukey";
proc glm data=sashelp.heart plots(maxpoints=none only)=(boxplot 
        diagnostics(unpack));
    class Chol_Status;
    model Weight=Chol_Status;
    means Chol_Status / hovtest=levene plots=none;
    lsmeans Chol_Status / adjust=tukey pdiff alpha=.05 plots=(meanplot diffplot);
    run;
quit;

title1 "One-Way Analysis of Variance - snk Student-Newman-Keuls";
proc glm data=sashelp.heart plots=none;
    class Chol_Status;
    model Weight=Chol_Status;
    means Chol_Status / snk alpha=.05 plots=none;
    run;
quit;

title1;

/*"The Class Level Information confirms that there are three levels for Chol_Status with a relatively small number of missing values.  The ANOVA table shows F test and p-values, but we need to check the diagnostics tests to confirm whether the assumptions were satisfied.  The model has 2 degrees of freedom (3 levels of the independent variable).  The mean squares for the model and error terms show an F-value (the ratio of the between-group variance and the within-group variance) of 25.90 with a corresponding p-value of less than .0001." */

/* "The Residual Plots show the residuals (the differences between the mean of each group and each individual score) in that group with the predicted values (means of each group) shown on the x-axis.  [Residuals by Predicted for Weight] displays the residuals as actual scores, while [Studentized Residuals by Predicted for Weight] displays the residuals as t scores (the number of standard deviations above or below the mean of the group.)" */

/* "[Q-Q Plot of Residuals for Weight] shows small deviations from a straight line towards the bookends; one of the assumptions for running a one-way ANOVA is that the errors (the residuals are estimates of these errors) are normally distributed which appear as a straight line on a Q-Q plot.  A Histogram for Residuals [Distribution of Residuals for Weight] appear to be relatively normally distributed." */

/* "The Box Plot for Weight by Cholesterol Level [Distribution of Weight] graphically displays the distribution of weights in the 3 groups.  The line in the center of the box represents the median, and the small diamond represents the mean.  The means and medians of the three groups are not very different, but the results are highly significant because of the large (> n=5,000) sample size (which give you high power to see even small differences)." */

/* "Next, the output table [Levene's Test for Homogeneity of Weight Variance / ANOVA of Squared Deviations from Group Means] shows a p-value of .2194, you do not reject the null hypothesis of equal variance." */

/* "The next table shows the Group Means and Standard Deviations for the three groups." */

/* "The table that follows [Least Squares Means / Adjustment for Multiple Comparisons: Tukey-Kramer] show the least square means equal to the means in the previous table because this is a one-way model; in unbalanced models with more than one factor, this may not be the case.  We then see p-values for all of the pairwise differences: Borderline and Desirable shows a p-value = <.0001, High and Desirable shows a p-value = <.0001, and Borderline and High shows a p-value = .4869 (not significant)." */

/* "The plot Pairwise Comparison of Means [Weight Comparisons for Chol_Status] displays pairwise differences.  At the intersection of any two groups, you see a diagonal line representing a 95% confidence interval for the difference between the two group means.  If the interval crosses the main diagonal line (that represents no difference), the two group means are not significantly different at the .05 level.  Also, significant differences are shown in blue and non-significant differences are shown in red." */

/* "Further down this set of plots and tables, we see the output from the Student-Newman-Keuls Test for Weight.  SNK is an alternative method of determining pairwise differences [instead of Tukey], and has a slightly higher power to detect differences.  The SNK display [Weight SNK Grouping for Means of Chol_Status ] shows the three means in order from highest to lowest, and means covered by the same bar are not significantly different.  High and Borderline means show up as not being significantly different at the .05 level, consistent with the prior Tukey pairwise differences table and plot." */

/* Performing a One-Way Analysis of Variance - generated code - end */

SAS Output

Results: biostats_by_ex_SAScode.sas

Results: biostats_by_ex_SAScode.sas

One-Way Analysis of Variance - tukey

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
Chol_Status 3 Borderline Desirable High

Number of Observations

Number of Observations Read 5209
Number of Observations Used 5051

One-Way Analysis of Variance - tukey

Dependent Variable: Weight

Analysis of Variance

Weight

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 2 42864.375 21432.188 25.90 <.0001
Error 5048 4176597.649 827.377    
Corrected Total 5050 4219462.024      

Fit Statistics

R-Square Coeff Var Root MSE Weight Mean
0.010159 18.79164 28.76416 153.0689

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
Chol_Status 2 42864.37515 21432.18758 25.90 <.0001

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
Chol_Status 2 42864.37515 21432.18758 25.90 <.0001

Diagnostic Plots

Residual by Predicted

Y = 0
Plot of Residual by Predicted for Weight

RStudent by Predicted

Y = 2 Y = -2
Plot of RStudent by Predicted for Weight

RStudent by Leverage

X = 0.0012 Y = -2 Y = 2
Plot of RStudent by Leverage for Weight

Q-Q Plot

Slope = 28.758 Y = 22E-15
Q-Q Plot of Residuals for Weight

Weight by Predicted

Slope = 1 Y = 0
Plot of Weight by Predicted

Cook's D Plot

Y = .00079
Needleplot of Cook's D statistic by Observation for Weight

Residual Histogram

Residual = 166.5 Percent = 0.0004 Residual = 164.63 Percent = .00095 Residual = 164.63 Percent = .00095 Residual = 162.77 Percent = 0.002 Residual = 162.77 Percent = 0.002 Residual = 160.9 Percent = 0.0038 Residual = 160.9 Percent = 0.0038 Residual = 159.03 Percent = 0.0066 Residual = 159.03 Percent = 0.0066 Residual = 157.17 Percent = 0.0103 Residual = 157.17 Percent = 0.0103 Residual = 153.44 Percent = 0.0191 Residual = 153.44 Percent = 0.0191 Residual = 151.57 Percent = 0.023 Residual = 151.57 Percent = 0.023 Residual = 149.7 Percent = 0.0259 Residual = 149.7 Percent = 0.0259 Residual = 147.84 Percent = 0.0275 Residual = 147.84 Percent = 0.0275 Residual = 145.97 Percent = 0.0282 Residual = 145.97 Percent = 0.0282 Residual = 144.1 Percent = 0.0285 Residual = 144.1 Percent = 0.0285 Residual = 142.24 Percent = 0.0291 Residual = 142.24 Percent = 0.0291 Residual = 140.37 Percent = 0.0304 Residual = 140.37 Percent = 0.0304 Residual = 138.5 Percent = 0.0327 Residual = 138.5 Percent = 0.0327 Residual = 136.64 Percent = 0.0359 Residual = 136.64 Percent = 0.0359 Residual = 134.77 Percent = 0.0396 Residual = 134.77 Percent = 0.0396 Residual = 132.91 Percent = 0.0436 Residual = 132.91 Percent = 0.0436 Residual = 131.04 Percent = 0.0474 Residual = 131.04 Percent = 0.0474 Residual = 129.17 Percent = 0.0507 Residual = 129.17 Percent = 0.0507 Residual = 127.31 Percent = 0.0533 Residual = 127.31 Percent = 0.0533 Residual = 125.44 Percent = 0.0552 Residual = 125.44 Percent = 0.0552 Residual = 123.57 Percent = 0.0561 Residual = 123.57 Percent = 0.0561 Residual = 121.71 Percent = 0.0558 Residual = 121.71 Percent = 0.0558 Residual = 119.84 Percent = 0.0538 Residual = 119.84 Percent = 0.0538 Residual = 117.98 Percent = 0.05 Residual = 117.98 Percent = 0.05 Residual = 114.24 Percent = 0.04 Residual = 114.24 Percent = 0.04 Residual = 112.38 Percent = 0.0371 Residual = 112.38 Percent = 0.0371 Residual = 110.51 Percent = 0.0384 Residual = 110.51 Percent = 0.0384 Residual = 108.64 Percent = 0.0451 Residual = 108.64 Percent = 0.0451 Residual = 106.78 Percent = 0.0577 Residual = 106.78 Percent = 0.0577 Residual = 104.91 Percent = 0.0754 Residual = 104.91 Percent = 0.0754 Residual = 103.04 Percent = 0.0965 Residual = 103.04 Percent = 0.0965 Residual = 97.446 Percent = 0.1645 Residual = 97.446 Percent = 0.1645 Residual = 95.58 Percent = 0.1881 Residual = 95.58 Percent = 0.1881 Residual = 93.713 Percent = 0.2147 Residual = 93.713 Percent = 0.2147 Residual = 91.847 Percent = 0.2462 Residual = 91.847 Percent = 0.2462 Residual = 89.981 Percent = 0.2839 Residual = 89.981 Percent = 0.2839 Residual = 88.114 Percent = 0.3276 Residual = 88.114 Percent = 0.3276 Residual = 86.248 Percent = 0.3759 Residual = 86.248 Percent = 0.3759 Residual = 84.382 Percent = 0.4269 Residual = 84.382 Percent = 0.4269 Residual = 82.515 Percent = 0.4801 Residual = 82.515 Percent = 0.4801 Residual = 80.649 Percent = 0.5363 Residual = 80.649 Percent = 0.5363 Residual = 78.783 Percent = 0.5981 Residual = 78.783 Percent = 0.5981 Residual = 76.917 Percent = 0.6687 Residual = 76.917 Percent = 0.6687 Residual = 75.05 Percent = 0.7496 Residual = 75.05 Percent = 0.7496 Residual = 73.184 Percent = 0.8404 Residual = 73.184 Percent = 0.8404 Residual = 71.318 Percent = 0.9391 Residual = 71.318 Percent = 0.9391 Residual = 69.451 Percent = 1.044 Residual = 69.451 Percent = 1.044 Residual = 67.585 Percent = 1.1549 Residual = 67.585 Percent = 1.1549 Residual = 65.719 Percent = 1.2745 Residual = 65.719 Percent = 1.2745 Residual = 63.852 Percent = 1.4071 Residual = 63.852 Percent = 1.4071 Residual = 61.986 Percent = 1.5576 Residual = 61.986 Percent = 1.5576 Residual = 60.12 Percent = 1.729 Residual = 60.12 Percent = 1.729 Residual = 58.254 Percent = 1.9215 Residual = 58.254 Percent = 1.9215 Residual = 56.387 Percent = 2.1328 Residual = 56.387 Percent = 2.1328 Residual = 54.521 Percent = 2.3605 Residual = 54.521 Percent = 2.3605 Residual = 52.655 Percent = 2.6047 Residual = 52.655 Percent = 2.6047 Residual = 50.788 Percent = 2.8693 Residual = 50.788 Percent = 2.8693 Residual = 48.922 Percent = 3.1616 Residual = 48.922 Percent = 3.1616 Residual = 47.056 Percent = 3.4884 Residual = 47.056 Percent = 3.4884 Residual = 45.189 Percent = 3.8525 Residual = 45.189 Percent = 3.8525 Residual = 43.323 Percent = 4.2502 Residual = 43.323 Percent = 4.2502 Residual = 35.858 Percent = 5.9741 Residual = 35.858 Percent = 5.9741 Residual = 26.526 Percent = 8.2365 Residual = 26.526 Percent = 8.2365 Residual = 24.66 Percent = 8.6725 Residual = 24.66 Percent = 8.6725 Residual = 22.794 Percent = 9.0734 Residual = 22.794 Percent = 9.0734 Residual = 20.927 Percent = 9.4342 Residual = 20.927 Percent = 9.4342 Residual = 19.061 Percent = 9.7574 Residual = 19.061 Percent = 9.7574 Residual = 17.195 Percent = 10.05 Residual = 17.195 Percent = 10.05 Residual = 15.329 Percent = 10.319 Residual = 15.329 Percent = 10.319 Residual = 11.596 Percent = 10.832 Residual = 11.596 Percent = 10.832 Residual = 9.7296 Percent = 11.104 Residual = 9.7296 Percent = 11.104 Residual = 7.8633 Percent = 11.404 Residual = 7.8633 Percent = 11.404 Residual = 5.997 Percent = 11.74 Residual = 5.997 Percent = 11.74 Residual = 2.2644 Percent = 12.469 Residual = 2.2644 Percent = 12.469 Residual = 0.3981 Percent = 12.813 Residual = 0.3981 Percent = 12.813 Residual = -1.468 Percent = 13.109 Residual = -1.468 Percent = 13.109 Residual = -3.335 Percent = 13.346 Residual = -3.335 Percent = 13.346 Residual = -5.201 Percent = 13.529 Residual = -5.201 Percent = 13.529 Residual = -7.067 Percent = 13.675 Residual = -7.067 Percent = 13.675 Residual = -8.933 Percent = 13.799 Residual = -8.933 Percent = 13.799 Residual = -10.8 Percent = 13.903 Residual = -10.8 Percent = 13.903 Residual = -12.67 Percent = 13.967 Residual = -12.67 Percent = 13.967 Residual = -14.53 Percent = 13.96 Residual = -14.53 Percent = 13.96 Residual = -16.4 Percent = 13.846 Residual = -16.4 Percent = 13.846 Residual = -18.26 Percent = 13.601 Residual = -18.26 Percent = 13.601 Residual = -20.13 Percent = 13.224 Residual = -20.13 Percent = 13.224 Residual = -22 Percent = 12.73 Residual = -22 Percent = 12.73 Residual = -23.86 Percent = 12.147 Residual = -23.86 Percent = 12.147 Residual = -25.73 Percent = 11.506 Residual = -25.73 Percent = 11.506 Residual = -42.53 Percent = 5.245 Residual = -42.53 Percent = 5.245 Residual = -44.39 Percent = 4.5642 Residual = -44.39 Percent = 4.5642 Residual = -46.26 Percent = 3.924 Residual = -46.26 Percent = 3.924 Residual = -48.13 Percent = 3.3361 Residual = -48.13 Percent = 3.3361 Residual = -49.99 Percent = 2.8045 Residual = -49.99 Percent = 2.8045 Residual = -51.86 Percent = 2.3277 Residual = -51.86 Percent = 2.3277 Residual = -53.72 Percent = 1.9025 Residual = -53.72 Percent = 1.9025 Residual = -55.59 Percent = 1.5269 Residual = -55.59 Percent = 1.5269 Residual = -57.46 Percent = 1.2008 Residual = -57.46 Percent = 1.2008 Residual = -59.32 Percent = 0.9252 Residual = -59.32 Percent = 0.9252 Residual = -61.19 Percent = 0.7002 Residual = -61.19 Percent = 0.7002 Residual = -63.06 Percent = 0.5234 Residual = -63.06 Percent = 0.5234 Residual = -64.92 Percent = 0.3894 Residual = -64.92 Percent = 0.3894 Residual = -66.79 Percent = 0.2909 Residual = -66.79 Percent = 0.2909 Residual = -68.66 Percent = 0.2194 Residual = -68.66 Percent = 0.2194 Residual = -70.52 Percent = 0.1673 Residual = -70.52 Percent = 0.1673 Residual = -72.39 Percent = 0.1286 Residual = -72.39 Percent = 0.1286 Residual = -74.25 Percent = 0.0996 Residual = -74.25 Percent = 0.0996 Residual = -76.12 Percent = 0.0779 Residual = -76.12 Percent = 0.0779 Residual = -77.99 Percent = 0.0622 Residual = -77.99 Percent = 0.0622 Residual = -79.85 Percent = 0.0512 Residual = -79.85 Percent = 0.0512 Residual = -81.72 Percent = 0.0436 Residual = -81.72 Percent = 0.0436 Residual = -83.59 Percent = 0.0379 Residual = -83.59 Percent = 0.0379 Residual = -87.32 Percent = 0.0275 Residual = -87.32 Percent = 0.0275 Residual = -91.05 Percent = 0.0164 Residual = -91.05 Percent = 0.0164 Residual = -92.92 Percent = 0.0113 Residual = -92.92 Percent = 0.0113 Residual = -94.78 Percent = 0.0071 Residual = -94.78 Percent = 0.0071 Residual = -96.65 Percent = 0.0041 Residual = -96.65 Percent = 0.0041 Residual = -98.52 Percent = 0.0021 Residual = -98.52 Percent = 0.0021 Residual = -100.4 Percent = .00099 Residual = -100.4 Percent = .00099 Residual = -102.2 Percent = .00042 Residual = 155 Percent = 6.8E-6 Residual = 153.74 Percent = 8.6E-6 Residual = 153.74 Percent = 8.6E-6 Residual = 152.47 Percent = 1.1E-5 Residual = 152.47 Percent = 1.1E-5 Residual = 151.21 Percent = 1.4E-5 Residual = 151.21 Percent = 1.4E-5 Residual = 149.95 Percent = 1.7E-5 Residual = 149.95 Percent = 1.7E-5 Residual = 148.69 Percent = 2.2E-5 Residual = 148.69 Percent = 2.2E-5 Residual = 147.42 Percent = 2.7E-5 Residual = 147.42 Percent = 2.7E-5 Residual = 146.16 Percent = 3.4E-5 Residual = 146.16 Percent = 3.4E-5 Residual = 144.9 Percent = 4.3E-5 Residual = 144.9 Percent = 4.3E-5 Residual = 143.64 Percent = 5.3E-5 Residual = 143.64 Percent = 5.3E-5 Residual = 142.37 Percent = 6.6E-5 Residual = 142.37 Percent = 6.6E-5 Residual = 141.11 Percent = 8.2E-5 Residual = 141.11 Percent = 8.2E-5 Residual = 139.85 Percent = 0.0001 Residual = 139.85 Percent = 0.0001 Residual = 138.59 Percent = .00013 Residual = 138.59 Percent = .00013 Residual = 137.32 Percent = .00016 Residual = 137.32 Percent = .00016 Residual = 136.06 Percent = .00019 Residual = 136.06 Percent = .00019 Residual = 134.8 Percent = .00024 Residual = 134.8 Percent = .00024 Residual = 133.54 Percent = .00029 Residual = 133.54 Percent = .00029 Residual = 132.27 Percent = .00035 Residual = 132.27 Percent = .00035 Residual = 131.01 Percent = .00043 Residual = 131.01 Percent = .00043 Residual = 129.75 Percent = .00053 Residual = 129.75 Percent = .00053 Residual = 128.48 Percent = .00064 Residual = 128.48 Percent = .00064 Residual = 127.22 Percent = .00078 Residual = 127.22 Percent = .00078 Residual = 125.96 Percent = .00095 Residual = 125.96 Percent = .00095 Residual = 124.7 Percent = 0.0011 Residual = 124.7 Percent = 0.0011 Residual = 123.43 Percent = 0.0014 Residual = 123.43 Percent = 0.0014 Residual = 122.17 Percent = 0.0017 Residual = 122.17 Percent = 0.0017 Residual = 120.91 Percent = 0.002 Residual = 120.91 Percent = 0.002 Residual = 119.65 Percent = 0.0024 Residual = 119.65 Percent = 0.0024 Residual = 118.38 Percent = 0.0029 Residual = 118.38 Percent = 0.0029 Residual = 117.12 Percent = 0.0035 Residual = 117.12 Percent = 0.0035 Residual = 115.86 Percent = 0.0041 Residual = 115.86 Percent = 0.0041 Residual = 114.6 Percent = 0.0049 Residual = 114.6 Percent = 0.0049 Residual = 113.33 Percent = 0.0059 Residual = 113.33 Percent = 0.0059 Residual = 112.07 Percent = 0.007 Residual = 112.07 Percent = 0.007 Residual = 110.81 Percent = 0.0083 Residual = 110.81 Percent = 0.0083 Residual = 109.55 Percent = 0.0098 Residual = 109.55 Percent = 0.0098 Residual = 108.28 Percent = 0.0116 Residual = 108.28 Percent = 0.0116 Residual = 107.02 Percent = 0.0136 Residual = 107.02 Percent = 0.0136 Residual = 105.76 Percent = 0.0161 Residual = 105.76 Percent = 0.0161 Residual = 104.49 Percent = 0.0188 Residual = 104.49 Percent = 0.0188 Residual = 103.23 Percent = 0.0221 Residual = 103.23 Percent = 0.0221 Residual = 101.97 Percent = 0.0258 Residual = 101.97 Percent = 0.0258 Residual = 100.71 Percent = 0.0302 Residual = 100.71 Percent = 0.0302 Residual = 99.444 Percent = 0.0351 Residual = 99.444 Percent = 0.0351 Residual = 98.182 Percent = 0.0408 Residual = 98.182 Percent = 0.0408 Residual = 96.919 Percent = 0.0474 Residual = 96.919 Percent = 0.0474 Residual = 95.657 Percent = 0.0549 Residual = 95.657 Percent = 0.0549 Residual = 94.394 Percent = 0.0635 Residual = 94.394 Percent = 0.0635 Residual = 93.131 Percent = 0.0733 Residual = 93.131 Percent = 0.0733 Residual = 91.869 Percent = 0.0844 Residual = 91.869 Percent = 0.0844 Residual = 90.606 Percent = 0.097 Residual = 90.606 Percent = 0.097 Residual = 89.343 Percent = 0.1113 Residual = 89.343 Percent = 0.1113 Residual = 88.081 Percent = 0.1274 Residual = 88.081 Percent = 0.1274 Residual = 86.818 Percent = 0.1456 Residual = 86.818 Percent = 0.1456 Residual = 85.556 Percent = 0.1661 Residual = 85.556 Percent = 0.1661 Residual = 84.293 Percent = 0.1891 Residual = 84.293 Percent = 0.1891 Residual = 83.03 Percent = 0.2148 Residual = 83.03 Percent = 0.2148 Residual = 81.768 Percent = 0.2436 Residual = 81.768 Percent = 0.2436 Residual = 80.505 Percent = 0.2757 Residual = 80.505 Percent = 0.2757 Residual = 79.242 Percent = 0.3115 Residual = 79.242 Percent = 0.3115 Residual = 77.98 Percent = 0.3512 Residual = 77.98 Percent = 0.3512 Residual = 76.717 Percent = 0.3952 Residual = 76.717 Percent = 0.3952 Residual = 75.455 Percent = 0.4439 Residual = 75.455 Percent = 0.4439 Residual = 74.192 Percent = 0.4976 Residual = 74.192 Percent = 0.4976 Residual = 72.929 Percent = 0.5568 Residual = 72.929 Percent = 0.5568 Residual = 71.667 Percent = 0.6218 Residual = 71.667 Percent = 0.6218 Residual = 70.404 Percent = 0.693 Residual = 70.404 Percent = 0.693 Residual = 69.141 Percent = 0.7709 Residual = 69.141 Percent = 0.7709 Residual = 67.879 Percent = 0.8559 Residual = 67.879 Percent = 0.8559 Residual = 66.616 Percent = 0.9484 Residual = 66.616 Percent = 0.9484 Residual = 65.354 Percent = 1.0489 Residual = 65.354 Percent = 1.0489 Residual = 64.091 Percent = 1.1579 Residual = 64.091 Percent = 1.1579 Residual = 62.828 Percent = 1.2756 Residual = 62.828 Percent = 1.2756 Residual = 61.566 Percent = 1.4027 Residual = 61.566 Percent = 1.4027 Residual = 60.303 Percent = 1.5395 Residual = 60.303 Percent = 1.5395 Residual = 59.04 Percent = 1.6863 Residual = 59.04 Percent = 1.6863 Residual = 57.778 Percent = 1.8436 Residual = 57.778 Percent = 1.8436 Residual = 56.515 Percent = 2.0116 Residual = 56.515 Percent = 2.0116 Residual = 55.253 Percent = 2.1908 Residual = 55.253 Percent = 2.1908 Residual = 53.99 Percent = 2.3813 Residual = 53.99 Percent = 2.3813 Residual = 52.727 Percent = 2.5834 Residual = 52.727 Percent = 2.5834 Residual = 51.465 Percent = 2.7973 Residual = 51.465 Percent = 2.7973 Residual = 50.202 Percent = 3.023 Residual = 50.202 Percent = 3.023 Residual = 48.939 Percent = 3.2607 Residual = 48.939 Percent = 3.2607 Residual = 47.677 Percent = 3.5102 Residual = 47.677 Percent = 3.5102 Residual = 46.414 Percent = 3.7716 Residual = 46.414 Percent = 3.7716 Residual = 45.152 Percent = 4.0446 Residual = 45.152 Percent = 4.0446 Residual = 43.889 Percent = 4.3291 Residual = 43.889 Percent = 4.3291 Residual = 42.626 Percent = 4.6247 Residual = 42.626 Percent = 4.6247 Residual = 41.364 Percent = 4.9309 Residual = 41.364 Percent = 4.9309 Residual = 40.101 Percent = 5.2472 Residual = 40.101 Percent = 5.2472 Residual = 37.576 Percent = 5.9079 Residual = 37.576 Percent = 5.9079 Residual = 24.949 Percent = 9.5216 Residual = 24.949 Percent = 9.5216 Residual = 22.424 Percent = 10.236 Residual = 22.424 Percent = 10.236 Residual = 19.899 Percent = 10.919 Residual = 19.899 Percent = 10.919 Residual = 18.636 Percent = 11.245 Residual = 18.636 Percent = 11.245 Residual = 17.374 Percent = 11.558 Residual = 17.374 Percent = 11.558 Residual = 16.111 Percent = 11.858 Residual = 16.111 Percent = 11.858 Residual = 14.848 Percent = 12.141 Residual = 14.848 Percent = 12.141 Residual = 13.586 Percent = 12.407 Residual = 13.586 Percent = 12.407 Residual = 12.323 Percent = 12.655 Residual = 12.323 Percent = 12.655 Residual = 11.061 Percent = 12.883 Residual = 11.061 Percent = 12.883 Residual = 9.798 Percent = 13.09 Residual = 9.798 Percent = 13.09 Residual = 8.5354 Percent = 13.274 Residual = 8.5354 Percent = 13.274 Residual = 7.2727 Percent = 13.436 Residual = 7.2727 Percent = 13.436 Residual = 6.0101 Percent = 13.573 Residual = 6.0101 Percent = 13.573 Residual = 4.7475 Percent = 13.684 Residual = 4.7475 Percent = 13.684 Residual = 3.4848 Percent = 13.771 Residual = 3.4848 Percent = 13.771 Residual = 2.2222 Percent = 13.831 Residual = 2.2222 Percent = 13.831 Residual = 0.9596 Percent = 13.864 Residual = 0.9596 Percent = 13.864 Residual = 22E-15 Percent = 13.872 Residual = 22E-15 Percent = 13.872 Residual = -0.303 Percent = 13.871 Residual = -0.303 Percent = 13.871 Residual = -1.566 Percent = 13.852 Residual = -1.566 Percent = 13.852 Residual = -2.828 Percent = 13.805 Residual = -2.828 Percent = 13.805 Residual = -4.091 Percent = 13.733 Residual = -4.091 Percent = 13.733 Residual = -5.354 Percent = 13.634 Residual = -5.354 Percent = 13.634 Residual = -6.616 Percent = 13.51 Residual = -6.616 Percent = 13.51 Residual = -7.879 Percent = 13.361 Residual = -7.879 Percent = 13.361 Residual = -9.141 Percent = 13.189 Residual = -9.141 Percent = 13.189 Residual = -10.4 Percent = 12.993 Residual = -10.4 Percent = 12.993 Residual = -11.67 Percent = 12.776 Residual = -11.67 Percent = 12.776 Residual = -12.93 Percent = 12.539 Residual = -12.93 Percent = 12.539 Residual = -14.19 Percent = 12.282 Residual = -14.19 Percent = 12.282 Residual = -15.45 Percent = 12.007 Residual = -15.45 Percent = 12.007 Residual = -16.72 Percent = 11.716 Residual = -16.72 Percent = 11.716 Residual = -17.98 Percent = 11.41 Residual = -17.98 Percent = 11.41 Residual = -19.24 Percent = 11.09 Residual = -19.24 Percent = 11.09 Residual = -20.51 Percent = 10.758 Residual = -20.51 Percent = 10.758 Residual = -31.87 Percent = 7.5074 Residual = -31.87 Percent = 7.5074 Residual = -35.66 Percent = 6.4318 Residual = -35.66 Percent = 6.4318 Residual = -38.18 Percent = 5.7461 Residual = -38.18 Percent = 5.7461 Residual = -40.71 Percent = 5.0941 Residual = -40.71 Percent = 5.0941 Residual = -41.97 Percent = 4.7826 Residual = -41.97 Percent = 4.7826 Residual = -43.23 Percent = 4.4814 Residual = -43.23 Percent = 4.4814 Residual = -44.49 Percent = 4.1912 Residual = -44.49 Percent = 4.1912 Residual = -45.76 Percent = 3.9121 Residual = -45.76 Percent = 3.9121 Residual = -47.02 Percent = 3.6447 Residual = -47.02 Percent = 3.6447 Residual = -48.28 Percent = 3.3889 Residual = -48.28 Percent = 3.3889 Residual = -49.55 Percent = 3.1451 Residual = -49.55 Percent = 3.1451 Residual = -50.81 Percent = 2.9132 Residual = -50.81 Percent = 2.9132 Residual = -52.07 Percent = 2.6931 Residual = -52.07 Percent = 2.6931 Residual = -53.33 Percent = 2.4849 Residual = -53.33 Percent = 2.4849 Residual = -54.6 Percent = 2.2884 Residual = -54.6 Percent = 2.2884 Residual = -55.86 Percent = 2.1034 Residual = -55.86 Percent = 2.1034 Residual = -57.12 Percent = 1.9296 Residual = -57.12 Percent = 1.9296 Residual = -58.38 Percent = 1.7667 Residual = -58.38 Percent = 1.7667 Residual = -59.65 Percent = 1.6145 Residual = -59.65 Percent = 1.6145 Residual = -60.91 Percent = 1.4726 Residual = -60.91 Percent = 1.4726 Residual = -62.17 Percent = 1.3405 Residual = -62.17 Percent = 1.3405 Residual = -63.43 Percent = 1.218 Residual = -63.43 Percent = 1.218 Residual = -64.7 Percent = 1.1045 Residual = -64.7 Percent = 1.1045 Residual = -65.96 Percent = 0.9996 Residual = -65.96 Percent = 0.9996 Residual = -67.22 Percent = 0.903 Residual = -67.22 Percent = 0.903 Residual = -68.48 Percent = 0.8142 Residual = -68.48 Percent = 0.8142 Residual = -69.75 Percent = 0.7326 Residual = -69.75 Percent = 0.7326 Residual = -71.01 Percent = 0.658 Residual = -71.01 Percent = 0.658 Residual = -72.27 Percent = 0.5898 Residual = -72.27 Percent = 0.5898 Residual = -73.54 Percent = 0.5277 Residual = -73.54 Percent = 0.5277 Residual = -74.8 Percent = 0.4712 Residual = -74.8 Percent = 0.4712 Residual = -76.06 Percent = 0.4199 Residual = -76.06 Percent = 0.4199 Residual = -77.32 Percent = 0.3736 Residual = -77.32 Percent = 0.3736 Residual = -78.59 Percent = 0.3316 Residual = -78.59 Percent = 0.3316 Residual = -79.85 Percent = 0.2939 Residual = -79.85 Percent = 0.2939 Residual = -81.11 Percent = 0.2599 Residual = -81.11 Percent = 0.2599 Residual = -82.37 Percent = 0.2294 Residual = -82.37 Percent = 0.2294 Residual = -83.64 Percent = 0.2021 Residual = -83.64 Percent = 0.2021 Residual = -84.9 Percent = 0.1777 Residual = -84.9 Percent = 0.1777 Residual = -86.16 Percent = 0.1559 Residual = -86.16 Percent = 0.1559 Residual = -87.42 Percent = 0.1366 Residual = -87.42 Percent = 0.1366 Residual = -88.69 Percent = 0.1194 Residual = -88.69 Percent = 0.1194 Residual = -89.95 Percent = 0.1042 Residual = -89.95 Percent = 0.1042 Residual = -91.21 Percent = 0.0907 Residual = -91.21 Percent = 0.0907 Residual = -92.47 Percent = 0.0789 Residual = -92.47 Percent = 0.0789 Residual = -93.74 Percent = 0.0684 Residual = -93.74 Percent = 0.0684 Residual = -95 Percent = 0.0592 Residual = 150 Percent = 0.0396 Residual = 150 Percent = 0.0396 Residual = 140 Percent = 0.0198 Residual = 140 Percent = 0.0198 Residual = 130 Percent = 0.0594 Residual = 130 Percent = 0.0594 Residual = 120 Percent = 0.0594 Residual = 120 Percent = 0.0594 Residual = 110 Percent = 0.0198 Residual = 110 Percent = 0.0198 Residual = 100 Percent = 0.1188 Residual = 100 Percent = 0.1188 Residual = 90 Percent = 0.2772 Residual = 90 Percent = 0.2772 Residual = 80 Percent = 0.5147 Residual = 80 Percent = 0.5147 Residual = 70 Percent = 0.9899 Residual = 70 Percent = 0.9899 Residual = 60 Percent = 1.6234 Residual = 60 Percent = 1.6234 Residual = 50 Percent = 2.8707 Residual = 50 Percent = 2.8707 Residual = 40 Percent = 4.9693 Residual = 40 Percent = 4.9693 Residual = 30 Percent = 7.3253 Residual = 30 Percent = 7.3253 Residual = 20 Percent = 9.8198 Residual = 20 Percent = 9.8198 Residual = 10 Percent = 10.731 Residual = 10 Percent = 10.731 Residual = 0 Percent = 13.265 Residual = 0 Percent = 13.265 Residual = -10 Percent = 13.68 Residual = -10 Percent = 13.68 Residual = -20 Percent = 13.76 Residual = -20 Percent = 13.76 Residual = -30 Percent = 9.9188 Residual = -30 Percent = 9.9188 Residual = -40 Percent = 6.375 Residual = -40 Percent = 6.375 Residual = -50 Percent = 2.6925 Residual = -50 Percent = 2.6925 Residual = -60 Percent = 0.6731 Residual = -60 Percent = 0.6731 Residual = -70 Percent = 0.1386 Residual = -70 Percent = 0.1386 Residual = -80 Percent = 0.0396 Residual = -80 Percent = 0.0396 Residual = -90 Percent = 0.0198 Residual = -90 Percent = 0.0198
Histogram of Residuals for Weight with normal and kernel densities overlaid

RF Plot

Residual-Fit Spread Plot for Weight

Box Plot

Cholesterol Status = High Weight = 235 Observation = 2577 Cholesterol Status = High Weight = 235 Observation = 4961 Cholesterol Status = High Weight = 236 Observation = 3125 Cholesterol Status = High Weight = 236 Observation = 2947 Cholesterol Status = High Weight = 237 Observation = 2548 Cholesterol Status = High Weight = 238 Observation = 1797 Cholesterol Status = High Weight = 239 Observation = 1680 Cholesterol Status = High Weight = 241 Observation = 2610 Cholesterol Status = High Weight = 244 Observation = 1945 Cholesterol Status = High Weight = 244 Observation = 1237 Cholesterol Status = High Weight = 245 Observation = 1665 Cholesterol Status = High Weight = 250 Observation = 3845 Cholesterol Status = High Weight = 255 Observation = 5200 Cholesterol Status = High Weight = 256 Observation = 5006 Cholesterol Status = High Weight = 261 Observation = 3124 Cholesterol Status = High Weight = 293 Observation = 3252 Cholesterol Status = Desirable Weight = 225 Observation = 2370 Cholesterol Status = Desirable Weight = 226 Observation = 4312 Cholesterol Status = Desirable Weight = 226 Observation = 2135 Cholesterol Status = Desirable Weight = 227 Observation = 4055 Cholesterol Status = Desirable Weight = 228 Observation = 3514 Cholesterol Status = Desirable Weight = 229 Observation = 3671 Cholesterol Status = Desirable Weight = 231 Observation = 41 Cholesterol Status = Desirable Weight = 231 Observation = 141 Cholesterol Status = Desirable Weight = 234 Observation = 2762 Cholesterol Status = Desirable Weight = 234 Observation = 2308 Cholesterol Status = Desirable Weight = 239 Observation = 1624 Cholesterol Status = Desirable Weight = 239 Observation = 1648 Cholesterol Status = Desirable Weight = 242 Observation = 2100 Cholesterol Status = Desirable Weight = 243 Observation = 672 Cholesterol Status = Desirable Weight = 245 Observation = 3872 Cholesterol Status = Desirable Weight = 246 Observation = 4533 Cholesterol Status = Desirable Weight = 247 Observation = 492 Cholesterol Status = Desirable Weight = 250 Observation = 837 Cholesterol Status = Desirable Weight = 269 Observation = 4240 Cholesterol Status = Desirable Weight = 275 Observation = 5134 Cholesterol Status = Desirable Weight = 276 Observation = 2120 Cholesterol Status = Desirable Weight = 281 Observation = 4858 Cholesterol Status = Desirable Weight = 300 Observation = 4704 Cholesterol Status = Borderline Weight = 235 Observation = 2349 Cholesterol Status = Borderline Weight = 236 Observation = 5063 Cholesterol Status = Borderline Weight = 237 Observation = 2914 Cholesterol Status = Borderline Weight = 238 Observation = 1773 Cholesterol Status = Borderline Weight = 239 Observation = 3661 Cholesterol Status = Borderline Weight = 240 Observation = 1779 Cholesterol Status = Borderline Weight = 241 Observation = 437 Cholesterol Status = Borderline Weight = 244 Observation = 3315 Cholesterol Status = Borderline Weight = 271 Observation = 2438 Cholesterol Status = Borderline Weight = 273 Observation = 2593 Cholesterol Status = Borderline Weight = 300 Observation = 3360 Cholesterol Status = Borderline Weight = 72 Observation = 2250 Cholesterol Status = Borderline Weight = 67 Observation = 5098 Cholesterol Status = High Data Minimum = 85 Minimum Whisker = 85 First Quartile = 135 Median = 153 Third Quartile = 174 Maximum Whisker = 231 Data Maximum = 293 Mean = 155.41 Standard Deviation = 28.237 Number of Observations = 1788 Sum of Weight = . Cholesterol Status = High Data Minimum = 85 Minimum Whisker = 85 First Quartile = 135 Median = 153 Third Quartile = 174 Maximum Whisker = 231 Data Maximum = 293 Mean = 155.41 Standard Deviation = 28.237 Number of Observations = 1788 Sum of Weight = . Cholesterol Status = High Data Minimum = 85 Minimum Whisker = 85 First Quartile = 135 Median = 153 Third Quartile = 174 Maximum Whisker = 231 Data Maximum = 293 Mean = 155.41 Standard Deviation = 28.237 Number of Observations = 1788 Sum of Weight = . Cholesterol Status = High Data Minimum = 85 Minimum Whisker = 85 First Quartile = 135 Median = 153 Third Quartile = 174 Maximum Whisker = 231 Data Maximum = 293 Mean = 155.41 Standard Deviation = 28.237 Number of Observations = 1788 Sum of Weight = . Cholesterol Status = High Data Minimum = 85 Minimum Whisker = 85 First Quartile = 135 Median = 153 Third Quartile = 174 Maximum Whisker = 231 Data Maximum = 293 Mean = 155.41 Standard Deviation = 28.237 Number of Observations = 1788 Sum of Weight = . Cholesterol Status = High Data Minimum = 85 Minimum Whisker = 85 First Quartile = 135 Median = 153 Third Quartile = 174 Maximum Whisker = 231 Data Maximum = 293 Mean = 155.41 Standard Deviation = 28.237 Number of Observations = 1788 Sum of Weight = . Cholesterol Status = High Data Minimum = 85 Minimum Whisker = 85 First Quartile = 135 Median = 153 Third Quartile = 174 Maximum Whisker = 231 Data Maximum = 293 Mean = 155.41 Standard Deviation = 28.237 Number of Observations = 1788 Sum of Weight = . Cholesterol Status = High Data Minimum = 85 Minimum Whisker = 85 First Quartile = 135 Median = 153 Third Quartile = 174 Maximum Whisker = 231 Data Maximum = 293 Mean = 155.41 Standard Deviation = 28.237 Number of Observations = 1788 Sum of Weight = . Cholesterol Status = Desirable Data Minimum = 71 Minimum Whisker = 71 First Quartile = 127 Median = 144 Third Quartile = 166 Maximum Whisker = 222 Data Maximum = 300 Mean = 148.43 Standard Deviation = 29.636 Number of Observations = 1403 Sum of Weight = . Cholesterol Status = Desirable Data Minimum = 71 Minimum Whisker = 71 First Quartile = 127 Median = 144 Third Quartile = 166 Maximum Whisker = 222 Data Maximum = 300 Mean = 148.43 Standard Deviation = 29.636 Number of Observations = 1403 Sum of Weight = . Cholesterol Status = Desirable Data Minimum = 71 Minimum Whisker = 71 First Quartile = 127 Median = 144 Third Quartile = 166 Maximum Whisker = 222 Data Maximum = 300 Mean = 148.43 Standard Deviation = 29.636 Number of Observations = 1403 Sum of Weight = . Cholesterol Status = Desirable Data Minimum = 71 Minimum Whisker = 71 First Quartile = 127 Median = 144 Third Quartile = 166 Maximum Whisker = 222 Data Maximum = 300 Mean = 148.43 Standard Deviation = 29.636 Number of Observations = 1403 Sum of Weight = . Cholesterol Status = Desirable Data Minimum = 71 Minimum Whisker = 71 First Quartile = 127 Median = 144 Third Quartile = 166 Maximum Whisker = 222 Data Maximum = 300 Mean = 148.43 Standard Deviation = 29.636 Number of Observations = 1403 Sum of Weight = . Cholesterol Status = Desirable Data Minimum = 71 Minimum Whisker = 71 First Quartile = 127 Median = 144 Third Quartile = 166 Maximum Whisker = 222 Data Maximum = 300 Mean = 148.43 Standard Deviation = 29.636 Number of Observations = 1403 Sum of Weight = . Cholesterol Status = Desirable Data Minimum = 71 Minimum Whisker = 71 First Quartile = 127 Median = 144 Third Quartile = 166 Maximum Whisker = 222 Data Maximum = 300 Mean = 148.43 Standard Deviation = 29.636 Number of Observations = 1403 Sum of Weight = . Cholesterol Status = Desirable Data Minimum = 71 Minimum Whisker = 71 First Quartile = 127 Median = 144 Third Quartile = 166 Maximum Whisker = 222 Data Maximum = 300 Mean = 148.43 Standard Deviation = 29.636 Number of Observations = 1403 Sum of Weight = . Cholesterol Status = Borderline Data Minimum = 67 Minimum Whisker = 82 First Quartile = 134 Median = 152 Third Quartile = 174 Maximum Whisker = 232 Data Maximum = 300 Mean = 154.32 Standard Deviation = 28.598 Number of Observations = 1860 Sum of Weight = . Cholesterol Status = Borderline Data Minimum = 67 Minimum Whisker = 82 First Quartile = 134 Median = 152 Third Quartile = 174 Maximum Whisker = 232 Data Maximum = 300 Mean = 154.32 Standard Deviation = 28.598 Number of Observations = 1860 Sum of Weight = . Cholesterol Status = Borderline Data Minimum = 67 Minimum Whisker = 82 First Quartile = 134 Median = 152 Third Quartile = 174 Maximum Whisker = 232 Data Maximum = 300 Mean = 154.32 Standard Deviation = 28.598 Number of Observations = 1860 Sum of Weight = . Cholesterol Status = Borderline Data Minimum = 67 Minimum Whisker = 82 First Quartile = 134 Median = 152 Third Quartile = 174 Maximum Whisker = 232 Data Maximum = 300 Mean = 154.32 Standard Deviation = 28.598 Number of Observations = 1860 Sum of Weight = . Cholesterol Status = Borderline Data Minimum = 67 Minimum Whisker = 82 First Quartile = 134 Median = 152 Third Quartile = 174 Maximum Whisker = 232 Data Maximum = 300 Mean = 154.32 Standard Deviation = 28.598 Number of Observations = 1860 Sum of Weight = . Cholesterol Status = Borderline Data Minimum = 67 Minimum Whisker = 82 First Quartile = 134 Median = 152 Third Quartile = 174 Maximum Whisker = 232 Data Maximum = 300 Mean = 154.32 Standard Deviation = 28.598 Number of Observations = 1860 Sum of Weight = . Cholesterol Status = Borderline Data Minimum = 67 Minimum Whisker = 82 First Quartile = 134 Median = 152 Third Quartile = 174 Maximum Whisker = 232 Data Maximum = 300 Mean = 154.32 Standard Deviation = 28.598 Number of Observations = 1860 Sum of Weight = . Cholesterol Status = Borderline Data Minimum = 67 Minimum Whisker = 82 First Quartile = 134 Median = 152 Third Quartile = 174 Maximum Whisker = 232 Data Maximum = 300 Mean = 154.32 Standard Deviation = 28.598 Number of Observations = 1860 Sum of Weight = .
Fit Plot for Weight by Cholesterol Status

One-Way Analysis of Variance - tukey

Means

Chol_Status

Weight

Levene's HoV Test

Levene's Test for Homogeneity of Weight Variance
ANOVA of Squared Deviations from Group Means
Source DF Sum of Squares Mean Square F Value Pr > F
Chol_Status 2 5399505 2699752 1.52 0.2194
Error 5048 8.9813E9 1779186    

One-Way Analysis of Variance - tukey

Chol_Status

Means

Level of
Chol_Status		 N Weight
Mean Std Dev
Borderline 1860 154.318280 28.5982126
Desirable 1403 148.431219 29.6364336
High 1788 155.408277 28.2367277

One-Way Analysis of Variance - tukey

Least Squares Means

Adjustment for Multiple Comparisons: Tukey-Kramer

Least Squares Means

Chol_Status

Weight

LSMeans

Chol_Status Weight LSMEAN LSMEAN Number
Borderline 154.318280 1
Desirable 148.431219 2
High 155.408277 3

Difference Matrix

Least Squares Means for effect Chol_Status
Pr > |t| for H0: LSMean(i)=LSMean(j)

Dependent Variable: Weight
i/j 1 2 3
1   <.0001 0.4869
2 <.0001   <.0001
3 0.4869 <.0001  

Chol_Status Mean Plot

Chol_Status = High LS-Mean = 155.41 Group = 1 Chol_Status = Desirable LS-Mean = 148.43 Group = 1 Chol_Status = Borderline LS-Mean = 154.32 Group = 1
Plot of Weight least-squares means for Chol_Status.

Chol_Status Diffogram

Comparison = High vs. Desirable Comparison = High vs. Desirable Comparison = Borderline vs. Desirable Comparison = Borderline vs. Desirable Comparison = High vs. Borderline Comparison = High vs. Borderline Slope = 1 Y = 0 Mean = 155.408 (High) Mean = 155.408 (High) Mean = 148.431 (Desirable) Mean = 148.431 (Desirable) Mean = 154.318 (Borderline) Mean = 154.318 (Borderline) Mean = 155.408 (High) Mean = 155.408 (High) Mean = 148.431 (Desirable) Mean = 148.431 (Desirable) Mean = 154.318 (Borderline) Mean = 154.318 (Borderline)
Plot of all pairwise Weight least-squares means differences for Chol_Status with Tukey-Kramer adjustment at significance level 0.05.

One-Way Analysis of Variance - snk Student-Newman-Keuls

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
Chol_Status 3 Borderline Desirable High

Number of Observations

Number of Observations Read 5209
Number of Observations Used 5051

One-Way Analysis of Variance - snk Student-Newman-Keuls

Dependent Variable: Weight

Analysis of Variance

Weight

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 2 42864.375 21432.188 25.90 <.0001
Error 5048 4176597.649 827.377    
Corrected Total 5050 4219462.024      

Fit Statistics

R-Square Coeff Var Root MSE Weight Mean
0.010159 18.79164 28.76416 153.0689

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
Chol_Status 2 42864.37515 21432.18758 25.90 <.0001

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
Chol_Status 2 42864.37515 21432.18758 25.90 <.0001

Means

Chol_Status

Weight

Multiple Comparison Lines

Student-Newman-Keuls

One-Way Analysis of Variance - snk Student-Newman-Keuls

Student-Newman-Keuls Test for Weight

Note:This test controls the Type I experimentwise error rate under the complete null hypothesis but not under partial null hypotheses.

Information

Alpha 0.05
Error Degrees of Freedom 5048
Error Mean Square 827.3767
Harmonic Mean of Cell Sizes 1657.754

Note:Cell sizes are not equal.

Critical Ranges

Number of Means 2 3
Critical Range 1.958659 2.3422709

LinesPlot

_LineColumn = 1 _LineStop = 2.4 _LineStart = 1.6 _Line = 2 _LineColumn = 1 _LineStop = 1.4 _LineStart = -0.4 _Line = 1 _Row = 2 _Row = 1 _Row = 0
#LN00130
  • “The Class Level Information confirms that there are three levels for Chol_Status with a relatively small number of missing values. The ANOVA table shows F test and p-values, but we need to check the diagnostics tests to confirm whether the assumptions were satisfied. The model has 2 degrees of freedom (3 levels of the independent variable). The mean squares for the model and error terms show an F-value (the ratio of the between-group variance and the within-group variance) of 25.90 with a corresponding p-value of less than .0001.”
  • “The Residual Plots show the residuals (the differences between the mean of each group and each individual score) in that group with the predicted values (means of each group) shown on the x-axis. [Residuals by Predicted for Weight] displays the residuals as actual scores, while [Studentized Residuals by Predicted for Weight] displays the residuals as t scores (the number of standard deviations above or below the mean of the group.)”
  • “[Q-Q Plot of Residuals for Weight] shows small deviations from a straight line towards the bookends; one of the assumptions for running a one-way ANOVA is that the errors (the residuals are estimates of these errors) are normally distributed which appear as a straight line on a Q-Q plot. A Histogram for Residuals [Distribution of Residuals for Weight] appear to be relatively normally distributed.”
  • “The Box Plot for Weight by Cholesterol Level [Distribution of Weight] graphically displays the distribution of weights in the 3 groups. The line in the center of the box represents the median, and the small diamond represents the mean. The means and medians of the three groups are not very different, but the results are highly significant because of the large (> n=5,000) sample size (which give you high power to see even small differences).”
  • “Next, the output table [Levene’s Test for Homogeneity of Weight Variance / ANOVA of Squared Deviations from Group Means] shows a p-value of .2194, you do not reject the null hypothesis of equal variance.”
  • “The next table shows the Group Means and Standard Deviations for the three groups.”
  • “The table that follows [Least Squares Means / Adjustment for Multiple Comparisons: Tukey-Kramer] show the least square means equal to the means in the previous table because this is a one-way model; in unbalanced models with more than one factor, this may not be the case. We then see p-values for all of the pairwise differences: Borderline and Desirable shows a p-value = <.0001, High and Desirable shows a p-value = <.0001, and Borderline and High shows a p-value = .4869 (not significant).” - “The plot Pairwise Comparison of Means [Weight Comparisons for Chol_Status] displays pairwise differences. At the intersection of any two groups, you see a diagonal line representing a 95% confidence interval for the difference between the two group means. If the interval crosses the main diagonal line (that represents no difference), the two group means are not significantly different at the .05 level. Also, significant differences are shown in blue and non-significant differences are shown in red.”
  • “Further down this set of plots and tables, we see the output from the Student-Newman-Keuls Test for Weight. SNK is an alternative method of determining pairwise differences [instead of Tukey], and has a slightly higher power to detect differences. The SNK display [Weight SNK Grouping for Means of Chol_Status ] shows the three means in order from highest to lowest, and means covered by the same bar are not significantly different. High and Borderline means show up as not being significantly different at the .05 level, consistent with the prior Tukey pairwise differences table and plot.”

Nonparametric One-Way Tests.

SAS Code, click to expand

SAS Code:

#  (&path1 and biostats libname previously defined)
/* Performing a Nonparametric One-Way Tests - generated code - start */
title1 "Nonparametric One-Way Test on 3 Fish Species";
ods noproctitle;
proc npar1way data=sashelp.fish (where=(Species EQ 'Bream' OR Species EQ 'Pike' OR Species EQ 'Roach'))
  wilcoxon dscf plots(only)=(wilcoxonboxplot);
  class Species;
  var Weight;
  run;
  
  /* "Using Nonparametric One-Way ANOVA + Pairwise multiple comparison analysis (asymptotic only) if you feel that the distribution assumptions are not satisfied." */  

  /* "The Kruskal-Wallis test implies that the three fish weights are not all equal (p <.0001).  */  

  /* "The box plot show that Roach are lighter than Bream or Pike. To determine which pairs of fish are unequal, look at Pairwise Comparisons table to see the p-values; it shows that the comparisons of Bream vs. Roach and Roach vs. Pike are significantly different (p <.0001) while the comparison of Bream vs. Pike is not." */  
title1;
/* Performing a Nonparametric One-Way Tests - generated code - end */

SAS Output

Results: biostats_by_ex_SAScode.sas

Results: biostats_by_ex_SAScode.sas

Nonparametric One-Way Test on 3 Fish Species

The Npar1way Procedure

Variable Weight

Wilcoxon Analysis

Scores

Wilcoxon Scores (Rank Sums) for Variable Weight
Classified by Variable Species
Species N Sum of
Scores		 Expected
Under H0		 Std Dev
Under H0		 Mean
Score
Average scores were used for ties.
Bream 34 1580.00 1224.0 86.852273 46.470588
Roach 20 224.50 720.0 78.206158 11.225000
Pike 17 751.50 612.0 74.192876 44.205882

Kruskal-Wallis Test

Kruskal-Wallis Test
Chi-Square DF Pr > ChiSq
40.2791 2 <.0001

Box Plot

Species = Pike Data Minimum = 17.5 Minimum Whisker = 17.5 First Quartile = 27 Median = 42 Third Quartile = 63.5 Maximum Whisker = 71 Data Maximum = 71 Mean = 44.206 Standard Deviation = 18.823 Number of Observations = 17 Sum of Weight = . Species = Pike Data Minimum = 17.5 Minimum Whisker = 17.5 First Quartile = 27 Median = 42 Third Quartile = 63.5 Maximum Whisker = 71 Data Maximum = 71 Mean = 44.206 Standard Deviation = 18.823 Number of Observations = 17 Sum of Weight = . Species = Pike Data Minimum = 17.5 Minimum Whisker = 17.5 First Quartile = 27 Median = 42 Third Quartile = 63.5 Maximum Whisker = 71 Data Maximum = 71 Mean = 44.206 Standard Deviation = 18.823 Number of Observations = 17 Sum of Weight = . Species = Pike Data Minimum = 17.5 Minimum Whisker = 17.5 First Quartile = 27 Median = 42 Third Quartile = 63.5 Maximum Whisker = 71 Data Maximum = 71 Mean = 44.206 Standard Deviation = 18.823 Number of Observations = 17 Sum of Weight = . Species = Pike Data Minimum = 17.5 Minimum Whisker = 17.5 First Quartile = 27 Median = 42 Third Quartile = 63.5 Maximum Whisker = 71 Data Maximum = 71 Mean = 44.206 Standard Deviation = 18.823 Number of Observations = 17 Sum of Weight = . Species = Pike Data Minimum = 17.5 Minimum Whisker = 17.5 First Quartile = 27 Median = 42 Third Quartile = 63.5 Maximum Whisker = 71 Data Maximum = 71 Mean = 44.206 Standard Deviation = 18.823 Number of Observations = 17 Sum of Weight = . Species = Pike Data Minimum = 17.5 Minimum Whisker = 17.5 First Quartile = 27 Median = 42 Third Quartile = 63.5 Maximum Whisker = 71 Data Maximum = 71 Mean = 44.206 Standard Deviation = 18.823 Number of Observations = 17 Sum of Weight = . Species = Pike Data Minimum = 17.5 Minimum Whisker = 17.5 First Quartile = 27 Median = 42 Third Quartile = 63.5 Maximum Whisker = 71 Data Maximum = 71 Mean = 44.206 Standard Deviation = 18.823 Number of Observations = 17 Sum of Weight = . Species = Roach Data Minimum = 1 Minimum Whisker = 1 First Quartile = 5.5 Median = 10.5 Third Quartile = 15.5 Maximum Whisker = 29.5 Data Maximum = 29.5 Mean = 11.225 Standard Deviation = 7.3044 Number of Observations = 20 Sum of Weight = . Species = Roach Data Minimum = 1 Minimum Whisker = 1 First Quartile = 5.5 Median = 10.5 Third Quartile = 15.5 Maximum Whisker = 29.5 Data Maximum = 29.5 Mean = 11.225 Standard Deviation = 7.3044 Number of Observations = 20 Sum of Weight = . Species = Roach Data Minimum = 1 Minimum Whisker = 1 First Quartile = 5.5 Median = 10.5 Third Quartile = 15.5 Maximum Whisker = 29.5 Data Maximum = 29.5 Mean = 11.225 Standard Deviation = 7.3044 Number of Observations = 20 Sum of Weight = . Species = Roach Data Minimum = 1 Minimum Whisker = 1 First Quartile = 5.5 Median = 10.5 Third Quartile = 15.5 Maximum Whisker = 29.5 Data Maximum = 29.5 Mean = 11.225 Standard Deviation = 7.3044 Number of Observations = 20 Sum of Weight = . Species = Roach Data Minimum = 1 Minimum Whisker = 1 First Quartile = 5.5 Median = 10.5 Third Quartile = 15.5 Maximum Whisker = 29.5 Data Maximum = 29.5 Mean = 11.225 Standard Deviation = 7.3044 Number of Observations = 20 Sum of Weight = . Species = Roach Data Minimum = 1 Minimum Whisker = 1 First Quartile = 5.5 Median = 10.5 Third Quartile = 15.5 Maximum Whisker = 29.5 Data Maximum = 29.5 Mean = 11.225 Standard Deviation = 7.3044 Number of Observations = 20 Sum of Weight = . Species = Roach Data Minimum = 1 Minimum Whisker = 1 First Quartile = 5.5 Median = 10.5 Third Quartile = 15.5 Maximum Whisker = 29.5 Data Maximum = 29.5 Mean = 11.225 Standard Deviation = 7.3044 Number of Observations = 20 Sum of Weight = . Species = Roach Data Minimum = 1 Minimum Whisker = 1 First Quartile = 5.5 Median = 10.5 Third Quartile = 15.5 Maximum Whisker = 29.5 Data Maximum = 29.5 Mean = 11.225 Standard Deviation = 7.3044 Number of Observations = 20 Sum of Weight = . Species = Bream Data Minimum = 19 Minimum Whisker = 19 First Quartile = 36 Median = 48.5 Third Quartile = 57 Maximum Whisker = 67 Data Maximum = 67 Mean = 46.471 Standard Deviation = 13.451 Number of Observations = 34 Sum of Weight = . Species = Bream Data Minimum = 19 Minimum Whisker = 19 First Quartile = 36 Median = 48.5 Third Quartile = 57 Maximum Whisker = 67 Data Maximum = 67 Mean = 46.471 Standard Deviation = 13.451 Number of Observations = 34 Sum of Weight = . Species = Bream Data Minimum = 19 Minimum Whisker = 19 First Quartile = 36 Median = 48.5 Third Quartile = 57 Maximum Whisker = 67 Data Maximum = 67 Mean = 46.471 Standard Deviation = 13.451 Number of Observations = 34 Sum of Weight = . Species = Bream Data Minimum = 19 Minimum Whisker = 19 First Quartile = 36 Median = 48.5 Third Quartile = 57 Maximum Whisker = 67 Data Maximum = 67 Mean = 46.471 Standard Deviation = 13.451 Number of Observations = 34 Sum of Weight = . Species = Bream Data Minimum = 19 Minimum Whisker = 19 First Quartile = 36 Median = 48.5 Third Quartile = 57 Maximum Whisker = 67 Data Maximum = 67 Mean = 46.471 Standard Deviation = 13.451 Number of Observations = 34 Sum of Weight = . Species = Bream Data Minimum = 19 Minimum Whisker = 19 First Quartile = 36 Median = 48.5 Third Quartile = 57 Maximum Whisker = 67 Data Maximum = 67 Mean = 46.471 Standard Deviation = 13.451 Number of Observations = 34 Sum of Weight = . Species = Bream Data Minimum = 19 Minimum Whisker = 19 First Quartile = 36 Median = 48.5 Third Quartile = 57 Maximum Whisker = 67 Data Maximum = 67 Mean = 46.471 Standard Deviation = 13.451 Number of Observations = 34 Sum of Weight = . Species = Bream Data Minimum = 19 Minimum Whisker = 19 First Quartile = 36 Median = 48.5 Third Quartile = 57 Maximum Whisker = 67 Data Maximum = 67 Mean = 46.471 Standard Deviation = 13.451 Number of Observations = 34 Sum of Weight = .
Box Plot of Wilcoxon Scores for Weight Classified by Species

Nonparametric One-Way Test on 3 Fish Species

Multiple Comparison Analysis

DSCF

Pairwise Two-Sided Multiple Comparison Analysis
Dwass, Steel, Critchlow-Fligner Method
Variable: Weight
Species Wilcoxon Z DSCF Value Pr > DSCF
Bream vs. Roach 5.9671 8.4388 <.0001
Bream vs. Pike 0.4599 0.6504 0.8900
Roach vs. Pike -4.9544 7.0066 <.0001
  • “Using Nonparametric One-Way ANOVA + Pairwise multiple comparison analysis (asymptotic only) if you feel that the distribution assumptions are not satisfied.”
  • “The Kruskal-Wallis test implies that the three fish weights are not all equal (p <.0001).”
  • “The box plot show that Roach are lighter than Bream or Pike. To determine which pairs of fish are unequal, look at Pairwise Comparisons table to see the p-values; it shows that the comparisons of Bream vs. Roach and Roach vs. Pike are significantly different (p <.0001) while the comparison of Bream vs. Pike is not.”

Practice: One-way ANOVA with test for Tukey multiple comparisons.

SAS Code, click to expand

SAS Code:

#  (&path1 and biostats libname previously defined)
/* Practice: One-way ANOVA with test for Tukey multiple comparisons, CHF - generated code - start */

title1 "Practice: One-way ANOVA with test for Tukey multiple comparisons, CHF";
/* Placebo: 55 58 62 48 57 57 80 40 55 52 */ 
/* Calcium: 57 65 55 78 57 84 72 80 78 81 */ 
/* Lasix:   60 60 65 67 48 62 64 70 57 40 */ 
data work.congestive_heart_failure;
  do Group = 'Placebo','Calcium','Lasix';
    do Subj = 1 to 10;
      input LVEF @@;
      output; 
    end;
  end;
datalines;
  55 58 62 48 57 57 80 40 55 52
  57 65 55 78 57 84 72 80 78 81
  60 60 65 67 48 62 64 70 57 40
    ; 
/* proc print u data=work.congestive_heart_failure ; run; */

ods noproctitle;
ods graphics / imagemap=on;
proc glm data=work.congestive_heart_failure
  plots(maxpoints=none only)=(boxplot diagnostics(unpack));
    class Group;
    model LVEF=Group;
    means Group / hovtest=levene welch plots=none;
    lsmeans Group / adjust=tukey pdiff alpha=.05 plots=(meanplot diffplot);
    run;
quit;

/* The ANOVA table shows F-value of 5.45 and with a corresponding p-value of 0.0102. */ 

/* The Q-Q Plot of Residuals for left ventricular ejection fraction (LVEF) shows deviations from the straight line which means leads me to request Welch's variance-weighted ANOVA. The Histogram for Residuals [Distribution of Residuals for LVEF] appear to be relatively normally distributed. */ 

/* To confirm the assumption of homogeneity of variance / homoscedasticity, we require a p-value above the chosen significance level. The output table [Levene's Test for Homogeneity of LVEF Variance / ANOVA of Squared Deviations from Group Means] shows a p-value of .8069, so do not reject the null hypothesis of equal variance at the .05 level. However, the output table [Welch's ANOVA for LVEF] shows a p-value of .0228, so reject the null hypothesis of equal variance at the .05 level?!? */ 

/* The table [Least Squares Means / Adjustment for Multiple Comparisons: Tukey] shows p-values for all of the pairwise differences: Lasix vs. Placebo shows a p-value = 0.8031 (not significant at the .05 level), Calcium vs. Lasix shows a p-value = 0.0488 (significant at the .05 level), and Calcium vs. Placebo shows a p-value = 0.0114 (significant at the .05 level).  This is confirmed by the plot Pairwise Comparison of Means [LVEF Comparisons for Group]. */ 

title1;
/* Practice: One-way ANOVA with test for Tukey multiple comparisons, CHF - generated code - end */

SAS Output

Results: biostats_by_ex_SAScode.sas

Results: biostats_by_ex_SAScode.sas

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
Group 3 Calcium Lasix Placebo

Number of Observations

Number of Observations Read 30
Number of Observations Used 30

Dependent Variable: LVEF

Analysis of Variance

LVEF

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 2 1142.866667 571.433333 5.45 0.0102
Error 27 2828.600000 104.762963    
Corrected Total 29 3971.466667      

Fit Statistics

R-Square Coeff Var Root MSE LVEF Mean
0.287769 16.47325 10.23538 62.13333

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
Group 2 1142.866667 571.433333 5.45 0.0102

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
Group 2 1142.866667 571.433333 5.45 0.0102

Diagnostic Plots

Residual by Predicted

Residual = -19.3 Predicted Value = 59.3 Observation = 30 Residual = -2.3 Predicted Value = 59.3 Observation = 29 Residual = 10.7 Predicted Value = 59.3 Observation = 28 Residual = 4.7 Predicted Value = 59.3 Observation = 27 Residual = 2.7 Predicted Value = 59.3 Observation = 26 Residual = -11.3 Predicted Value = 59.3 Observation = 25 Residual = 7.7 Predicted Value = 59.3 Observation = 24 Residual = 5.7 Predicted Value = 59.3 Observation = 23 Residual = 0.7 Predicted Value = 59.3 Observation = 22 Residual = 0.7 Predicted Value = 59.3 Observation = 21 Residual = 10.3 Predicted Value = 70.7 Observation = 20 Residual = 7.3 Predicted Value = 70.7 Observation = 19 Residual = 9.3 Predicted Value = 70.7 Observation = 18 Residual = 1.3 Predicted Value = 70.7 Observation = 17 Residual = 13.3 Predicted Value = 70.7 Observation = 16 Residual = -13.7 Predicted Value = 70.7 Observation = 15 Residual = 7.3 Predicted Value = 70.7 Observation = 14 Residual = -15.7 Predicted Value = 70.7 Observation = 13 Residual = -5.7 Predicted Value = 70.7 Observation = 12 Residual = -13.7 Predicted Value = 70.7 Observation = 11 Residual = -4.4 Predicted Value = 56.4 Observation = 10 Residual = -1.4 Predicted Value = 56.4 Observation = 9 Residual = -16.4 Predicted Value = 56.4 Observation = 8 Residual = 23.6 Predicted Value = 56.4 Observation = 7 Residual = 0.6 Predicted Value = 56.4 Observation = 6 Residual = 0.6 Predicted Value = 56.4 Observation = 5 Residual = -8.4 Predicted Value = 56.4 Observation = 4 Residual = 5.6 Predicted Value = 56.4 Observation = 3 Residual = 1.6 Predicted Value = 56.4 Observation = 2 Residual = -1.4 Predicted Value = 56.4 Observation = 1 Y = 0
Plot of Residual by Predicted for LVEF

RStudent by Predicted

RStudent = -2.111 Predicted Value = 59.3 Observation = 30 RStudent = -0.233 Predicted Value = 59.3 Observation = 29 RStudent = 1.1065 Predicted Value = 59.3 Observation = 28 RStudent = 0.4771 Predicted Value = 59.3 Observation = 27 RStudent = 0.2733 Predicted Value = 59.3 Observation = 26 RStudent = -1.172 Predicted Value = 59.3 Observation = 25 RStudent = 0.7874 Predicted Value = 59.3 Observation = 24 RStudent = 0.5798 Predicted Value = 59.3 Observation = 23 RStudent = 0.0707 Predicted Value = 59.3 Observation = 22 RStudent = 0.0707 Predicted Value = 59.3 Observation = 21 RStudent = 1.0633 Predicted Value = 70.7 Observation = 20 RStudent = 0.7456 Predicted Value = 70.7 Observation = 19 RStudent = 0.9562 Predicted Value = 70.7 Observation = 18 RStudent = 0.1314 Predicted Value = 70.7 Observation = 17 RStudent = 1.3934 Predicted Value = 70.7 Observation = 16 RStudent = -1.439 Predicted Value = 70.7 Observation = 15 RStudent = 0.7456 Predicted Value = 70.7 Observation = 14 RStudent = -1.67 Predicted Value = 70.7 Observation = 13 RStudent = -0.58 Predicted Value = 70.7 Observation = 12 RStudent = -1.439 Predicted Value = 70.7 Observation = 11 RStudent = -0.446 Predicted Value = 56.4 Observation = 10 RStudent = -0.142 Predicted Value = 56.4 Observation = 9 RStudent = -1.753 Predicted Value = 56.4 Observation = 8 RStudent = 2.6984 Predicted Value = 56.4 Observation = 7 RStudent = 0.0606 Predicted Value = 56.4 Observation = 6 RStudent = 0.0606 Predicted Value = 56.4 Observation = 5 RStudent = -0.861 Predicted Value = 56.4 Observation = 4 RStudent = 0.5695 Predicted Value = 56.4 Observation = 3 RStudent = 0.1618 Predicted Value = 56.4 Observation = 2 RStudent = -0.142 Predicted Value = 56.4 Observation = 1 Y = 2 Y = -2
Plot of RStudent by Predicted for LVEF

RStudent by Leverage

RStudent = -2.111 Leverage = 0.1 Observation = 30 RStudent = 2.6984 Leverage = 0.1 Observation = 7 RStudent = -0.233 Leverage = 0.1 Observation = 29 RStudent = 1.1065 Leverage = 0.1 Observation = 28 RStudent = 0.4771 Leverage = 0.1 Observation = 27 RStudent = 0.2733 Leverage = 0.1 Observation = 26 RStudent = -1.172 Leverage = 0.1 Observation = 25 RStudent = 0.7874 Leverage = 0.1 Observation = 24 RStudent = 0.5798 Leverage = 0.1 Observation = 23 RStudent = 0.0707 Leverage = 0.1 Observation = 22 RStudent = 0.0707 Leverage = 0.1 Observation = 21 RStudent = 1.0633 Leverage = 0.1 Observation = 20 RStudent = 0.7456 Leverage = 0.1 Observation = 19 RStudent = 0.9562 Leverage = 0.1 Observation = 18 RStudent = 0.1314 Leverage = 0.1 Observation = 17 RStudent = 1.3934 Leverage = 0.1 Observation = 16 RStudent = -1.439 Leverage = 0.1 Observation = 15 RStudent = 0.7456 Leverage = 0.1 Observation = 14 RStudent = -1.67 Leverage = 0.1 Observation = 13 RStudent = -0.58 Leverage = 0.1 Observation = 12 RStudent = -1.439 Leverage = 0.1 Observation = 11 RStudent = -0.446 Leverage = 0.1 Observation = 10 RStudent = -0.142 Leverage = 0.1 Observation = 9 RStudent = -1.753 Leverage = 0.1 Observation = 8 RStudent = 0.0606 Leverage = 0.1 Observation = 6 RStudent = 0.0606 Leverage = 0.1 Observation = 5 RStudent = -0.861 Leverage = 0.1 Observation = 4 RStudent = 0.5695 Leverage = 0.1 Observation = 3 RStudent = 0.1618 Leverage = 0.1 Observation = 2 RStudent = -0.142 Leverage = 0.1 Observation = 1 X = 0.2 Y = -2 Y = 2
Plot of RStudent by Leverage for LVEF

Q-Q Plot

Quantile = 2.0403 Residual = 23.6 Quantile = 1.6098 Residual = 13.3 Quantile = 1.3609 Residual = 10.7 Quantile = 1.1758 Residual = 10.3 Quantile = 1.0241 Residual = 9.3 Quantile = 0.8929 Residual = 7.7 Quantile = 0.7755 Residual = 7.3 Quantile = 0.668 Residual = 7.3 Quantile = 0.5677 Residual = 5.7 Quantile = 0.4728 Residual = 5.6 Quantile = 0.382 Residual = 4.7 Quantile = 0.2942 Residual = 2.7 Quantile = 0.2087 Residual = 1.6 Quantile = 0.1246 Residual = 1.3 Quantile = 0.0414 Residual = 0.7 Quantile = -0.041 Residual = 0.7 Quantile = -0.125 Residual = 0.6 Quantile = -0.209 Residual = 0.6 Quantile = -0.294 Residual = -1.4 Quantile = -0.382 Residual = -1.4 Quantile = -0.473 Residual = -2.3 Quantile = -0.568 Residual = -4.4 Quantile = -0.668 Residual = -5.7 Quantile = -0.776 Residual = -8.4 Quantile = -0.893 Residual = -11.3 Quantile = -1.024 Residual = -13.7 Quantile = -1.176 Residual = -13.7 Quantile = -1.361 Residual = -15.7 Quantile = -1.61 Residual = -16.4 Quantile = -2.04 Residual = -19.3 Slope = 9.8761 Y = 47E-17
Q-Q Plot of Residuals for LVEF

LVEF by Predicted

LVEF = 40 Predicted Value = 59.3 Observation = 30 LVEF = 57 Predicted Value = 59.3 Observation = 29 LVEF = 70 Predicted Value = 59.3 Observation = 28 LVEF = 64 Predicted Value = 59.3 Observation = 27 LVEF = 62 Predicted Value = 59.3 Observation = 26 LVEF = 48 Predicted Value = 59.3 Observation = 25 LVEF = 67 Predicted Value = 59.3 Observation = 24 LVEF = 65 Predicted Value = 59.3 Observation = 23 LVEF = 60 Predicted Value = 59.3 Observation = 22 LVEF = 60 Predicted Value = 59.3 Observation = 21 LVEF = 81 Predicted Value = 70.7 Observation = 20 LVEF = 78 Predicted Value = 70.7 Observation = 19 LVEF = 80 Predicted Value = 70.7 Observation = 18 LVEF = 72 Predicted Value = 70.7 Observation = 17 LVEF = 84 Predicted Value = 70.7 Observation = 16 LVEF = 57 Predicted Value = 70.7 Observation = 15 LVEF = 78 Predicted Value = 70.7 Observation = 14 LVEF = 55 Predicted Value = 70.7 Observation = 13 LVEF = 65 Predicted Value = 70.7 Observation = 12 LVEF = 57 Predicted Value = 70.7 Observation = 11 LVEF = 52 Predicted Value = 56.4 Observation = 10 LVEF = 55 Predicted Value = 56.4 Observation = 9 LVEF = 40 Predicted Value = 56.4 Observation = 8 LVEF = 80 Predicted Value = 56.4 Observation = 7 LVEF = 57 Predicted Value = 56.4 Observation = 6 LVEF = 57 Predicted Value = 56.4 Observation = 5 LVEF = 48 Predicted Value = 56.4 Observation = 4 LVEF = 62 Predicted Value = 56.4 Observation = 3 LVEF = 58 Predicted Value = 56.4 Observation = 2 LVEF = 55 Predicted Value = 56.4 Observation = 1 Slope = 1 Y = 0
Plot of LVEF by Predicted

Cook's D Plot

Cook's D = 0.1463 Observation = 30 Cook's D = 0.0021 Observation = 29 Cook's D = 0.045 Observation = 28 Cook's D = 0.0087 Observation = 27 Cook's D = 0.0029 Observation = 26 Cook's D = 0.0502 Observation = 25 Cook's D = 0.0233 Observation = 24 Cook's D = 0.0128 Observation = 23 Cook's D = .00019 Observation = 22 Cook's D = .00019 Observation = 21 Cook's D = 0.0417 Observation = 20 Cook's D = 0.0209 Observation = 19 Cook's D = 0.034 Observation = 18 Cook's D = .00066 Observation = 17 Cook's D = 0.0695 Observation = 16 Cook's D = 0.0737 Observation = 15 Cook's D = 0.0209 Observation = 14 Cook's D = 0.0968 Observation = 13 Cook's D = 0.0128 Observation = 12 Cook's D = 0.0737 Observation = 11 Cook's D = 0.0076 Observation = 10 Cook's D = .00077 Observation = 9 Cook's D = 0.1057 Observation = 8 Cook's D = 0.2188 Observation = 7 Cook's D = .00014 Observation = 6 Cook's D = .00014 Observation = 5 Cook's D = 0.0277 Observation = 4 Cook's D = 0.0123 Observation = 3 Cook's D = 0.001 Observation = 2 Cook's D = .00077 Observation = 1 Cook's D = 0.1463 Observation = 30 Cook's D = 0.0021 Observation = 29 Cook's D = 0.045 Observation = 28 Cook's D = 0.0087 Observation = 27 Cook's D = 0.0029 Observation = 26 Cook's D = 0.0502 Observation = 25 Cook's D = 0.0233 Observation = 24 Cook's D = 0.0128 Observation = 23 Cook's D = .00019 Observation = 22 Cook's D = .00019 Observation = 21 Cook's D = 0.0417 Observation = 20 Cook's D = 0.0209 Observation = 19 Cook's D = 0.034 Observation = 18 Cook's D = .00066 Observation = 17 Cook's D = 0.0695 Observation = 16 Cook's D = 0.0737 Observation = 15 Cook's D = 0.0209 Observation = 14 Cook's D = 0.0968 Observation = 13 Cook's D = 0.0128 Observation = 12 Cook's D = 0.0737 Observation = 11 Cook's D = 0.0076 Observation = 10 Cook's D = .00077 Observation = 9 Cook's D = 0.1057 Observation = 8 Cook's D = 0.2188 Observation = 7 Cook's D = .00014 Observation = 6 Cook's D = .00014 Observation = 5 Cook's D = 0.0277 Observation = 4 Cook's D = 0.0123 Observation = 3 Cook's D = 0.001 Observation = 2 Cook's D = .00077 Observation = 1 Y = 0.1333
Needleplot of Cook's D statistic by Observation for LVEF

Residual Histogram

Residual = 36.671 Percent = 0.1054 Residual = 36.336 Percent = 0.1239 Residual = 36.336 Percent = 0.1239 Residual = 36.001 Percent = 0.1451 Residual = 36.001 Percent = 0.1451 Residual = 35.666 Percent = 0.1692 Residual = 35.666 Percent = 0.1692 Residual = 35.33 Percent = 0.1964 Residual = 35.33 Percent = 0.1964 Residual = 34.995 Percent = 0.2272 Residual = 34.995 Percent = 0.2272 Residual = 34.66 Percent = 0.2616 Residual = 34.66 Percent = 0.2616 Residual = 34.325 Percent = 0.3 Residual = 34.325 Percent = 0.3 Residual = 33.99 Percent = 0.3425 Residual = 33.99 Percent = 0.3425 Residual = 33.655 Percent = 0.3896 Residual = 33.655 Percent = 0.3896 Residual = 33.32 Percent = 0.4412 Residual = 33.32 Percent = 0.4412 Residual = 32.984 Percent = 0.4977 Residual = 32.984 Percent = 0.4977 Residual = 32.649 Percent = 0.559 Residual = 32.649 Percent = 0.559 Residual = 32.314 Percent = 0.6254 Residual = 32.314 Percent = 0.6254 Residual = 31.979 Percent = 0.6968 Residual = 31.979 Percent = 0.6968 Residual = 31.644 Percent = 0.7732 Residual = 31.644 Percent = 0.7732 Residual = 31.309 Percent = 0.8545 Residual = 31.309 Percent = 0.8545 Residual = 30.973 Percent = 0.9405 Residual = 30.973 Percent = 0.9405 Residual = 30.638 Percent = 1.0312 Residual = 30.638 Percent = 1.0312 Residual = 30.303 Percent = 1.1261 Residual = 30.303 Percent = 1.1261 Residual = 29.968 Percent = 1.2249 Residual = 29.968 Percent = 1.2249 Residual = 29.298 Percent = 1.4327 Residual = 29.298 Percent = 1.4327 Residual = 27.287 Percent = 2.0999 Residual = 27.287 Percent = 2.0999 Residual = 26.281 Percent = 2.4323 Residual = 26.281 Percent = 2.4323 Residual = 23.935 Percent = 3.163 Residual = 23.935 Percent = 3.163 Residual = 23.265 Percent = 3.3754 Residual = 23.265 Percent = 3.3754 Residual = 22.93 Percent = 3.4875 Residual = 22.93 Percent = 3.4875 Residual = 22.595 Percent = 3.6057 Residual = 22.595 Percent = 3.6057 Residual = 22.259 Percent = 3.7319 Residual = 22.259 Percent = 3.7319 Residual = 21.924 Percent = 3.8682 Residual = 21.924 Percent = 3.8682 Residual = 21.589 Percent = 4.0168 Residual = 21.589 Percent = 4.0168 Residual = 21.254 Percent = 4.1799 Residual = 21.254 Percent = 4.1799 Residual = 20.919 Percent = 4.36 Residual = 20.919 Percent = 4.36 Residual = 20.584 Percent = 4.5596 Residual = 20.584 Percent = 4.5596 Residual = 20.248 Percent = 4.7811 Residual = 20.248 Percent = 4.7811 Residual = 19.913 Percent = 5.0271 Residual = 19.913 Percent = 5.0271 Residual = 19.578 Percent = 5.3 Residual = 19.578 Percent = 5.3 Residual = 19.243 Percent = 5.6022 Residual = 19.243 Percent = 5.6022 Residual = 18.908 Percent = 5.9359 Residual = 18.908 Percent = 5.9359 Residual = 18.573 Percent = 6.303 Residual = 18.573 Percent = 6.303 Residual = 18.237 Percent = 6.7055 Residual = 18.237 Percent = 6.7055 Residual = 17.902 Percent = 7.1449 Residual = 17.902 Percent = 7.1449 Residual = 17.567 Percent = 7.6225 Residual = 17.567 Percent = 7.6225 Residual = 17.232 Percent = 8.1393 Residual = 17.232 Percent = 8.1393 Residual = 16.897 Percent = 8.696 Residual = 16.897 Percent = 8.696 Residual = 16.562 Percent = 9.293 Residual = 16.562 Percent = 9.293 Residual = 16.227 Percent = 9.93 Residual = 16.227 Percent = 9.93 Residual = 15.891 Percent = 10.607 Residual = 15.891 Percent = 10.607 Residual = 15.556 Percent = 11.323 Residual = 15.556 Percent = 11.323 Residual = 15.221 Percent = 12.076 Residual = 15.221 Percent = 12.076 Residual = 14.886 Percent = 12.866 Residual = 14.886 Percent = 12.866 Residual = 14.551 Percent = 13.69 Residual = 14.551 Percent = 13.69 Residual = 14.216 Percent = 14.546 Residual = 14.216 Percent = 14.546 Residual = 13.88 Percent = 15.431 Residual = 13.88 Percent = 15.431 Residual = 13.21 Percent = 17.279 Residual = 13.21 Percent = 17.279 Residual = 10.864 Percent = 24.198 Residual = 10.864 Percent = 24.198 Residual = 9.8586 Percent = 27.155 Residual = 9.8586 Percent = 27.155 Residual = 9.1883 Percent = 29.05 Residual = 9.1883 Percent = 29.05 Residual = 8.518 Percent = 30.852 Residual = 8.518 Percent = 30.852 Residual = 8.1828 Percent = 31.711 Residual = 8.1828 Percent = 31.711 Residual = 7.8477 Percent = 32.537 Residual = 7.8477 Percent = 32.537 Residual = 7.5125 Percent = 33.328 Residual = 7.5125 Percent = 33.328 Residual = 7.1773 Percent = 34.081 Residual = 7.1773 Percent = 34.081 Residual = 6.8422 Percent = 34.794 Residual = 6.8422 Percent = 34.794 Residual = 6.507 Percent = 35.464 Residual = 6.507 Percent = 35.464 Residual = 6.1719 Percent = 36.089 Residual = 6.1719 Percent = 36.089 Residual = 5.8367 Percent = 36.667 Residual = 5.8367 Percent = 36.667 Residual = 5.5016 Percent = 37.195 Residual = 5.5016 Percent = 37.195 Residual = 5.1664 Percent = 37.672 Residual = 5.1664 Percent = 37.672 Residual = 4.8312 Percent = 38.095 Residual = 4.8312 Percent = 38.095 Residual = 4.4961 Percent = 38.462 Residual = 4.4961 Percent = 38.462 Residual = 4.1609 Percent = 38.773 Residual = 4.1609 Percent = 38.773 Residual = 3.8258 Percent = 39.025 Residual = 3.8258 Percent = 39.025 Residual = 3.4906 Percent = 39.217 Residual = 3.4906 Percent = 39.217 Residual = 3.1555 Percent = 39.347 Residual = 3.1555 Percent = 39.347 Residual = 2.8203 Percent = 39.416 Residual = 2.8203 Percent = 39.416 Residual = 2.4852 Percent = 39.422 Residual = 2.4852 Percent = 39.422 Residual = 2.15 Percent = 39.364 Residual = 2.15 Percent = 39.364 Residual = 1.8148 Percent = 39.244 Residual = 1.8148 Percent = 39.244 Residual = 1.4797 Percent = 39.06 Residual = 1.4797 Percent = 39.06 Residual = 1.1445 Percent = 38.815 Residual = 1.1445 Percent = 38.815 Residual = 0.8094 Percent = 38.509 Residual = 0.8094 Percent = 38.509 Residual = 0.4742 Percent = 38.144 Residual = 0.4742 Percent = 38.144 Residual = 0.1391 Percent = 37.722 Residual = 0.1391 Percent = 37.722 Residual = -0.196 Percent = 37.245 Residual = -0.196 Percent = 37.245 Residual = -0.531 Percent = 36.717 Residual = -0.531 Percent = 36.717 Residual = -0.866 Percent = 36.142 Residual = -0.866 Percent = 36.142 Residual = -1.202 Percent = 35.523 Residual = -1.202 Percent = 35.523 Residual = -1.537 Percent = 34.864 Residual = -1.537 Percent = 34.864 Residual = -1.872 Percent = 34.171 Residual = -1.872 Percent = 34.171 Residual = -4.553 Percent = 28.012 Residual = -4.553 Percent = 28.012 Residual = -5.223 Percent = 26.502 Residual = -5.223 Percent = 26.502 Residual = -5.559 Percent = 25.778 Residual = -5.559 Percent = 25.778 Residual = -5.894 Percent = 25.081 Residual = -5.894 Percent = 25.081 Residual = -6.229 Percent = 24.413 Residual = -6.229 Percent = 24.413 Residual = -6.564 Percent = 23.778 Residual = -6.564 Percent = 23.778 Residual = -6.899 Percent = 23.178 Residual = -6.899 Percent = 23.178 Residual = -7.234 Percent = 22.614 Residual = -7.234 Percent = 22.614 Residual = -7.57 Percent = 22.088 Residual = -7.57 Percent = 22.088 Residual = -7.905 Percent = 21.6 Residual = -7.905 Percent = 21.6 Residual = -8.24 Percent = 21.149 Residual = -8.24 Percent = 21.149 Residual = -8.575 Percent = 20.736 Residual = -8.575 Percent = 20.736 Residual = -8.91 Percent = 20.359 Residual = -8.91 Percent = 20.359 Residual = -9.245 Percent = 20.016 Residual = -9.245 Percent = 20.016 Residual = -9.58 Percent = 19.704 Residual = -9.58 Percent = 19.704 Residual = -9.916 Percent = 19.422 Residual = -9.916 Percent = 19.422 Residual = -10.25 Percent = 19.166 Residual = -10.25 Percent = 19.166 Residual = -10.59 Percent = 18.933 Residual = -10.59 Percent = 18.933 Residual = -10.92 Percent = 18.719 Residual = -10.92 Percent = 18.719 Residual = -11.26 Percent = 18.52 Residual = -11.26 Percent = 18.52 Residual = -11.59 Percent = 18.332 Residual = -11.59 Percent = 18.332 Residual = -12.26 Percent = 17.976 Residual = -12.26 Percent = 17.976 Residual = -12.93 Percent = 17.618 Residual = -12.93 Percent = 17.618 Residual = -13.27 Percent = 17.429 Residual = -13.27 Percent = 17.429 Residual = -13.6 Percent = 17.23 Residual = -13.6 Percent = 17.23 Residual = -13.94 Percent = 17.017 Residual = -13.94 Percent = 17.017 Residual = -14.27 Percent = 16.787 Residual = -14.27 Percent = 16.787 Residual = -14.61 Percent = 16.539 Residual = -14.61 Percent = 16.539 Residual = -14.94 Percent = 16.27 Residual = -14.94 Percent = 16.27 Residual = -15.28 Percent = 15.98 Residual = -15.28 Percent = 15.98 Residual = -15.61 Percent = 15.667 Residual = -15.61 Percent = 15.667 Residual = -15.95 Percent = 15.331 Residual = -15.95 Percent = 15.331 Residual = -16.28 Percent = 14.971 Residual = -16.28 Percent = 14.971 Residual = -16.62 Percent = 14.589 Residual = -16.62 Percent = 14.589 Residual = -16.95 Percent = 14.184 Residual = -16.95 Percent = 14.184 Residual = -17.29 Percent = 13.758 Residual = -17.29 Percent = 13.758 Residual = -17.62 Percent = 13.312 Residual = -17.62 Percent = 13.312 Residual = -17.96 Percent = 12.849 Residual = -17.96 Percent = 12.849 Residual = -20.98 Percent = 8.2574 Residual = -20.98 Percent = 8.2574 Residual = -21.65 Percent = 7.2479 Residual = -21.65 Percent = 7.2479 Residual = -22.32 Percent = 6.284 Residual = -22.32 Percent = 6.284 Residual = -22.65 Percent = 5.824 Residual = -22.65 Percent = 5.824 Residual = -22.99 Percent = 5.3806 Residual = -22.99 Percent = 5.3806 Residual = -23.32 Percent = 4.9552 Residual = -23.32 Percent = 4.9552 Residual = -23.66 Percent = 4.5489 Residual = -23.66 Percent = 4.5489 Residual = -23.99 Percent = 4.1624 Residual = -23.99 Percent = 4.1624 Residual = -24.33 Percent = 3.7964 Residual = -24.33 Percent = 3.7964 Residual = -24.66 Percent = 3.4514 Residual = -24.66 Percent = 3.4514 Residual = -25 Percent = 3.1274 Residual = -25 Percent = 3.1274 Residual = -25.33 Percent = 2.8244 Residual = -25.33 Percent = 2.8244 Residual = -25.67 Percent = 2.5423 Residual = -25.67 Percent = 2.5423 Residual = -26 Percent = 2.2808 Residual = -26 Percent = 2.2808 Residual = -26.34 Percent = 2.0393 Residual = -26.34 Percent = 2.0393 Residual = -26.67 Percent = 1.8172 Residual = -26.67 Percent = 1.8172 Residual = -27.01 Percent = 1.6137 Residual = -27.01 Percent = 1.6137 Residual = -27.34 Percent = 1.4282 Residual = -27.34 Percent = 1.4282 Residual = -27.68 Percent = 1.2596 Residual = -27.68 Percent = 1.2596 Residual = -28.01 Percent = 1.1071 Residual = -28.01 Percent = 1.1071 Residual = -28.35 Percent = 0.9697 Residual = -28.35 Percent = 0.9697 Residual = -28.68 Percent = 0.8464 Residual = -28.68 Percent = 0.8464 Residual = -29.02 Percent = 0.7362 Residual = -29.02 Percent = 0.7362 Residual = -29.35 Percent = 0.638 Residual = -29.35 Percent = 0.638 Residual = -29.69 Percent = 0.551 Residual = -29.69 Percent = 0.551 Residual = -30.03 Percent = 0.4742 Residual = -30.03 Percent = 0.4742 Residual = -30.36 Percent = 0.4066 Residual = -30.36 Percent = 0.4066 Residual = -30.7 Percent = 0.3474 Residual = -30.7 Percent = 0.3474 Residual = -31.03 Percent = 0.2957 Residual = -31.03 Percent = 0.2957 Residual = -31.37 Percent = 0.2508 Residual = -31.37 Percent = 0.2508 Residual = -31.7 Percent = 0.212 Residual = -31.7 Percent = 0.212 Residual = -32.04 Percent = 0.1785 Residual = -32.04 Percent = 0.1785 Residual = -32.37 Percent = 0.1497 Residual = 29.628 Percent = 0.4487 Residual = 29.329 Percent = 0.4912 Residual = 29.329 Percent = 0.4912 Residual = 29.03 Percent = 0.5372 Residual = 29.03 Percent = 0.5372 Residual = 28.731 Percent = 0.587 Residual = 28.731 Percent = 0.587 Residual = 28.431 Percent = 0.6408 Residual = 28.431 Percent = 0.6408 Residual = 28.132 Percent = 0.6989 Residual = 28.132 Percent = 0.6989 Residual = 27.833 Percent = 0.7616 Residual = 27.833 Percent = 0.7616 Residual = 27.533 Percent = 0.8291 Residual = 27.533 Percent = 0.8291 Residual = 27.234 Percent = 0.9018 Residual = 27.234 Percent = 0.9018 Residual = 26.935 Percent = 0.9799 Residual = 26.935 Percent = 0.9799 Residual = 26.636 Percent = 1.0638 Residual = 26.636 Percent = 1.0638 Residual = 26.336 Percent = 1.1539 Residual = 26.336 Percent = 1.1539 Residual = 26.037 Percent = 1.2504 Residual = 26.037 Percent = 1.2504 Residual = 25.738 Percent = 1.3538 Residual = 25.738 Percent = 1.3538 Residual = 25.439 Percent = 1.4644 Residual = 25.439 Percent = 1.4644 Residual = 25.139 Percent = 1.5825 Residual = 25.139 Percent = 1.5825 Residual = 24.84 Percent = 1.7086 Residual = 24.84 Percent = 1.7086 Residual = 24.541 Percent = 1.8431 Residual = 24.541 Percent = 1.8431 Residual = 24.241 Percent = 1.9864 Residual = 24.241 Percent = 1.9864 Residual = 23.942 Percent = 2.1387 Residual = 23.942 Percent = 2.1387 Residual = 23.643 Percent = 2.3007 Residual = 23.643 Percent = 2.3007 Residual = 23.344 Percent = 2.4727 Residual = 23.344 Percent = 2.4727 Residual = 23.044 Percent = 2.6551 Residual = 23.044 Percent = 2.6551 Residual = 22.745 Percent = 2.8483 Residual = 22.745 Percent = 2.8483 Residual = 22.446 Percent = 3.0528 Residual = 22.446 Percent = 3.0528 Residual = 22.146 Percent = 3.2689 Residual = 22.146 Percent = 3.2689 Residual = 21.847 Percent = 3.4972 Residual = 21.847 Percent = 3.4972 Residual = 21.548 Percent = 3.7379 Residual = 21.548 Percent = 3.7379 Residual = 21.249 Percent = 3.9916 Residual = 21.249 Percent = 3.9916 Residual = 20.949 Percent = 4.2585 Residual = 20.949 Percent = 4.2585 Residual = 20.65 Percent = 4.5392 Residual = 20.65 Percent = 4.5392 Residual = 20.351 Percent = 4.8339 Residual = 20.351 Percent = 4.8339 Residual = 20.052 Percent = 5.143 Residual = 20.052 Percent = 5.143 Residual = 19.752 Percent = 5.4668 Residual = 19.752 Percent = 5.4668 Residual = 19.453 Percent = 5.8057 Residual = 19.453 Percent = 5.8057 Residual = 19.154 Percent = 6.16 Residual = 19.154 Percent = 6.16 Residual = 18.854 Percent = 6.5298 Residual = 18.854 Percent = 6.5298 Residual = 18.555 Percent = 6.9156 Residual = 18.555 Percent = 6.9156 Residual = 18.256 Percent = 7.3173 Residual = 18.256 Percent = 7.3173 Residual = 17.957 Percent = 7.7354 Residual = 17.957 Percent = 7.7354 Residual = 17.657 Percent = 8.1698 Residual = 17.657 Percent = 8.1698 Residual = 17.358 Percent = 8.6206 Residual = 17.358 Percent = 8.6206 Residual = 17.059 Percent = 9.0881 Residual = 17.059 Percent = 9.0881 Residual = 16.759 Percent = 9.572 Residual = 16.759 Percent = 9.572 Residual = 16.46 Percent = 10.072 Residual = 16.46 Percent = 10.072 Residual = 16.161 Percent = 10.589 Residual = 16.161 Percent = 10.589 Residual = 15.562 Percent = 11.672 Residual = 15.562 Percent = 11.672 Residual = 14.964 Percent = 12.818 Residual = 14.964 Percent = 12.818 Residual = 14.365 Percent = 14.025 Residual = 14.365 Percent = 14.025 Residual = 13.767 Percent = 15.289 Residual = 13.767 Percent = 15.289 Residual = 13.168 Percent = 16.607 Residual = 13.168 Percent = 16.607 Residual = 8.679 Percent = 27.455 Residual = 8.679 Percent = 27.455 Residual = 7.7812 Percent = 29.616 Residual = 7.7812 Percent = 29.616 Residual = 7.1826 Percent = 31.008 Residual = 7.1826 Percent = 31.008 Residual = 6.5841 Percent = 32.345 Residual = 6.5841 Percent = 32.345 Residual = 5.9855 Percent = 33.617 Residual = 5.9855 Percent = 33.617 Residual = 5.6863 Percent = 34.225 Residual = 5.6863 Percent = 34.225 Residual = 5.387 Percent = 34.811 Residual = 5.387 Percent = 34.811 Residual = 5.0877 Percent = 35.375 Residual = 5.0877 Percent = 35.375 Residual = 4.7884 Percent = 35.915 Residual = 4.7884 Percent = 35.915 Residual = 4.4891 Percent = 36.43 Residual = 4.4891 Percent = 36.43 Residual = 4.1899 Percent = 36.918 Residual = 4.1899 Percent = 36.918 Residual = 3.8906 Percent = 37.379 Residual = 3.8906 Percent = 37.379 Residual = 3.5913 Percent = 37.81 Residual = 3.5913 Percent = 37.81 Residual = 3.292 Percent = 38.212 Residual = 3.292 Percent = 38.212 Residual = 2.9928 Percent = 38.582 Residual = 2.9928 Percent = 38.582 Residual = 2.6935 Percent = 38.92 Residual = 2.6935 Percent = 38.92 Residual = 2.3942 Percent = 39.225 Residual = 2.3942 Percent = 39.225 Residual = 2.0949 Percent = 39.496 Residual = 2.0949 Percent = 39.496 Residual = 1.7957 Percent = 39.732 Residual = 1.7957 Percent = 39.732 Residual = 1.4964 Percent = 39.934 Residual = 1.4964 Percent = 39.934 Residual = 1.1971 Percent = 40.099 Residual = 1.1971 Percent = 40.099 Residual = 0.8978 Percent = 40.228 Residual = 0.8978 Percent = 40.228 Residual = 0.5986 Percent = 40.32 Residual = 0.5986 Percent = 40.32 Residual = 0.2993 Percent = 40.376 Residual = 0.2993 Percent = 40.376 Residual = 47E-17 Percent = 40.395 Residual = 47E-17 Percent = 40.395 Residual = -0.299 Percent = 40.376 Residual = -0.299 Percent = 40.376 Residual = -0.599 Percent = 40.32 Residual = -0.599 Percent = 40.32 Residual = -0.898 Percent = 40.228 Residual = -0.898 Percent = 40.228 Residual = -1.197 Percent = 40.099 Residual = -1.197 Percent = 40.099 Residual = -1.496 Percent = 39.934 Residual = -1.496 Percent = 39.934 Residual = -1.796 Percent = 39.732 Residual = -1.796 Percent = 39.732 Residual = -2.095 Percent = 39.496 Residual = -2.095 Percent = 39.496 Residual = -2.394 Percent = 39.225 Residual = -2.394 Percent = 39.225 Residual = -2.693 Percent = 38.92 Residual = -2.693 Percent = 38.92 Residual = -2.993 Percent = 38.582 Residual = -2.993 Percent = 38.582 Residual = -3.292 Percent = 38.212 Residual = -3.292 Percent = 38.212 Residual = -3.591 Percent = 37.81 Residual = -3.591 Percent = 37.81 Residual = -3.891 Percent = 37.379 Residual = -3.891 Percent = 37.379 Residual = -4.19 Percent = 36.918 Residual = -4.19 Percent = 36.918 Residual = -4.489 Percent = 36.43 Residual = -4.489 Percent = 36.43 Residual = -4.788 Percent = 35.915 Residual = -4.788 Percent = 35.915 Residual = -5.088 Percent = 35.375 Residual = -5.088 Percent = 35.375 Residual = -5.387 Percent = 34.811 Residual = -5.387 Percent = 34.811 Residual = -5.686 Percent = 34.225 Residual = -5.686 Percent = 34.225 Residual = -5.986 Percent = 33.617 Residual = -5.986 Percent = 33.617 Residual = -6.584 Percent = 32.345 Residual = -6.584 Percent = 32.345 Residual = -7.183 Percent = 31.008 Residual = -7.183 Percent = 31.008 Residual = -10.77 Percent = 22.279 Residual = -10.77 Percent = 22.279 Residual = -11.97 Percent = 19.377 Residual = -11.97 Percent = 19.377 Residual = -12.87 Percent = 17.283 Residual = -12.87 Percent = 17.283 Residual = -13.47 Percent = 15.942 Residual = -13.47 Percent = 15.942 Residual = -14.07 Percent = 14.65 Residual = -14.07 Percent = 14.65 Residual = -14.66 Percent = 13.414 Residual = -14.66 Percent = 13.414 Residual = -15.26 Percent = 12.237 Residual = -15.26 Percent = 12.237 Residual = -15.86 Percent = 11.123 Residual = -15.86 Percent = 11.123 Residual = -16.16 Percent = 10.589 Residual = -16.16 Percent = 10.589 Residual = -16.46 Percent = 10.072 Residual = -16.46 Percent = 10.072 Residual = -16.76 Percent = 9.572 Residual = -16.76 Percent = 9.572 Residual = -17.06 Percent = 9.0881 Residual = -17.06 Percent = 9.0881 Residual = -17.36 Percent = 8.6206 Residual = -17.36 Percent = 8.6206 Residual = -17.66 Percent = 8.1698 Residual = -17.66 Percent = 8.1698 Residual = -17.96 Percent = 7.7354 Residual = -17.96 Percent = 7.7354 Residual = -18.26 Percent = 7.3173 Residual = -18.26 Percent = 7.3173 Residual = -18.56 Percent = 6.9156 Residual = -18.56 Percent = 6.9156 Residual = -18.85 Percent = 6.5298 Residual = -18.85 Percent = 6.5298 Residual = -19.15 Percent = 6.16 Residual = -19.15 Percent = 6.16 Residual = -19.45 Percent = 5.8057 Residual = -19.45 Percent = 5.8057 Residual = -19.75 Percent = 5.4668 Residual = -19.75 Percent = 5.4668 Residual = -20.05 Percent = 5.143 Residual = -20.05 Percent = 5.143 Residual = -20.35 Percent = 4.8339 Residual = -20.35 Percent = 4.8339 Residual = -20.65 Percent = 4.5392 Residual = -20.65 Percent = 4.5392 Residual = -20.95 Percent = 4.2585 Residual = -20.95 Percent = 4.2585 Residual = -21.25 Percent = 3.9916 Residual = -21.25 Percent = 3.9916 Residual = -21.55 Percent = 3.7379 Residual = -21.55 Percent = 3.7379 Residual = -21.85 Percent = 3.4972 Residual = -21.85 Percent = 3.4972 Residual = -22.15 Percent = 3.2689 Residual = -22.15 Percent = 3.2689 Residual = -22.45 Percent = 3.0528 Residual = -22.45 Percent = 3.0528 Residual = -22.75 Percent = 2.8483 Residual = -22.75 Percent = 2.8483 Residual = -23.04 Percent = 2.6551 Residual = -23.04 Percent = 2.6551 Residual = -23.34 Percent = 2.4727 Residual = -23.34 Percent = 2.4727 Residual = -23.64 Percent = 2.3007 Residual = -23.64 Percent = 2.3007 Residual = -23.94 Percent = 2.1387 Residual = -23.94 Percent = 2.1387 Residual = -24.24 Percent = 1.9864 Residual = -24.24 Percent = 1.9864 Residual = -24.54 Percent = 1.8431 Residual = -24.54 Percent = 1.8431 Residual = -24.84 Percent = 1.7086 Residual = -24.84 Percent = 1.7086 Residual = -25.14 Percent = 1.5825 Residual = -25.14 Percent = 1.5825 Residual = -25.44 Percent = 1.4644 Residual = -25.44 Percent = 1.4644 Residual = -25.74 Percent = 1.3538 Residual = -25.74 Percent = 1.3538 Residual = -26.04 Percent = 1.2504 Residual = -26.04 Percent = 1.2504 Residual = -26.34 Percent = 1.1539 Residual = -26.34 Percent = 1.1539 Residual = -26.64 Percent = 1.0638 Residual = -26.64 Percent = 1.0638 Residual = -26.93 Percent = 0.9799 Residual = -26.93 Percent = 0.9799 Residual = -27.23 Percent = 0.9018 Residual = -27.23 Percent = 0.9018 Residual = -27.53 Percent = 0.8291 Residual = -27.53 Percent = 0.8291 Residual = -27.83 Percent = 0.7616 Residual = -27.83 Percent = 0.7616 Residual = -28.13 Percent = 0.6989 Residual = -28.13 Percent = 0.6989 Residual = -28.43 Percent = 0.6408 Residual = -28.43 Percent = 0.6408 Residual = -28.73 Percent = 0.587 Residual = -28.73 Percent = 0.587 Residual = -29.03 Percent = 0.5372 Residual = -29.03 Percent = 0.5372 Residual = -29.33 Percent = 0.4912 Residual = -29.33 Percent = 0.4912 Residual = -29.63 Percent = 0.4487 Residual = 20 Percent = 3.3333 Residual = 20 Percent = 3.3333 Residual = 10 Percent = 30 Residual = 10 Percent = 30 Residual = 0 Percent = 40 Residual = 0 Percent = 40 Residual = -10 Percent = 16.667 Residual = -10 Percent = 16.667 Residual = -20 Percent = 10 Residual = -20 Percent = 10
Histogram of Residuals for LVEF with normal and kernel densities overlaid

RF Plot

Proportion Less = 0.9793 Fit-Mean = 8.5667 Proportion Less = 0.9463 Fit-Mean = 8.5667 Proportion Less = 0.9132 Fit-Mean = 8.5667 Proportion Less = 0.8802 Fit-Mean = 8.5667 Proportion Less = 0.8471 Fit-Mean = 8.5667 Proportion Less = 0.814 Fit-Mean = 8.5667 Proportion Less = 0.781 Fit-Mean = 8.5667 Proportion Less = 0.7479 Fit-Mean = 8.5667 Proportion Less = 0.7149 Fit-Mean = 8.5667 Proportion Less = 0.6818 Fit-Mean = 8.5667 Proportion Less = 0.6488 Fit-Mean = -2.833 Proportion Less = 0.6157 Fit-Mean = -2.833 Proportion Less = 0.5826 Fit-Mean = -2.833 Proportion Less = 0.5496 Fit-Mean = -2.833 Proportion Less = 0.5165 Fit-Mean = -2.833 Proportion Less = 0.4835 Fit-Mean = -2.833 Proportion Less = 0.4504 Fit-Mean = -2.833 Proportion Less = 0.4174 Fit-Mean = -2.833 Proportion Less = 0.3843 Fit-Mean = -2.833 Proportion Less = 0.3512 Fit-Mean = -2.833 Proportion Less = 0.3182 Fit-Mean = -5.733 Proportion Less = 0.2851 Fit-Mean = -5.733 Proportion Less = 0.2521 Fit-Mean = -5.733 Proportion Less = 0.219 Fit-Mean = -5.733 Proportion Less = 0.186 Fit-Mean = -5.733 Proportion Less = 0.1529 Fit-Mean = -5.733 Proportion Less = 0.1198 Fit-Mean = -5.733 Proportion Less = 0.0868 Fit-Mean = -5.733 Proportion Less = 0.0537 Fit-Mean = -5.733 Proportion Less = 0.0207 Fit-Mean = -5.733 Proportion Less = 0.9793 Residual = 23.6 Proportion Less = 0.9463 Residual = 13.3 Proportion Less = 0.9132 Residual = 10.7 Proportion Less = 0.8802 Residual = 10.3 Proportion Less = 0.8471 Residual = 9.3 Proportion Less = 0.814 Residual = 7.7 Proportion Less = 0.781 Residual = 7.3 Proportion Less = 0.7479 Residual = 7.3 Proportion Less = 0.7149 Residual = 5.7 Proportion Less = 0.6818 Residual = 5.6 Proportion Less = 0.6488 Residual = 4.7 Proportion Less = 0.6157 Residual = 2.7 Proportion Less = 0.5826 Residual = 1.6 Proportion Less = 0.5496 Residual = 1.3 Proportion Less = 0.5165 Residual = 0.7 Proportion Less = 0.4835 Residual = 0.7 Proportion Less = 0.4504 Residual = 0.6 Proportion Less = 0.4174 Residual = 0.6 Proportion Less = 0.3843 Residual = -1.4 Proportion Less = 0.3512 Residual = -1.4 Proportion Less = 0.3182 Residual = -2.3 Proportion Less = 0.2851 Residual = -4.4 Proportion Less = 0.2521 Residual = -5.7 Proportion Less = 0.219 Residual = -8.4 Proportion Less = 0.186 Residual = -11.3 Proportion Less = 0.1529 Residual = -13.7 Proportion Less = 0.1198 Residual = -13.7 Proportion Less = 0.0868 Residual = -15.7 Proportion Less = 0.0537 Residual = -16.4 Proportion Less = 0.0207 Residual = -19.3
Residual-Fit Spread Plot for LVEF

Box Plot

Group = Placebo LVEF = 80 Observation = 7 Group = Placebo LVEF = 40 Observation = 8 Group = Lasix LVEF = 40 Observation = 30 Group = Placebo Data Minimum = 40 Minimum Whisker = 48 First Quartile = 52 Median = 56 Third Quartile = 58 Maximum Whisker = 62 Data Maximum = 80 Mean = 56.4 Standard Deviation = 10.298 Number of Observations = 10 Sum of Weight = . Group = Placebo Data Minimum = 40 Minimum Whisker = 48 First Quartile = 52 Median = 56 Third Quartile = 58 Maximum Whisker = 62 Data Maximum = 80 Mean = 56.4 Standard Deviation = 10.298 Number of Observations = 10 Sum of Weight = . Group = Placebo Data Minimum = 40 Minimum Whisker = 48 First Quartile = 52 Median = 56 Third Quartile = 58 Maximum Whisker = 62 Data Maximum = 80 Mean = 56.4 Standard Deviation = 10.298 Number of Observations = 10 Sum of Weight = . Group = Placebo Data Minimum = 40 Minimum Whisker = 48 First Quartile = 52 Median = 56 Third Quartile = 58 Maximum Whisker = 62 Data Maximum = 80 Mean = 56.4 Standard Deviation = 10.298 Number of Observations = 10 Sum of Weight = . Group = Placebo Data Minimum = 40 Minimum Whisker = 48 First Quartile = 52 Median = 56 Third Quartile = 58 Maximum Whisker = 62 Data Maximum = 80 Mean = 56.4 Standard Deviation = 10.298 Number of Observations = 10 Sum of Weight = . Group = Placebo Data Minimum = 40 Minimum Whisker = 48 First Quartile = 52 Median = 56 Third Quartile = 58 Maximum Whisker = 62 Data Maximum = 80 Mean = 56.4 Standard Deviation = 10.298 Number of Observations = 10 Sum of Weight = . Group = Placebo Data Minimum = 40 Minimum Whisker = 48 First Quartile = 52 Median = 56 Third Quartile = 58 Maximum Whisker = 62 Data Maximum = 80 Mean = 56.4 Standard Deviation = 10.298 Number of Observations = 10 Sum of Weight = . Group = Placebo Data Minimum = 40 Minimum Whisker = 48 First Quartile = 52 Median = 56 Third Quartile = 58 Maximum Whisker = 62 Data Maximum = 80 Mean = 56.4 Standard Deviation = 10.298 Number of Observations = 10 Sum of Weight = . Group = Lasix Data Minimum = 40 Minimum Whisker = 48 First Quartile = 57 Median = 61 Third Quartile = 65 Maximum Whisker = 70 Data Maximum = 70 Mean = 59.3 Standard Deviation = 9.0805 Number of Observations = 10 Sum of Weight = . Group = Lasix Data Minimum = 40 Minimum Whisker = 48 First Quartile = 57 Median = 61 Third Quartile = 65 Maximum Whisker = 70 Data Maximum = 70 Mean = 59.3 Standard Deviation = 9.0805 Number of Observations = 10 Sum of Weight = . Group = Lasix Data Minimum = 40 Minimum Whisker = 48 First Quartile = 57 Median = 61 Third Quartile = 65 Maximum Whisker = 70 Data Maximum = 70 Mean = 59.3 Standard Deviation = 9.0805 Number of Observations = 10 Sum of Weight = . Group = Lasix Data Minimum = 40 Minimum Whisker = 48 First Quartile = 57 Median = 61 Third Quartile = 65 Maximum Whisker = 70 Data Maximum = 70 Mean = 59.3 Standard Deviation = 9.0805 Number of Observations = 10 Sum of Weight = . Group = Lasix Data Minimum = 40 Minimum Whisker = 48 First Quartile = 57 Median = 61 Third Quartile = 65 Maximum Whisker = 70 Data Maximum = 70 Mean = 59.3 Standard Deviation = 9.0805 Number of Observations = 10 Sum of Weight = . Group = Lasix Data Minimum = 40 Minimum Whisker = 48 First Quartile = 57 Median = 61 Third Quartile = 65 Maximum Whisker = 70 Data Maximum = 70 Mean = 59.3 Standard Deviation = 9.0805 Number of Observations = 10 Sum of Weight = . Group = Lasix Data Minimum = 40 Minimum Whisker = 48 First Quartile = 57 Median = 61 Third Quartile = 65 Maximum Whisker = 70 Data Maximum = 70 Mean = 59.3 Standard Deviation = 9.0805 Number of Observations = 10 Sum of Weight = . Group = Lasix Data Minimum = 40 Minimum Whisker = 48 First Quartile = 57 Median = 61 Third Quartile = 65 Maximum Whisker = 70 Data Maximum = 70 Mean = 59.3 Standard Deviation = 9.0805 Number of Observations = 10 Sum of Weight = . Group = Calcium Data Minimum = 55 Minimum Whisker = 55 First Quartile = 57 Median = 75 Third Quartile = 80 Maximum Whisker = 84 Data Maximum = 84 Mean = 70.7 Standard Deviation = 11.216 Number of Observations = 10 Sum of Weight = . Group = Calcium Data Minimum = 55 Minimum Whisker = 55 First Quartile = 57 Median = 75 Third Quartile = 80 Maximum Whisker = 84 Data Maximum = 84 Mean = 70.7 Standard Deviation = 11.216 Number of Observations = 10 Sum of Weight = . Group = Calcium Data Minimum = 55 Minimum Whisker = 55 First Quartile = 57 Median = 75 Third Quartile = 80 Maximum Whisker = 84 Data Maximum = 84 Mean = 70.7 Standard Deviation = 11.216 Number of Observations = 10 Sum of Weight = . Group = Calcium Data Minimum = 55 Minimum Whisker = 55 First Quartile = 57 Median = 75 Third Quartile = 80 Maximum Whisker = 84 Data Maximum = 84 Mean = 70.7 Standard Deviation = 11.216 Number of Observations = 10 Sum of Weight = . Group = Calcium Data Minimum = 55 Minimum Whisker = 55 First Quartile = 57 Median = 75 Third Quartile = 80 Maximum Whisker = 84 Data Maximum = 84 Mean = 70.7 Standard Deviation = 11.216 Number of Observations = 10 Sum of Weight = . Group = Calcium Data Minimum = 55 Minimum Whisker = 55 First Quartile = 57 Median = 75 Third Quartile = 80 Maximum Whisker = 84 Data Maximum = 84 Mean = 70.7 Standard Deviation = 11.216 Number of Observations = 10 Sum of Weight = . Group = Calcium Data Minimum = 55 Minimum Whisker = 55 First Quartile = 57 Median = 75 Third Quartile = 80 Maximum Whisker = 84 Data Maximum = 84 Mean = 70.7 Standard Deviation = 11.216 Number of Observations = 10 Sum of Weight = . Group = Calcium Data Minimum = 55 Minimum Whisker = 55 First Quartile = 57 Median = 75 Third Quartile = 80 Maximum Whisker = 84 Data Maximum = 84 Mean = 70.7 Standard Deviation = 11.216 Number of Observations = 10 Sum of Weight = .
Fit Plot for LVEF by Group

Means

Group

LVEF

Levene's HoV Test

Levene's Test for Homogeneity of LVEF Variance
ANOVA of Squared Deviations from Group Means
Source DF Sum of Squares Mean Square F Value Pr > F
Group 2 7625.0 3812.5 0.22 0.8069
Error 27 475849 17624.0    

Group

LVEF

Welch's ANOVA

Welch's ANOVA for LVEF
Source DF F Value Pr > F
Group 2.0000 4.71 0.0228
Error 17.8619    

Group

Means

Level of
Group		 N LVEF
Mean Std Dev
Calcium 10 70.7000000 11.2155646
Lasix 10 59.3000000 9.0805041
Placebo 10 56.4000000 10.2977883

Least Squares Means

Adjustment for Multiple Comparisons: Tukey

Least Squares Means

Group

LVEF

LSMeans

Group LVEF LSMEAN LSMEAN Number
Calcium 70.7000000 1
Lasix 59.3000000 2
Placebo 56.4000000 3

Difference Matrix

Least Squares Means for effect Group
Pr > |t| for H0: LSMean(i)=LSMean(j)

Dependent Variable: LVEF
i/j 1 2 3
1   0.0488 0.0114
2 0.0488   0.8031
3 0.0114 0.8031  

Group Mean Plot

Group = Placebo LS-Mean = 56.4 Group = Lasix LS-Mean = 59.3 Group = Calcium LS-Mean = 70.7
Plot of LVEF least-squares means for Group.

Group Diffogram

Comparison = Calcium vs. Placebo Comparison = Calcium vs. Placebo Comparison = Calcium vs. Lasix Comparison = Calcium vs. Lasix Comparison = Lasix vs. Placebo Comparison = Lasix vs. Placebo Slope = 1 Y = 0 Mean = 56.4 (Placebo) Mean = 56.4 (Placebo) Mean = 59.3 (Lasix) Mean = 59.3 (Lasix) Mean = 70.7 (Calcium) Mean = 70.7 (Calcium) Mean = 56.4 (Placebo) Mean = 56.4 (Placebo) Mean = 59.3 (Lasix) Mean = 59.3 (Lasix) Mean = 70.7 (Calcium) Mean = 70.7 (Calcium)
Plot of all pairwise LVEF least-squares means differences for Group with Tukey adjustment at significance level 0.05.
  • The ANOVA table shows F-value of 5.45 and with a corresponding p-value of 0.0102.
  • The Q-Q Plot of Residuals for left ventricular ejection fraction (LVEF) shows deviations from the straight line which means leads me to request Welch’s variance-weighted ANOVA. The Histogram for Residuals [Distribution of Residuals for LVEF] appear to be relatively normally distributed.
  • To confirm the assumption of homogeneity of variance / homoscedasticity, we require a p-value above the chosen significance level. The output table [Levene’s Test for Homogeneity of LVEF Variance / ANOVA of Squared Deviations from Group Means] shows a p-value of .8069, so do not reject the null hypothesis of equal variance at the .05 level. However, the output table [Welch’s ANOVA for LVEF] shows a p-value of .0228, so reject the null hypothesis of equal variance at the .05 level?!?
  • The table [Least Squares Means / Adjustment for Multiple Comparisons: Tukey] shows p-values for all of the pairwise differences: Lasix vs. Placebo shows a p-value = 0.8031 (not significant at the .05 level), Calcium vs. Lasix shows a p-value = 0.0488 (significant at the .05 level), and Calcium vs. Placebo shows a p-value = 0.0114 (significant at the .05 level). This is confirmed by the plot Pairwise Comparison of Means [LVEF Comparisons for Group].

Chapter 9: N-Way ANOVA

Performing a Two-Way Analysis of Variance.

SAS Code, click to expand

SAS Code:

#  (&path1 and biostats libname previously defined)
/*** Chapter 9: N-Way ANOVA ***/

/* Chapter 9: Performing a Two-Way Analysis of Variance - generated code - start */

/* Perform N-way ANOVA */
/* Model Effects Full Factorial, Type 3 Sum of Squares, Perform Multiple Comparisons default Main effects Tukey 0.05 level  Interaction plot Diagnostic plots*/
title1 "N-Way ANOVA: Birth Weight where Interaction Term is not Significant";
ods noproctitle;
ods graphics / imagemap=on;
proc glm data=work.Birth_Wt_Sample
  plots(only maxpoints=none)=(diagnostics(unpack) intplot);
    class Black MomSmoke;
    model Weight=Black MomSmoke Black*MomSmoke / ss3;
    lsmeans Black MomSmoke / adjust=tukey pdiff=all alpha=0.05 
      cl ;
quit;

/* The ANOVA table shows the F and p-values for the model as a whole, then the sum of squares, mean squares, F and p-values for each of the two factors and the interaction term.  Both of the main factors are highly significant (Black and MomSmoke) while the interaction term (Black*MomSmoke where p = 0.4842) is not significant at the .05 level. 
Checking the diagnostic plots to verify ANOVA assumptions, we see that the first plot (Residuals by Predicted for Weight) shows few outliers on the low side and similar variance in each of the four categories.  The 7th plot/histogram of residuals (Distribution of Residuals for Weight) looks symmetric and close enough to a normal distribution.  
Babies born from black mothers are lighter than babies born from non-black mothers (difference of about 235.6 grams or about half a pound).  (Note that the 95% confidence limits do not include 0 because the difference is significant at the .05 level.)  Babies born to mothers who smoke are approximately 263.4 grams or about half a pound lighter than babies born to mothers who do not smoke.  */

/* Model Effects Full Factorial, Type 3 Sum of Squares, Perform Multiple Comparisons ALL effects Tukey 0.05 level  Interaction plot LSMeans plot Diagnostic plots*/
title1 "N-Way ANOVA: Birth Weight where Interaction Term is Significant";
ods noproctitle;
ods graphics / imagemap=on;
proc glm data=work.Birth_Wt_Sample
  plots(only maxpoints=none)=(diagnostics(unpack) intplot);
    class MomSmoke Married;
    model Weight=MomSmoke Married MomSmoke*Married / ss3;
    lsmeans MomSmoke Married MomSmoke*Married / adjust=tukey pdiff=all alpha=0.05 
      cl plots=(meanplot(cl));
quit;

/* The ANOVA table shows the F and p-values for the model as a whole, then the sum of squares, mean squares, F and p-values for each of the two factors and the interaction term.  Both of the main factors are highly significant (MomSmoke and Married) and the interaction term (MomSmoke*Married where p = 0.0001) is also significant at the .05 level. 
In this model, Babies born to mothers who smoke are approximately 221.8 grams lighter than babies born to mothers who do not smoke.  Babies born from married mothers are heavier by about 120.5 grams than babies born from unmarried mothers.  (Note that the 95% confidence limits [both of which are negative numbers since they are heavier] do not include 0 because the difference is significant at the .05 level.)
Scrolling down to the interaction tables (Least Squares Means - Adjustment for Multiple Comparisons: Tukey-Kramer), we see that nonsmoking married mothers (MomSmoke=0, Married=1, LSMEAN number identifier 2) show the heaviest birth weight, while smoking unmarried mothers (MomSmoke=1, Married=0, LSMEAN number identifier 3) show the lightest birth weight.  "Looking at the last plot (LS-Means for MomSmoke*Married With 95% Confidence Limits), we see the means and confidence limits for all 4 combinations of the two factors; drawing straight lines between the means of (0 * 0) and (0 * 1), and (1 * 0) and (1 * 1) we see that there is some interaction between the two terms because there are different slopes (no interaction would show parallel lines drawn)."  */

title1;
/* Performing a Two-Way Analysis of Variance - generated code - end */

SAS Output

Results: biostats_by_ex_SAScode.sas

Results: biostats_by_ex_SAScode.sas

N-Way ANOVA: Birth Weight where Interaction Term is not Significant

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
Black 2 0 1
MomSmoke 2 0 1

Number of Observations

Number of Observations Read 12500
Number of Observations Used 12500

N-Way ANOVA: Birth Weight where Interaction Term is not Significant

Dependent Variable: Weight Infant Birth Weight

Analysis of Variance

Weight

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 3 201913196 67304399 224.76 <.0001
Error 12496 3741913496 299449    
Corrected Total 12499 3943826691      

Fit Statistics

R-Square Coeff Var Root MSE Weight Mean
0.051197 16.22229 547.2192 3373.254

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
Black 1 34754959.61 34754959.61 116.06 <.0001
MomSmoke 1 43453129.92 43453129.92 145.11 <.0001
Black*MomSmoke 1 146558.23 146558.23 0.49 0.4842

Diagnostic Plots

Residual by Predicted

Y = 0
Plot of Residual by Predicted for Weight

RStudent by Predicted

Y = 2 Y = -2
Plot of RStudent by Predicted for Weight

RStudent by Leverage

X = .00064 Y = -2 Y = 2
Plot of RStudent by Leverage for Weight

Q-Q Plot

Slope = 547.15 Y = -8E-13
Q-Q Plot of Residuals for Weight

Weight by Predicted

Slope = 1 Y = 0
Plot of Weight by Predicted

Cook's D Plot

Y = .00032
Needleplot of Cook's D statistic by Observation for Weight

Residual Histogram

Residual = 2739.6 Percent = .00011 Residual = 2695.9 Percent = .00047 Residual = 2695.9 Percent = .00047 Residual = 2652.1 Percent = 0.0015 Residual = 2652.1 Percent = 0.0015 Residual = 2608.4 Percent = 0.0033 Residual = 2608.4 Percent = 0.0033 Residual = 2564.6 Percent = 0.0053 Residual = 2564.6 Percent = 0.0053 Residual = 2520.9 Percent = 0.0062 Residual = 2520.9 Percent = 0.0062 Residual = 2477.1 Percent = 0.0053 Residual = 2477.1 Percent = 0.0053 Residual = 2433.3 Percent = 0.0033 Residual = 2433.3 Percent = 0.0033 Residual = 2389.6 Percent = 0.0015 Residual = 2389.6 Percent = 0.0015 Residual = 2345.8 Percent = .00047 Residual = 2345.8 Percent = .00047 Residual = 2302.1 Percent = .00014 Residual = 2302.1 Percent = .00014 Residual = 2258.3 Percent = .00019 Residual = 2258.3 Percent = .00019 Residual = 2214.6 Percent = .00063 Residual = 2214.6 Percent = .00063 Residual = 2170.8 Percent = 0.0018 Residual = 2170.8 Percent = 0.0018 Residual = 2083.3 Percent = 0.0055 Residual = 2083.3 Percent = 0.0055 Residual = 2039.5 Percent = 0.0063 Residual = 2039.5 Percent = 0.0063 Residual = 1995.8 Percent = 0.0061 Residual = 1995.8 Percent = 0.0061 Residual = 1952 Percent = 0.0071 Residual = 1952 Percent = 0.0071 Residual = 1908.2 Percent = 0.0132 Residual = 1908.2 Percent = 0.0132 Residual = 1864.5 Percent = 0.0275 Residual = 1864.5 Percent = 0.0275 Residual = 1820.7 Percent = 0.0496 Residual = 1820.7 Percent = 0.0496 Residual = 1777 Percent = 0.0735 Residual = 1777 Percent = 0.0735 Residual = 1733.2 Percent = 0.091 Residual = 1733.2 Percent = 0.091 Residual = 1689.5 Percent = 0.0997 Residual = 1689.5 Percent = 0.0997 Residual = 1645.7 Percent = 0.1054 Residual = 1645.7 Percent = 0.1054 Residual = 1601.9 Percent = 0.1179 Residual = 1601.9 Percent = 0.1179 Residual = 1558.2 Percent = 0.1422 Residual = 1558.2 Percent = 0.1422 Residual = 1514.4 Percent = 0.1749 Residual = 1514.4 Percent = 0.1749 Residual = 1470.7 Percent = 0.2086 Residual = 1470.7 Percent = 0.2086 Residual = 1426.9 Percent = 0.2453 Residual = 1426.9 Percent = 0.2453 Residual = 1383.2 Percent = 0.2986 Residual = 1383.2 Percent = 0.2986 Residual = 1339.4 Percent = 0.3801 Residual = 1339.4 Percent = 0.3801 Residual = 1295.6 Percent = 0.4884 Residual = 1295.6 Percent = 0.4884 Residual = 1251.9 Percent = 0.6139 Residual = 1251.9 Percent = 0.6139 Residual = 1164.4 Percent = 0.8837 Residual = 1164.4 Percent = 0.8837 Residual = 1120.6 Percent = 1.0261 Residual = 1120.6 Percent = 1.0261 Residual = 1076.9 Percent = 1.1893 Residual = 1076.9 Percent = 1.1893 Residual = 1033.1 Percent = 1.392 Residual = 1033.1 Percent = 1.392 Residual = 989.33 Percent = 1.6502 Residual = 989.33 Percent = 1.6502 Residual = 945.58 Percent = 1.9732 Residual = 945.58 Percent = 1.9732 Residual = 770.55 Percent = 3.5039 Residual = 770.55 Percent = 3.5039 Residual = 726.79 Percent = 3.9492 Residual = 726.79 Percent = 3.9492 Residual = 683.03 Percent = 4.4934 Residual = 683.03 Percent = 4.4934 Residual = 639.27 Percent = 5.1224 Residual = 639.27 Percent = 5.1224 Residual = 595.51 Percent = 5.8039 Residual = 595.51 Percent = 5.8039 Residual = 551.76 Percent = 6.5287 Residual = 551.76 Percent = 6.5287 Residual = 464.24 Percent = 8.0677 Residual = 464.24 Percent = 8.0677 Residual = 420.48 Percent = 8.7898 Residual = 420.48 Percent = 8.7898 Residual = 376.73 Percent = 9.4508 Residual = 376.73 Percent = 9.4508 Residual = 332.97 Percent = 10.082 Residual = 332.97 Percent = 10.082 Residual = 289.21 Percent = 10.695 Residual = 289.21 Percent = 10.695 Residual = 245.45 Percent = 11.258 Residual = 245.45 Percent = 11.258 Residual = 201.69 Percent = 11.737 Residual = 201.69 Percent = 11.737 Residual = 157.94 Percent = 12.109 Residual = 157.94 Percent = 12.109 Residual = 114.18 Percent = 12.359 Residual = 114.18 Percent = 12.359 Residual = 70.421 Percent = 12.487 Residual = 70.421 Percent = 12.487 Residual = 26.663 Percent = 12.502 Residual = 26.663 Percent = 12.502 Residual = -17.09 Percent = 12.425 Residual = -17.09 Percent = 12.425 Residual = -60.85 Percent = 12.278 Residual = -60.85 Percent = 12.278 Residual = -104.6 Percent = 12.06 Residual = -104.6 Percent = 12.06 Residual = -148.4 Percent = 11.737 Residual = -148.4 Percent = 11.737 Residual = -192.1 Percent = 11.277 Residual = -192.1 Percent = 11.277 Residual = -235.9 Percent = 10.696 Residual = -235.9 Percent = 10.696 Residual = -279.6 Percent = 10.034 Residual = -279.6 Percent = 10.034 Residual = -323.4 Percent = 9.3068 Residual = -323.4 Percent = 9.3068 Residual = -410.9 Percent = 7.7113 Residual = -410.9 Percent = 7.7113 Residual = -454.7 Percent = 6.9436 Residual = -454.7 Percent = 6.9436 Residual = -498.4 Percent = 6.2422 Residual = -498.4 Percent = 6.2422 Residual = -585.9 Percent = 4.9429 Residual = -585.9 Percent = 4.9429 Residual = -629.7 Percent = 4.3298 Residual = -629.7 Percent = 4.3298 Residual = -673.5 Percent = 3.7872 Residual = -673.5 Percent = 3.7872 Residual = -717.2 Percent = 3.3367 Residual = -717.2 Percent = 3.3367 Residual = -761 Percent = 2.9508 Residual = -761 Percent = 2.9508 Residual = -848.5 Percent = 2.2229 Residual = -848.5 Percent = 2.2229 Residual = -892.3 Percent = 1.884 Residual = -892.3 Percent = 1.884 Residual = -936 Percent = 1.5948 Residual = -936 Percent = 1.5948 Residual = -979.8 Percent = 1.3618 Residual = -979.8 Percent = 1.3618 Residual = -1024 Percent = 1.1693 Residual = -1024 Percent = 1.1693 Residual = -1067 Percent = 1.0023 Residual = -1067 Percent = 1.0023 Residual = -1111 Percent = 0.863 Residual = -1111 Percent = 0.863 Residual = -1155 Percent = 0.7595 Residual = -1155 Percent = 0.7595 Residual = -1199 Percent = 0.6859 Residual = -1199 Percent = 0.6859 Residual = -1242 Percent = 0.6231 Residual = -1242 Percent = 0.6231 Residual = -1286 Percent = 0.556 Residual = -1286 Percent = 0.556 Residual = -1330 Percent = 0.4855 Residual = -1330 Percent = 0.4855 Residual = -1374 Percent = 0.4221 Residual = -1374 Percent = 0.4221 Residual = -1417 Percent = 0.3703 Residual = -1417 Percent = 0.3703 Residual = -1461 Percent = 0.3273 Residual = -1461 Percent = 0.3273 Residual = -1505 Percent = 0.2923 Residual = -1505 Percent = 0.2923 Residual = -1549 Percent = 0.2682 Residual = -1549 Percent = 0.2682 Residual = -1592 Percent = 0.2548 Residual = -1592 Percent = 0.2548 Residual = -1636 Percent = 0.2484 Residual = -1636 Percent = 0.2484 Residual = -1680 Percent = 0.2463 Residual = -1680 Percent = 0.2463 Residual = -1724 Percent = 0.2461 Residual = -1724 Percent = 0.2461 Residual = -1767 Percent = 0.2428 Residual = -1767 Percent = 0.2428 Residual = -1811 Percent = 0.233 Residual = -1811 Percent = 0.233 Residual = -1855 Percent = 0.2202 Residual = -1855 Percent = 0.2202 Residual = -1899 Percent = 0.2096 Residual = -1899 Percent = 0.2096 Residual = -1942 Percent = 0.2 Residual = -1942 Percent = 0.2 Residual = -1986 Percent = 0.1862 Residual = -1986 Percent = 0.1862 Residual = -2030 Percent = 0.1692 Residual = -2030 Percent = 0.1692 Residual = -2074 Percent = 0.1544 Residual = -2074 Percent = 0.1544 Residual = -2117 Percent = 0.1444 Residual = -2117 Percent = 0.1444 Residual = -2161 Percent = 0.1375 Residual = -2161 Percent = 0.1375 Residual = -2205 Percent = 0.131 Residual = -2205 Percent = 0.131 Residual = -2293 Percent = 0.1164 Residual = -2293 Percent = 0.1164 Residual = -2336 Percent = 0.1107 Residual = -2336 Percent = 0.1107 Residual = -2380 Percent = 0.1062 Residual = -2380 Percent = 0.1062 Residual = -2424 Percent = 0.1007 Residual = -2424 Percent = 0.1007 Residual = -2468 Percent = 0.0948 Residual = -2468 Percent = 0.0948 Residual = -2511 Percent = 0.0925 Residual = -2511 Percent = 0.0925 Residual = -2555 Percent = 0.0963 Residual = -2555 Percent = 0.0963 Residual = -2599 Percent = 0.1034 Residual = -2599 Percent = 0.1034 Residual = -2643 Percent = 0.1073 Residual = -2643 Percent = 0.1073 Residual = -2686 Percent = 0.1033 Residual = -2686 Percent = 0.1033 Residual = -2730 Percent = 0.0924 Residual = -2730 Percent = 0.0924 Residual = -2774 Percent = 0.0796 Residual = -2774 Percent = 0.0796 Residual = -2818 Percent = 0.0681 Residual = -2818 Percent = 0.0681 Residual = -2861 Percent = 0.0576 Residual = -2861 Percent = 0.0576 Residual = -2905 Percent = 0.0467 Residual = -2905 Percent = 0.0467 Residual = -2949 Percent = 0.0366 Residual = -2949 Percent = 0.0366 Residual = -2993 Percent = 0.0298 Residual = -2993 Percent = 0.0298 Residual = -3036 Percent = 0.0256 Residual = -3036 Percent = 0.0256 Residual = -3080 Percent = 0.0209 Residual = -3080 Percent = 0.0209 Residual = -3168 Percent = 0.0078 Residual = -3168 Percent = 0.0078 Residual = -3211 Percent = 0.0032 Residual = -3211 Percent = 0.0032 Residual = -3255 Percent = .00096 Residual = -3255 Percent = .00096 Residual = -3299 Percent = .00021 Residual = 2550 Percent = .00021 Residual = 2521.2 Percent = .00027 Residual = 2521.2 Percent = .00027 Residual = 2492.4 Percent = .00034 Residual = 2492.4 Percent = .00034 Residual = 2463.6 Percent = .00043 Residual = 2463.6 Percent = .00043 Residual = 2434.8 Percent = .00055 Residual = 2434.8 Percent = .00055 Residual = 2406.1 Percent = .00069 Residual = 2406.1 Percent = .00069 Residual = 2377.3 Percent = .00087 Residual = 2377.3 Percent = .00087 Residual = 2348.5 Percent = 0.0011 Residual = 2348.5 Percent = 0.0011 Residual = 2319.7 Percent = 0.0014 Residual = 2319.7 Percent = 0.0014 Residual = 2290.9 Percent = 0.0017 Residual = 2290.9 Percent = 0.0017 Residual = 2262.1 Percent = 0.0021 Residual = 2262.1 Percent = 0.0021 Residual = 2233.3 Percent = 0.0026 Residual = 2233.3 Percent = 0.0026 Residual = 2204.5 Percent = 0.0033 Residual = 2204.5 Percent = 0.0033 Residual = 2175.8 Percent = 0.004 Residual = 2175.8 Percent = 0.004 Residual = 2147 Percent = 0.005 Residual = 2147 Percent = 0.005 Residual = 2118.2 Percent = 0.0061 Residual = 2118.2 Percent = 0.0061 Residual = 2089.4 Percent = 0.0075 Residual = 2089.4 Percent = 0.0075 Residual = 2060.6 Percent = 0.0091 Residual = 2060.6 Percent = 0.0091 Residual = 2031.8 Percent = 0.0111 Residual = 2031.8 Percent = 0.0111 Residual = 2003 Percent = 0.0135 Residual = 2003 Percent = 0.0135 Residual = 1974.2 Percent = 0.0163 Residual = 1974.2 Percent = 0.0163 Residual = 1945.5 Percent = 0.0197 Residual = 1945.5 Percent = 0.0197 Residual = 1916.7 Percent = 0.0237 Residual = 1916.7 Percent = 0.0237 Residual = 1887.9 Percent = 0.0284 Residual = 1887.9 Percent = 0.0284 Residual = 1859.1 Percent = 0.034 Residual = 1859.1 Percent = 0.034 Residual = 1830.3 Percent = 0.0406 Residual = 1830.3 Percent = 0.0406 Residual = 1801.5 Percent = 0.0484 Residual = 1801.5 Percent = 0.0484 Residual = 1772.7 Percent = 0.0575 Residual = 1772.7 Percent = 0.0575 Residual = 1743.9 Percent = 0.0681 Residual = 1743.9 Percent = 0.0681 Residual = 1715.2 Percent = 0.0804 Residual = 1715.2 Percent = 0.0804 Residual = 1686.4 Percent = 0.0947 Residual = 1686.4 Percent = 0.0947 Residual = 1657.6 Percent = 0.1112 Residual = 1657.6 Percent = 0.1112 Residual = 1628.8 Percent = 0.1302 Residual = 1628.8 Percent = 0.1302 Residual = 1600 Percent = 0.1521 Residual = 1600 Percent = 0.1521 Residual = 1571.2 Percent = 0.1771 Residual = 1571.2 Percent = 0.1771 Residual = 1542.4 Percent = 0.2057 Residual = 1542.4 Percent = 0.2057 Residual = 1513.6 Percent = 0.2383 Residual = 1513.6 Percent = 0.2383 Residual = 1484.8 Percent = 0.2752 Residual = 1484.8 Percent = 0.2752 Residual = 1456.1 Percent = 0.317 Residual = 1456.1 Percent = 0.317 Residual = 1427.3 Percent = 0.3642 Residual = 1427.3 Percent = 0.3642 Residual = 1398.5 Percent = 0.4172 Residual = 1398.5 Percent = 0.4172 Residual = 1369.7 Percent = 0.4766 Residual = 1369.7 Percent = 0.4766 Residual = 1340.9 Percent = 0.5429 Residual = 1340.9 Percent = 0.5429 Residual = 1312.1 Percent = 0.6168 Residual = 1312.1 Percent = 0.6168 Residual = 1283.3 Percent = 0.6987 Residual = 1283.3 Percent = 0.6987 Residual = 1254.5 Percent = 0.7894 Residual = 1254.5 Percent = 0.7894 Residual = 1225.8 Percent = 0.8894 Residual = 1225.8 Percent = 0.8894 Residual = 1197 Percent = 0.9993 Residual = 1197 Percent = 0.9993 Residual = 1168.2 Percent = 1.1196 Residual = 1168.2 Percent = 1.1196 Residual = 1139.4 Percent = 1.251 Residual = 1139.4 Percent = 1.251 Residual = 1110.6 Percent = 1.3939 Residual = 1110.6 Percent = 1.3939 Residual = 1081.8 Percent = 1.5489 Residual = 1081.8 Percent = 1.5489 Residual = 1053 Percent = 1.7163 Residual = 1053 Percent = 1.7163 Residual = 1024.2 Percent = 1.8966 Residual = 1024.2 Percent = 1.8966 Residual = 995.45 Percent = 2.09 Residual = 995.45 Percent = 2.09 Residual = 966.67 Percent = 2.2967 Residual = 966.67 Percent = 2.2967 Residual = 937.88 Percent = 2.517 Residual = 937.88 Percent = 2.517 Residual = 909.09 Percent = 2.7507 Residual = 909.09 Percent = 2.7507 Residual = 880.3 Percent = 2.9978 Residual = 880.3 Percent = 2.9978 Residual = 851.52 Percent = 3.2581 Residual = 851.52 Percent = 3.2581 Residual = 822.73 Percent = 3.5313 Residual = 822.73 Percent = 3.5313 Residual = 793.94 Percent = 3.8167 Residual = 793.94 Percent = 3.8167 Residual = 765.15 Percent = 4.1138 Residual = 765.15 Percent = 4.1138 Residual = 736.36 Percent = 4.4218 Residual = 736.36 Percent = 4.4218 Residual = 707.58 Percent = 4.7396 Residual = 707.58 Percent = 4.7396 Residual = 650 Percent = 5.4006 Residual = 650 Percent = 5.4006 Residual = 534.85 Percent = 6.7827 Residual = 534.85 Percent = 6.7827 Residual = 448.48 Percent = 7.8163 Residual = 448.48 Percent = 7.8163 Residual = 390.91 Percent = 8.4733 Residual = 390.91 Percent = 8.4733 Residual = 362.12 Percent = 8.7857 Residual = 362.12 Percent = 8.7857 Residual = 333.33 Percent = 9.0845 Residual = 333.33 Percent = 9.0845 Residual = 304.55 Percent = 9.3674 Residual = 304.55 Percent = 9.3674 Residual = 275.76 Percent = 9.6324 Residual = 275.76 Percent = 9.6324 Residual = 246.97 Percent = 9.8776 Residual = 246.97 Percent = 9.8776 Residual = 218.18 Percent = 10.101 Residual = 218.18 Percent = 10.101 Residual = 189.39 Percent = 10.301 Residual = 189.39 Percent = 10.301 Residual = 160.61 Percent = 10.476 Residual = 160.61 Percent = 10.476 Residual = 131.82 Percent = 10.624 Residual = 131.82 Percent = 10.624 Residual = 103.03 Percent = 10.745 Residual = 103.03 Percent = 10.745 Residual = 74.242 Percent = 10.837 Residual = 74.242 Percent = 10.837 Residual = 45.455 Percent = 10.899 Residual = 45.455 Percent = 10.899 Residual = 16.667 Percent = 10.932 Residual = 16.667 Percent = 10.932 Residual = -8E-13 Percent = 10.937 Residual = -8E-13 Percent = 10.937 Residual = -12.12 Percent = 10.934 Residual = -12.12 Percent = 10.934 Residual = -40.91 Percent = 10.906 Residual = -40.91 Percent = 10.906 Residual = -69.7 Percent = 10.848 Residual = -69.7 Percent = 10.848 Residual = -98.48 Percent = 10.761 Residual = -98.48 Percent = 10.761 Residual = -127.3 Percent = 10.645 Residual = -127.3 Percent = 10.645 Residual = -156.1 Percent = 10.501 Residual = -156.1 Percent = 10.501 Residual = -184.8 Percent = 10.33 Residual = -184.8 Percent = 10.33 Residual = -213.6 Percent = 10.134 Residual = -213.6 Percent = 10.134 Residual = -242.4 Percent = 9.9144 Residual = -242.4 Percent = 9.9144 Residual = -271.2 Percent = 9.6725 Residual = -271.2 Percent = 9.6725 Residual = -300 Percent = 9.4105 Residual = -300 Percent = 9.4105 Residual = -328.8 Percent = 9.1303 Residual = -328.8 Percent = 9.1303 Residual = -357.6 Percent = 8.8339 Residual = -357.6 Percent = 8.8339 Residual = -386.4 Percent = 8.5235 Residual = -386.4 Percent = 8.5235 Residual = -616.7 Percent = 5.7952 Residual = -616.7 Percent = 5.7952 Residual = -674.2 Percent = 5.1186 Residual = -674.2 Percent = 5.1186 Residual = -731.8 Percent = 4.4713 Residual = -731.8 Percent = 4.4713 Residual = -760.6 Percent = 4.1617 Residual = -760.6 Percent = 4.1617 Residual = -789.4 Percent = 3.8628 Residual = -789.4 Percent = 3.8628 Residual = -818.2 Percent = 3.5755 Residual = -818.2 Percent = 3.5755 Residual = -847 Percent = 3.3004 Residual = -847 Percent = 3.3004 Residual = -875.8 Percent = 3.0381 Residual = -875.8 Percent = 3.0381 Residual = -904.5 Percent = 2.7888 Residual = -904.5 Percent = 2.7888 Residual = -933.3 Percent = 2.553 Residual = -933.3 Percent = 2.553 Residual = -962.1 Percent = 2.3306 Residual = -962.1 Percent = 2.3306 Residual = -990.9 Percent = 2.1217 Residual = -990.9 Percent = 2.1217 Residual = -1020 Percent = 1.9262 Residual = -1020 Percent = 1.9262 Residual = -1048 Percent = 1.7439 Residual = -1048 Percent = 1.7439 Residual = -1077 Percent = 1.5745 Residual = -1077 Percent = 1.5745 Residual = -1106 Percent = 1.4176 Residual = -1106 Percent = 1.4176 Residual = -1135 Percent = 1.2728 Residual = -1135 Percent = 1.2728 Residual = -1164 Percent = 1.1396 Residual = -1164 Percent = 1.1396 Residual = -1192 Percent = 1.0176 Residual = -1192 Percent = 1.0176 Residual = -1221 Percent = 0.9061 Residual = -1221 Percent = 0.9061 Residual = -1250 Percent = 0.8046 Residual = -1250 Percent = 0.8046 Residual = -1279 Percent = 0.7125 Residual = -1279 Percent = 0.7125 Residual = -1308 Percent = 0.6292 Residual = -1308 Percent = 0.6292 Residual = -1336 Percent = 0.554 Residual = -1336 Percent = 0.554 Residual = -1365 Percent = 0.4866 Residual = -1365 Percent = 0.4866 Residual = -1394 Percent = 0.4261 Residual = -1394 Percent = 0.4261 Residual = -1423 Percent = 0.3721 Residual = -1423 Percent = 0.3721 Residual = -1452 Percent = 0.3241 Residual = -1452 Percent = 0.3241 Residual = -1480 Percent = 0.2815 Residual = -1480 Percent = 0.2815 Residual = -1509 Percent = 0.2438 Residual = -1509 Percent = 0.2438 Residual = -1538 Percent = 0.2106 Residual = -1538 Percent = 0.2106 Residual = -1567 Percent = 0.1814 Residual = -1567 Percent = 0.1814 Residual = -1595 Percent = 0.1558 Residual = -1595 Percent = 0.1558 Residual = -1624 Percent = 0.1335 Residual = -1624 Percent = 0.1335 Residual = -1653 Percent = 0.114 Residual = -1653 Percent = 0.114 Residual = -1682 Percent = 0.0971 Residual = -1682 Percent = 0.0971 Residual = -1711 Percent = 0.0825 Residual = -1711 Percent = 0.0825 Residual = -1739 Percent = 0.0699 Residual = -1739 Percent = 0.0699 Residual = -1768 Percent = 0.059 Residual = -1768 Percent = 0.059 Residual = -1797 Percent = 0.0497 Residual = -1797 Percent = 0.0497 Residual = -1826 Percent = 0.0418 Residual = -1826 Percent = 0.0418 Residual = -1855 Percent = 0.035 Residual = -1855 Percent = 0.035 Residual = -1883 Percent = 0.0293 Residual = -1883 Percent = 0.0293 Residual = -1912 Percent = 0.0244 Residual = -1912 Percent = 0.0244 Residual = -1941 Percent = 0.0203 Residual = -1941 Percent = 0.0203 Residual = -1970 Percent = 0.0168 Residual = -1970 Percent = 0.0168 Residual = -1998 Percent = 0.0139 Residual = -1998 Percent = 0.0139 Residual = -2027 Percent = 0.0114 Residual = -2027 Percent = 0.0114 Residual = -2056 Percent = 0.0094 Residual = -2056 Percent = 0.0094 Residual = -2085 Percent = 0.0077 Residual = -2085 Percent = 0.0077 Residual = -2114 Percent = 0.0063 Residual = -2114 Percent = 0.0063 Residual = -2142 Percent = 0.0051 Residual = -2142 Percent = 0.0051 Residual = -2171 Percent = 0.0042 Residual = -2171 Percent = 0.0042 Residual = -2200 Percent = 0.0034 Residual = -2200 Percent = 0.0034 Residual = -2229 Percent = 0.0027 Residual = -2229 Percent = 0.0027 Residual = -2258 Percent = 0.0022 Residual = -2258 Percent = 0.0022 Residual = -2286 Percent = 0.0018 Residual = -2286 Percent = 0.0018 Residual = -2315 Percent = 0.0014 Residual = -2315 Percent = 0.0014 Residual = -2344 Percent = 0.0011 Residual = -2344 Percent = 0.0011 Residual = -2373 Percent = 0.0009 Residual = -2373 Percent = 0.0009 Residual = -2402 Percent = .00072 Residual = -2402 Percent = .00072 Residual = -2430 Percent = .00057 Residual = -2430 Percent = .00057 Residual = -2459 Percent = .00045 Residual = -2459 Percent = .00045 Residual = -2488 Percent = .00035 Residual = -2488 Percent = .00035 Residual = -2517 Percent = .00028 Residual = -2517 Percent = .00028 Residual = -2545 Percent = .00022 Residual = -2545 Percent = .00022 Residual = -2574 Percent = .00017 Residual = -2574 Percent = .00017 Residual = -2603 Percent = .00013 Residual = -2603 Percent = .00013 Residual = -2632 Percent = 0.0001 Residual = -2632 Percent = 0.0001 Residual = -2661 Percent = .00008 Residual = -2661 Percent = .00008 Residual = -2689 Percent = 6.2E-5 Residual = -2689 Percent = 6.2E-5 Residual = -2718 Percent = 4.8E-5 Residual = -2718 Percent = 4.8E-5 Residual = -2747 Percent = 3.7E-5 Residual = -2747 Percent = 3.7E-5 Residual = -2776 Percent = 2.8E-5 Residual = -2776 Percent = 2.8E-5 Residual = -2805 Percent = 2.2E-5 Residual = -2805 Percent = 2.2E-5 Residual = -2833 Percent = 1.6E-5 Residual = -2833 Percent = 1.6E-5 Residual = -2862 Percent = 1.3E-5 Residual = -2862 Percent = 1.3E-5 Residual = -2891 Percent = 9.5E-6 Residual = -2891 Percent = 9.5E-6 Residual = -2920 Percent = 7.2E-6 Residual = -2920 Percent = 7.2E-6 Residual = -2948 Percent = 5.4E-6 Residual = -2948 Percent = 5.4E-6 Residual = -2977 Percent = 4.1E-6 Residual = -2977 Percent = 4.1E-6 Residual = -3006 Percent = 3.1E-6 Residual = -3006 Percent = 3.1E-6 Residual = -3035 Percent = 2.3E-6 Residual = -3035 Percent = 2.3E-6 Residual = -3064 Percent = 1.7E-6 Residual = -3064 Percent = 1.7E-6 Residual = -3092 Percent = 1.3E-6 Residual = -3092 Percent = 1.3E-6 Residual = -3121 Percent = 9.4E-7 Residual = -3121 Percent = 9.4E-7 Residual = -3150 Percent = 6.9E-7 Residual = 2475 Percent = 0.008 Residual = 2475 Percent = 0.008 Residual = 2325 Percent = 0 Residual = 2325 Percent = 0 Residual = 2175 Percent = 0 Residual = 2175 Percent = 0 Residual = 2025 Percent = 0.008 Residual = 2025 Percent = 0.008 Residual = 1875 Percent = 0.008 Residual = 1875 Percent = 0.008 Residual = 1725 Percent = 0.112 Residual = 1725 Percent = 0.112 Residual = 1575 Percent = 0.104 Residual = 1575 Percent = 0.104 Residual = 1425 Percent = 0.216 Residual = 1425 Percent = 0.216 Residual = 1275 Percent = 0.496 Residual = 1275 Percent = 0.496 Residual = 1125 Percent = 1.08 Residual = 1125 Percent = 1.08 Residual = 975 Percent = 1.592 Residual = 975 Percent = 1.592 Residual = 825 Percent = 2.944 Residual = 825 Percent = 2.944 Residual = 675 Percent = 4.928 Residual = 675 Percent = 4.928 Residual = 525 Percent = 6.808 Residual = 525 Percent = 6.808 Residual = 375 Percent = 8.976 Residual = 375 Percent = 8.976 Residual = 225 Percent = 12.496 Residual = 225 Percent = 12.496 Residual = 75 Percent = 12.648 Residual = 75 Percent = 12.648 Residual = -75 Percent = 11.472 Residual = -75 Percent = 11.472 Residual = -225 Percent = 10.672 Residual = -225 Percent = 10.672 Residual = -375 Percent = 9.32 Residual = -375 Percent = 9.32 Residual = -525 Percent = 5.56 Residual = -525 Percent = 5.56 Residual = -675 Percent = 3.528 Residual = -675 Percent = 3.528 Residual = -825 Percent = 2.568 Residual = -825 Percent = 2.568 Residual = -975 Percent = 1.304 Residual = -975 Percent = 1.304 Residual = -1125 Percent = 0.744 Residual = -1125 Percent = 0.744 Residual = -1275 Percent = 0.552 Residual = -1275 Percent = 0.552 Residual = -1425 Percent = 0.408 Residual = -1425 Percent = 0.408 Residual = -1575 Percent = 0.232 Residual = -1575 Percent = 0.232 Residual = -1725 Percent = 0.232 Residual = -1725 Percent = 0.232 Residual = -1875 Percent = 0.232 Residual = -1875 Percent = 0.232 Residual = -2025 Percent = 0.176 Residual = -2025 Percent = 0.176 Residual = -2175 Percent = 0.128 Residual = -2175 Percent = 0.128 Residual = -2325 Percent = 0.104 Residual = -2325 Percent = 0.104 Residual = -2475 Percent = 0.088 Residual = -2475 Percent = 0.088 Residual = -2625 Percent = 0.128 Residual = -2625 Percent = 0.128 Residual = -2775 Percent = 0.064 Residual = -2775 Percent = 0.064 Residual = -2925 Percent = 0.04 Residual = -2925 Percent = 0.04 Residual = -3075 Percent = 0.024 Residual = -3075 Percent = 0.024
Histogram of Residuals for Weight with normal and kernel densities overlaid

RF Plot

Residual-Fit Spread Plot for Weight

Interaction Plot

Smoking Mother = 1 Predicted Value = 2950.1 Black Mother = 1 Smoking Mother = 1 Predicted Value = 3170.4 Black Mother = 0 Smoking Mother = 0 Predicted Value = 3198.2 Black Mother = 1 Smoking Mother = 0 Predicted Value = 3449.1 Black Mother = 0
Interaction Plot for Infant Birth Weight by Black Mother

N-Way ANOVA: Birth Weight where Interaction Term is not Significant

Least Squares Means

Adjustment for Multiple Comparisons: Tukey-Kramer

Least Squares Means

Black

Weight

LSMeans

Black Weight LSMEAN H0:LSMean1=LSMean2
Pr > |t|
0 3309.77078 <.0001
1 3074.16668  

Confidence Intervals

Black Weight LSMEAN 95% Confidence Limits
0 3309.770783 3294.603120 3324.938446
1 3074.166679 3034.072463 3114.260895

Pairwise Differences

Least Squares Means for Effect Black
i j Difference Between Means Simultaneous 95% Confidence Limits for LSMean(i)-LSMean(j)
1 2 235.604104 192.736813 278.471395

N-Way ANOVA: Birth Weight where Interaction Term is not Significant

Least Squares Means

Adjustment for Multiple Comparisons: Tukey-Kramer

MomSmoke

Weight

LSMeans

MomSmoke Weight LSMEAN H0:LSMean1=LSMean2
Pr > |t|
0 3323.68972 <.0001
1 3060.24774  

Confidence Intervals

MomSmoke Weight LSMEAN 95% Confidence Limits
0 3323.689724 3309.767505 3337.611942
1 3060.247739 3019.704231 3100.791246

Pairwise Differences

Least Squares Means for Effect MomSmoke
i j Difference Between Means Simultaneous 95% Confidence Limits for LSMean(i)-LSMean(j)
1 2 263.441985 220.574694 306.309276
  • The ANOVA table shows the F and p-values for the model as a whole, then the sum of squares, mean squares, F and p-values for each of the two factors and the interaction term. Both of the main factors are highly significant (Black and MomSmoke) while the interaction term (Black*MomSmoke where p = 0.4842) is not significant at the .05 level.
  • Checking the diagnostic plots to verify ANOVA assumptions, we see that the first plot (Residuals by Predicted for Weight) shows few outliers on the low side and similar variance in each of the four categories. The 7th plot/histogram of residuals (Distribution of Residuals for Weight) looks symmetric and close enough to a normal distribution.
  • Babies born from black mothers are lighter than babies born from non-black mothers (difference of about 235.6 grams or about half a pound). (Note that the 95% confidence limits do not include 0 because the difference is significant at the .05 level.) Babies born to mothers who smoke are approximately 263.4 grams or about half a pound lighter than babies born to mothers who do not smoke.

SAS Output

Results: biostats_by_ex_SAScode.sas

Results: biostats_by_ex_SAScode.sas

N-Way ANOVA: Birth Weight where Interaction Term is Significant

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
MomSmoke 2 0 1
Married 2 0 1

Number of Observations

Number of Observations Read 12500
Number of Observations Used 12500

N-Way ANOVA: Birth Weight where Interaction Term is Significant

Dependent Variable: Weight Infant Birth Weight

Analysis of Variance

Weight

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 3 167654386 55884795 184.93 <.0001
Error 12496 3776172306 302190    
Corrected Total 12499 3943826691      

Fit Statistics

R-Square Coeff Var Root MSE Weight Mean
0.042511 16.29639 549.7186 3373.254

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
MomSmoke 1 67738620.58 67738620.58 224.16 <.0001
Married 1 20004153.29 20004153.29 66.20 <.0001
MomSmoke*Married 1 4535264.42 4535264.42 15.01 0.0001

Diagnostic Plots

Residual by Predicted

Y = 0
Plot of Residual by Predicted for Weight

RStudent by Predicted

Y = 2 Y = -2
Plot of RStudent by Predicted for Weight

RStudent by Leverage

X = .00064 Y = -2 Y = 2
Plot of RStudent by Leverage for Weight

Q-Q Plot

Slope = 549.65 Y = -6E-13
Q-Q Plot of Residuals for Weight

Weight by Predicted

Slope = 1 Y = 0
Plot of Weight by Predicted

Cook's D Plot

Y = .00032
Needleplot of Cook's D statistic by Observation for Weight

Residual Histogram

Residual = 2736 Percent = 0.0001 Residual = 2692 Percent = .00046 Residual = 2692 Percent = .00046 Residual = 2647.9 Percent = 0.0014 Residual = 2647.9 Percent = 0.0014 Residual = 2603.8 Percent = 0.0032 Residual = 2603.8 Percent = 0.0032 Residual = 2559.8 Percent = 0.0053 Residual = 2559.8 Percent = 0.0053 Residual = 2515.7 Percent = 0.0062 Residual = 2515.7 Percent = 0.0062 Residual = 2471.7 Percent = 0.0053 Residual = 2471.7 Percent = 0.0053 Residual = 2427.6 Percent = 0.0032 Residual = 2427.6 Percent = 0.0032 Residual = 2383.5 Percent = 0.0014 Residual = 2383.5 Percent = 0.0014 Residual = 2339.5 Percent = .00046 Residual = 2339.5 Percent = .00046 Residual = 2295.4 Percent = 0.0001 Residual = 2295.4 Percent = 0.0001 Residual = 2251.3 Percent = 1.7E-5 Residual = 2251.3 Percent = 1.7E-5 Residual = 2207.3 Percent = 2.1E-6 Residual = 2207.3 Percent = 2.1E-6 Residual = 2163.2 Percent = 9E-7 Residual = 2163.2 Percent = 9E-7 Residual = 2119.2 Percent = 7.2E-6 Residual = 2119.2 Percent = 7.2E-6 Residual = 2075.1 Percent = 5.4E-5 Residual = 2075.1 Percent = 5.4E-5 Residual = 2031 Percent = 0.0003 Residual = 2031 Percent = 0.0003 Residual = 1987 Percent = 0.0013 Residual = 1987 Percent = 0.0013 Residual = 1942.9 Percent = 0.0042 Residual = 1942.9 Percent = 0.0042 Residual = 1898.8 Percent = 0.0105 Residual = 1898.8 Percent = 0.0105 Residual = 1854.8 Percent = 0.0212 Residual = 1854.8 Percent = 0.0212 Residual = 1810.7 Percent = 0.0357 Residual = 1810.7 Percent = 0.0357 Residual = 1678.5 Percent = 0.0848 Residual = 1678.5 Percent = 0.0848 Residual = 1634.5 Percent = 0.1053 Residual = 1634.5 Percent = 0.1053 Residual = 1590.4 Percent = 0.137 Residual = 1590.4 Percent = 0.137 Residual = 1546.3 Percent = 0.1815 Residual = 1546.3 Percent = 0.1815 Residual = 1502.3 Percent = 0.2277 Residual = 1502.3 Percent = 0.2277 Residual = 1458.2 Percent = 0.2618 Residual = 1458.2 Percent = 0.2618 Residual = 1414.2 Percent = 0.2871 Residual = 1414.2 Percent = 0.2871 Residual = 1370.1 Percent = 0.326 Residual = 1370.1 Percent = 0.326 Residual = 1326 Percent = 0.3976 Residual = 1326 Percent = 0.3976 Residual = 1282 Percent = 0.5037 Residual = 1282 Percent = 0.5037 Residual = 1237.9 Percent = 0.6348 Residual = 1237.9 Percent = 0.6348 Residual = 1193.8 Percent = 0.7812 Residual = 1193.8 Percent = 0.7812 Residual = 1149.8 Percent = 0.9372 Residual = 1149.8 Percent = 0.9372 Residual = 1105.7 Percent = 1.1027 Residual = 1105.7 Percent = 1.1027 Residual = 1061.7 Percent = 1.2858 Residual = 1061.7 Percent = 1.2858 Residual = 1017.6 Percent = 1.501 Residual = 1017.6 Percent = 1.501 Residual = 973.53 Percent = 1.7661 Residual = 973.53 Percent = 1.7661 Residual = 929.47 Percent = 2.096 Residual = 929.47 Percent = 2.096 Residual = 885.4 Percent = 2.4868 Residual = 885.4 Percent = 2.4868 Residual = 797.28 Percent = 3.3363 Residual = 797.28 Percent = 3.3363 Residual = 753.22 Percent = 3.7773 Residual = 753.22 Percent = 3.7773 Residual = 709.15 Percent = 4.2713 Residual = 709.15 Percent = 4.2713 Residual = 665.09 Percent = 4.8426 Residual = 665.09 Percent = 4.8426 Residual = 621.03 Percent = 5.481 Residual = 621.03 Percent = 5.481 Residual = 576.97 Percent = 6.167 Residual = 576.97 Percent = 6.167 Residual = 488.84 Percent = 7.6212 Residual = 488.84 Percent = 7.6212 Residual = 444.78 Percent = 8.3308 Residual = 444.78 Percent = 8.3308 Residual = 400.72 Percent = 9.0042 Residual = 400.72 Percent = 9.0042 Residual = 312.59 Percent = 10.298 Residual = 312.59 Percent = 10.298 Residual = 268.53 Percent = 10.903 Residual = 268.53 Percent = 10.903 Residual = 224.47 Percent = 11.455 Residual = 224.47 Percent = 11.455 Residual = 180.4 Percent = 11.938 Residual = 180.4 Percent = 11.938 Residual = 136.34 Percent = 12.325 Residual = 136.34 Percent = 12.325 Residual = 92.278 Percent = 12.574 Residual = 92.278 Percent = 12.574 Residual = 48.215 Percent = 12.653 Residual = 48.215 Percent = 12.653 Residual = 4.1529 Percent = 12.556 Residual = 4.1529 Percent = 12.556 Residual = -39.91 Percent = 12.328 Residual = -39.91 Percent = 12.328 Residual = -83.97 Percent = 12.043 Residual = -83.97 Percent = 12.043 Residual = -128 Percent = 11.731 Residual = -128 Percent = 11.731 Residual = -172.1 Percent = 11.341 Residual = -172.1 Percent = 11.341 Residual = -216.2 Percent = 10.828 Residual = -216.2 Percent = 10.828 Residual = -260.2 Percent = 10.215 Residual = -260.2 Percent = 10.215 Residual = -304.3 Percent = 9.5423 Residual = -304.3 Percent = 9.5423 Residual = -348.3 Percent = 8.8168 Residual = -348.3 Percent = 8.8168 Residual = -436.5 Percent = 7.2552 Residual = -436.5 Percent = 7.2552 Residual = -480.5 Percent = 6.4955 Residual = -480.5 Percent = 6.4955 Residual = -524.6 Percent = 5.8059 Residual = -524.6 Percent = 5.8059 Residual = -568.7 Percent = 5.1996 Residual = -568.7 Percent = 5.1996 Residual = -700.8 Percent = 3.572 Residual = -700.8 Percent = 3.572 Residual = -744.9 Percent = 3.0524 Residual = -744.9 Percent = 3.0524 Residual = -789 Percent = 2.5845 Residual = -789 Percent = 2.5845 Residual = -833 Percent = 2.1929 Residual = -833 Percent = 2.1929 Residual = -877.1 Percent = 1.8819 Residual = -877.1 Percent = 1.8819 Residual = -921.2 Percent = 1.6411 Residual = -921.2 Percent = 1.6411 Residual = -965.2 Percent = 1.4513 Residual = -965.2 Percent = 1.4513 Residual = -1009 Percent = 1.2885 Residual = -1009 Percent = 1.2885 Residual = -1097 Percent = 0.983 Residual = -1097 Percent = 0.983 Residual = -1141 Percent = 0.8438 Residual = -1141 Percent = 0.8438 Residual = -1186 Percent = 0.7326 Residual = -1186 Percent = 0.7326 Residual = -1230 Percent = 0.6546 Residual = -1230 Percent = 0.6546 Residual = -1274 Percent = 0.5945 Residual = -1274 Percent = 0.5945 Residual = -1318 Percent = 0.5305 Residual = -1318 Percent = 0.5305 Residual = -1362 Percent = 0.4595 Residual = -1362 Percent = 0.4595 Residual = -1406 Percent = 0.3956 Residual = -1406 Percent = 0.3956 Residual = -1450 Percent = 0.3508 Residual = -1450 Percent = 0.3508 Residual = -1494 Percent = 0.3247 Residual = -1494 Percent = 0.3247 Residual = -1538 Percent = 0.3109 Residual = -1538 Percent = 0.3109 Residual = -1582 Percent = 0.3009 Residual = -1582 Percent = 0.3009 Residual = -1626 Percent = 0.2848 Residual = -1626 Percent = 0.2848 Residual = -1670 Percent = 0.2581 Residual = -1670 Percent = 0.2581 Residual = -1714 Percent = 0.2277 Residual = -1714 Percent = 0.2277 Residual = -1758 Percent = 0.2053 Residual = -1758 Percent = 0.2053 Residual = -1802 Percent = 0.1967 Residual = -1802 Percent = 0.1967 Residual = -1846 Percent = 0.1999 Residual = -1846 Percent = 0.1999 Residual = -1891 Percent = 0.2076 Residual = -1891 Percent = 0.2076 Residual = -1935 Percent = 0.2108 Residual = -1935 Percent = 0.2108 Residual = -1979 Percent = 0.2028 Residual = -1979 Percent = 0.2028 Residual = -2023 Percent = 0.1834 Residual = -2023 Percent = 0.1834 Residual = -2067 Percent = 0.1589 Residual = -2067 Percent = 0.1589 Residual = -2111 Percent = 0.1358 Residual = -2111 Percent = 0.1358 Residual = -2155 Percent = 0.1175 Residual = -2155 Percent = 0.1175 Residual = -2199 Percent = 0.1053 Residual = -2199 Percent = 0.1053 Residual = -2243 Percent = 0.1019 Residual = -2243 Percent = 0.1019 Residual = -2287 Percent = 0.1082 Residual = -2287 Percent = 0.1082 Residual = -2331 Percent = 0.1195 Residual = -2331 Percent = 0.1195 Residual = -2375 Percent = 0.1277 Residual = -2375 Percent = 0.1277 Residual = -2419 Percent = 0.1283 Residual = -2419 Percent = 0.1283 Residual = -2463 Percent = 0.1231 Residual = -2463 Percent = 0.1231 Residual = -2507 Percent = 0.1149 Residual = -2507 Percent = 0.1149 Residual = -2596 Percent = 0.0951 Residual = -2596 Percent = 0.0951 Residual = -2640 Percent = 0.0879 Residual = -2640 Percent = 0.0879 Residual = -2684 Percent = 0.0858 Residual = -2684 Percent = 0.0858 Residual = -2728 Percent = 0.0875 Residual = -2728 Percent = 0.0875 Residual = -2772 Percent = 0.0877 Residual = -2772 Percent = 0.0877 Residual = -2816 Percent = 0.0816 Residual = -2816 Percent = 0.0816 Residual = -2860 Percent = 0.0692 Residual = -2860 Percent = 0.0692 Residual = -2904 Percent = 0.0539 Residual = -2904 Percent = 0.0539 Residual = -2948 Percent = 0.0405 Residual = -2948 Percent = 0.0405 Residual = -2992 Percent = 0.0315 Residual = -2992 Percent = 0.0315 Residual = -3036 Percent = 0.0264 Residual = -3036 Percent = 0.0264 Residual = -3080 Percent = 0.0222 Residual = -3080 Percent = 0.0222 Residual = -3124 Percent = 0.0168 Residual = -3124 Percent = 0.0168 Residual = -3168 Percent = 0.0105 Residual = -3168 Percent = 0.0105 Residual = -3212 Percent = 0.0052 Residual = -3212 Percent = 0.0052 Residual = -3256 Percent = 0.002 Residual = -3256 Percent = 0.002 Residual = -3301 Percent = .00058 Residual = -3301 Percent = .00058 Residual = -3345 Percent = .00012 Residual = 2550 Percent = .00023 Residual = 2521.2 Percent = .00029 Residual = 2521.2 Percent = .00029 Residual = 2492.4 Percent = .00037 Residual = 2492.4 Percent = .00037 Residual = 2463.6 Percent = .00047 Residual = 2463.6 Percent = .00047 Residual = 2434.8 Percent = 0.0006 Residual = 2434.8 Percent = 0.0006 Residual = 2406.1 Percent = .00075 Residual = 2406.1 Percent = .00075 Residual = 2377.3 Percent = .00094 Residual = 2377.3 Percent = .00094 Residual = 2348.5 Percent = 0.0012 Residual = 2348.5 Percent = 0.0012 Residual = 2319.7 Percent = 0.0015 Residual = 2319.7 Percent = 0.0015 Residual = 2290.9 Percent = 0.0018 Residual = 2290.9 Percent = 0.0018 Residual = 2262.1 Percent = 0.0023 Residual = 2262.1 Percent = 0.0023 Residual = 2233.3 Percent = 0.0028 Residual = 2233.3 Percent = 0.0028 Residual = 2204.5 Percent = 0.0035 Residual = 2204.5 Percent = 0.0035 Residual = 2175.8 Percent = 0.0043 Residual = 2175.8 Percent = 0.0043 Residual = 2147 Percent = 0.0053 Residual = 2147 Percent = 0.0053 Residual = 2118.2 Percent = 0.0065 Residual = 2118.2 Percent = 0.0065 Residual = 2089.4 Percent = 0.0079 Residual = 2089.4 Percent = 0.0079 Residual = 2060.6 Percent = 0.0097 Residual = 2060.6 Percent = 0.0097 Residual = 2031.8 Percent = 0.0117 Residual = 2031.8 Percent = 0.0117 Residual = 2003 Percent = 0.0142 Residual = 2003 Percent = 0.0142 Residual = 1974.2 Percent = 0.0172 Residual = 1974.2 Percent = 0.0172 Residual = 1945.5 Percent = 0.0207 Residual = 1945.5 Percent = 0.0207 Residual = 1916.7 Percent = 0.0249 Residual = 1916.7 Percent = 0.0249 Residual = 1887.9 Percent = 0.0299 Residual = 1887.9 Percent = 0.0299 Residual = 1859.1 Percent = 0.0357 Residual = 1859.1 Percent = 0.0357 Residual = 1830.3 Percent = 0.0426 Residual = 1830.3 Percent = 0.0426 Residual = 1801.5 Percent = 0.0506 Residual = 1801.5 Percent = 0.0506 Residual = 1772.7 Percent = 0.06 Residual = 1772.7 Percent = 0.06 Residual = 1743.9 Percent = 0.071 Residual = 1743.9 Percent = 0.071 Residual = 1715.2 Percent = 0.0837 Residual = 1715.2 Percent = 0.0837 Residual = 1686.4 Percent = 0.0984 Residual = 1686.4 Percent = 0.0984 Residual = 1657.6 Percent = 0.1154 Residual = 1657.6 Percent = 0.1154 Residual = 1628.8 Percent = 0.1349 Residual = 1628.8 Percent = 0.1349 Residual = 1600 Percent = 0.1574 Residual = 1600 Percent = 0.1574 Residual = 1571.2 Percent = 0.183 Residual = 1571.2 Percent = 0.183 Residual = 1542.4 Percent = 0.2123 Residual = 1542.4 Percent = 0.2123 Residual = 1513.6 Percent = 0.2456 Residual = 1513.6 Percent = 0.2456 Residual = 1484.8 Percent = 0.2833 Residual = 1484.8 Percent = 0.2833 Residual = 1456.1 Percent = 0.3259 Residual = 1456.1 Percent = 0.3259 Residual = 1427.3 Percent = 0.3739 Residual = 1427.3 Percent = 0.3739 Residual = 1398.5 Percent = 0.4278 Residual = 1398.5 Percent = 0.4278 Residual = 1369.7 Percent = 0.4881 Residual = 1369.7 Percent = 0.4881 Residual = 1340.9 Percent = 0.5554 Residual = 1340.9 Percent = 0.5554 Residual = 1312.1 Percent = 0.6302 Residual = 1312.1 Percent = 0.6302 Residual = 1283.3 Percent = 0.7131 Residual = 1283.3 Percent = 0.7131 Residual = 1254.5 Percent = 0.8048 Residual = 1254.5 Percent = 0.8048 Residual = 1225.8 Percent = 0.9057 Residual = 1225.8 Percent = 0.9057 Residual = 1197 Percent = 1.0166 Residual = 1197 Percent = 1.0166 Residual = 1168.2 Percent = 1.1378 Residual = 1168.2 Percent = 1.1378 Residual = 1139.4 Percent = 1.27 Residual = 1139.4 Percent = 1.27 Residual = 1110.6 Percent = 1.4138 Residual = 1110.6 Percent = 1.4138 Residual = 1081.8 Percent = 1.5694 Residual = 1081.8 Percent = 1.5694 Residual = 1053 Percent = 1.7374 Residual = 1053 Percent = 1.7374 Residual = 1024.2 Percent = 1.9182 Residual = 1024.2 Percent = 1.9182 Residual = 995.45 Percent = 2.1119 Residual = 995.45 Percent = 2.1119 Residual = 966.67 Percent = 2.3189 Residual = 966.67 Percent = 2.3189 Residual = 937.88 Percent = 2.5392 Residual = 937.88 Percent = 2.5392 Residual = 909.09 Percent = 2.7727 Residual = 909.09 Percent = 2.7727 Residual = 880.3 Percent = 3.0195 Residual = 880.3 Percent = 3.0195 Residual = 851.52 Percent = 3.2792 Residual = 851.52 Percent = 3.2792 Residual = 822.73 Percent = 3.5514 Residual = 822.73 Percent = 3.5514 Residual = 793.94 Percent = 3.8358 Residual = 793.94 Percent = 3.8358 Residual = 765.15 Percent = 4.1316 Residual = 765.15 Percent = 4.1316 Residual = 736.36 Percent = 4.438 Residual = 736.36 Percent = 4.438 Residual = 707.58 Percent = 4.754 Residual = 707.58 Percent = 4.754 Residual = 650 Percent = 5.4105 Residual = 650 Percent = 5.4105 Residual = 534.85 Percent = 6.7812 Residual = 534.85 Percent = 6.7812 Residual = 448.48 Percent = 7.8045 Residual = 448.48 Percent = 7.8045 Residual = 390.91 Percent = 8.4544 Residual = 390.91 Percent = 8.4544 Residual = 362.12 Percent = 8.7632 Residual = 362.12 Percent = 8.7632 Residual = 333.33 Percent = 9.0584 Residual = 333.33 Percent = 9.0584 Residual = 304.55 Percent = 9.3379 Residual = 304.55 Percent = 9.3379 Residual = 275.76 Percent = 9.5997 Residual = 275.76 Percent = 9.5997 Residual = 246.97 Percent = 9.8418 Residual = 246.97 Percent = 9.8418 Residual = 218.18 Percent = 10.062 Residual = 218.18 Percent = 10.062 Residual = 189.39 Percent = 10.26 Residual = 189.39 Percent = 10.26 Residual = 160.61 Percent = 10.432 Residual = 160.61 Percent = 10.432 Residual = 131.82 Percent = 10.578 Residual = 131.82 Percent = 10.578 Residual = 103.03 Percent = 10.698 Residual = 103.03 Percent = 10.698 Residual = 74.242 Percent = 10.788 Residual = 74.242 Percent = 10.788 Residual = 45.455 Percent = 10.85 Residual = 45.455 Percent = 10.85 Residual = 16.667 Percent = 10.882 Residual = 16.667 Percent = 10.882 Residual = -6E-13 Percent = 10.887 Residual = -6E-13 Percent = 10.887 Residual = -12.12 Percent = 10.884 Residual = -12.12 Percent = 10.884 Residual = -40.91 Percent = 10.857 Residual = -40.91 Percent = 10.857 Residual = -69.7 Percent = 10.8 Residual = -69.7 Percent = 10.8 Residual = -98.48 Percent = 10.714 Residual = -98.48 Percent = 10.714 Residual = -127.3 Percent = 10.599 Residual = -127.3 Percent = 10.599 Residual = -156.1 Percent = 10.457 Residual = -156.1 Percent = 10.457 Residual = -184.8 Percent = 10.289 Residual = -184.8 Percent = 10.289 Residual = -213.6 Percent = 10.095 Residual = -213.6 Percent = 10.095 Residual = -242.4 Percent = 9.8781 Residual = -242.4 Percent = 9.8781 Residual = -271.2 Percent = 9.6393 Residual = -271.2 Percent = 9.6393 Residual = -300 Percent = 9.3805 Residual = -300 Percent = 9.3805 Residual = -328.8 Percent = 9.1036 Residual = -328.8 Percent = 9.1036 Residual = -357.6 Percent = 8.8108 Residual = -357.6 Percent = 8.8108 Residual = -386.4 Percent = 8.5039 Residual = -386.4 Percent = 8.5039 Residual = -616.7 Percent = 5.8021 Residual = -616.7 Percent = 5.8021 Residual = -674.2 Percent = 5.1306 Residual = -674.2 Percent = 5.1306 Residual = -731.8 Percent = 4.4873 Residual = -731.8 Percent = 4.4873 Residual = -760.6 Percent = 4.1793 Residual = -760.6 Percent = 4.1793 Residual = -789.4 Percent = 3.8818 Residual = -789.4 Percent = 3.8818 Residual = -818.2 Percent = 3.5956 Residual = -818.2 Percent = 3.5956 Residual = -847 Percent = 3.3213 Residual = -847 Percent = 3.3213 Residual = -875.8 Percent = 3.0596 Residual = -875.8 Percent = 3.0596 Residual = -904.5 Percent = 2.8108 Residual = -904.5 Percent = 2.8108 Residual = -933.3 Percent = 2.5751 Residual = -933.3 Percent = 2.5751 Residual = -962.1 Percent = 2.3528 Residual = -962.1 Percent = 2.3528 Residual = -990.9 Percent = 2.1437 Residual = -990.9 Percent = 2.1437 Residual = -1020 Percent = 1.9479 Residual = -1020 Percent = 1.9479 Residual = -1048 Percent = 1.7651 Residual = -1048 Percent = 1.7651 Residual = -1077 Percent = 1.5951 Residual = -1077 Percent = 1.5951 Residual = -1106 Percent = 1.4375 Residual = -1106 Percent = 1.4375 Residual = -1135 Percent = 1.292 Residual = -1135 Percent = 1.292 Residual = -1164 Percent = 1.158 Residual = -1164 Percent = 1.158 Residual = -1192 Percent = 1.035 Residual = -1192 Percent = 1.035 Residual = -1221 Percent = 0.9226 Residual = -1221 Percent = 0.9226 Residual = -1250 Percent = 0.8201 Residual = -1250 Percent = 0.8201 Residual = -1279 Percent = 0.727 Residual = -1279 Percent = 0.727 Residual = -1308 Percent = 0.6427 Residual = -1308 Percent = 0.6427 Residual = -1336 Percent = 0.5667 Residual = -1336 Percent = 0.5667 Residual = -1365 Percent = 0.4982 Residual = -1365 Percent = 0.4982 Residual = -1394 Percent = 0.4369 Residual = -1394 Percent = 0.4369 Residual = -1423 Percent = 0.382 Residual = -1423 Percent = 0.382 Residual = -1452 Percent = 0.3331 Residual = -1452 Percent = 0.3331 Residual = -1480 Percent = 0.2897 Residual = -1480 Percent = 0.2897 Residual = -1509 Percent = 0.2512 Residual = -1509 Percent = 0.2512 Residual = -1538 Percent = 0.2173 Residual = -1538 Percent = 0.2173 Residual = -1567 Percent = 0.1874 Residual = -1567 Percent = 0.1874 Residual = -1595 Percent = 0.1612 Residual = -1595 Percent = 0.1612 Residual = -1624 Percent = 0.1383 Residual = -1624 Percent = 0.1383 Residual = -1653 Percent = 0.1183 Residual = -1653 Percent = 0.1183 Residual = -1682 Percent = 0.1009 Residual = -1682 Percent = 0.1009 Residual = -1711 Percent = 0.0858 Residual = -1711 Percent = 0.0858 Residual = -1739 Percent = 0.0728 Residual = -1739 Percent = 0.0728 Residual = -1768 Percent = 0.0616 Residual = -1768 Percent = 0.0616 Residual = -1797 Percent = 0.052 Residual = -1797 Percent = 0.052 Residual = -1826 Percent = 0.0438 Residual = -1826 Percent = 0.0438 Residual = -1855 Percent = 0.0367 Residual = -1855 Percent = 0.0367 Residual = -1883 Percent = 0.0307 Residual = -1883 Percent = 0.0307 Residual = -1912 Percent = 0.0256 Residual = -1912 Percent = 0.0256 Residual = -1941 Percent = 0.0213 Residual = -1941 Percent = 0.0213 Residual = -1970 Percent = 0.0177 Residual = -1970 Percent = 0.0177 Residual = -1998 Percent = 0.0147 Residual = -1998 Percent = 0.0147 Residual = -2027 Percent = 0.0121 Residual = -2027 Percent = 0.0121 Residual = -2056 Percent = 0.01 Residual = -2056 Percent = 0.01 Residual = -2085 Percent = 0.0082 Residual = -2085 Percent = 0.0082 Residual = -2114 Percent = 0.0067 Residual = -2114 Percent = 0.0067 Residual = -2142 Percent = 0.0055 Residual = -2142 Percent = 0.0055 Residual = -2171 Percent = 0.0045 Residual = -2171 Percent = 0.0045 Residual = -2200 Percent = 0.0036 Residual = -2200 Percent = 0.0036 Residual = -2229 Percent = 0.0029 Residual = -2229 Percent = 0.0029 Residual = -2258 Percent = 0.0024 Residual = -2258 Percent = 0.0024 Residual = -2286 Percent = 0.0019 Residual = -2286 Percent = 0.0019 Residual = -2315 Percent = 0.0015 Residual = -2315 Percent = 0.0015 Residual = -2344 Percent = 0.0012 Residual = -2344 Percent = 0.0012 Residual = -2373 Percent = .00098 Residual = -2373 Percent = .00098 Residual = -2402 Percent = .00078 Residual = -2402 Percent = .00078 Residual = -2430 Percent = .00062 Residual = -2430 Percent = .00062 Residual = -2459 Percent = .00049 Residual = -2459 Percent = .00049 Residual = -2488 Percent = .00039 Residual = -2488 Percent = .00039 Residual = -2517 Percent = .00031 Residual = -2517 Percent = .00031 Residual = -2545 Percent = .00024 Residual = -2545 Percent = .00024 Residual = -2574 Percent = .00019 Residual = -2574 Percent = .00019 Residual = -2603 Percent = .00015 Residual = -2603 Percent = .00015 Residual = -2632 Percent = .00011 Residual = -2632 Percent = .00011 Residual = -2661 Percent = 8.9E-5 Residual = -2661 Percent = 8.9E-5 Residual = -2689 Percent = 6.9E-5 Residual = -2689 Percent = 6.9E-5 Residual = -2718 Percent = 5.3E-5 Residual = -2718 Percent = 5.3E-5 Residual = -2747 Percent = 4.1E-5 Residual = -2747 Percent = 4.1E-5 Residual = -2776 Percent = 3.2E-5 Residual = -2776 Percent = 3.2E-5 Residual = -2805 Percent = 2.4E-5 Residual = -2805 Percent = 2.4E-5 Residual = -2833 Percent = 1.8E-5 Residual = -2833 Percent = 1.8E-5 Residual = -2862 Percent = 1.4E-5 Residual = -2862 Percent = 1.4E-5 Residual = -2891 Percent = 1.1E-5 Residual = -2891 Percent = 1.1E-5 Residual = -2920 Percent = 8.1E-6 Residual = -2920 Percent = 8.1E-6 Residual = -2948 Percent = 6.1E-6 Residual = -2948 Percent = 6.1E-6 Residual = -2977 Percent = 4.6E-6 Residual = -2977 Percent = 4.6E-6 Residual = -3006 Percent = 3.5E-6 Residual = -3006 Percent = 3.5E-6 Residual = -3035 Percent = 2.6E-6 Residual = -3035 Percent = 2.6E-6 Residual = -3064 Percent = 2E-6 Residual = -3064 Percent = 2E-6 Residual = -3092 Percent = 1.5E-6 Residual = -3092 Percent = 1.5E-6 Residual = -3121 Percent = 1.1E-6 Residual = -3121 Percent = 1.1E-6 Residual = -3150 Percent = 8E-7 Residual = 2475 Percent = 0.008 Residual = 2475 Percent = 0.008 Residual = 2325 Percent = 0 Residual = 2325 Percent = 0 Residual = 2175 Percent = 0 Residual = 2175 Percent = 0 Residual = 2025 Percent = 0 Residual = 2025 Percent = 0 Residual = 1875 Percent = 0.008 Residual = 1875 Percent = 0.008 Residual = 1725 Percent = 0.064 Residual = 1725 Percent = 0.064 Residual = 1575 Percent = 0.144 Residual = 1575 Percent = 0.144 Residual = 1425 Percent = 0.256 Residual = 1425 Percent = 0.256 Residual = 1275 Percent = 0.52 Residual = 1275 Percent = 0.52 Residual = 1125 Percent = 1.04 Residual = 1125 Percent = 1.04 Residual = 975 Percent = 1.632 Residual = 975 Percent = 1.632 Residual = 825 Percent = 2.944 Residual = 825 Percent = 2.944 Residual = 675 Percent = 4.624 Residual = 675 Percent = 4.624 Residual = 525 Percent = 7.384 Residual = 525 Percent = 7.384 Residual = 375 Percent = 8.96 Residual = 375 Percent = 8.96 Residual = 225 Percent = 11.536 Residual = 225 Percent = 11.536 Residual = 75 Percent = 13.512 Residual = 75 Percent = 13.512 Residual = -75 Percent = 11.448 Residual = -75 Percent = 11.448 Residual = -225 Percent = 10.872 Residual = -225 Percent = 10.872 Residual = -375 Percent = 9 Residual = -375 Percent = 9 Residual = -525 Percent = 5.368 Residual = -525 Percent = 5.368 Residual = -675 Percent = 3.824 Residual = -675 Percent = 3.824 Residual = -825 Percent = 2.096 Residual = -825 Percent = 2.096 Residual = -975 Percent = 1.464 Residual = -975 Percent = 1.464 Residual = -1125 Percent = 0.832 Residual = -1125 Percent = 0.832 Residual = -1275 Percent = 0.608 Residual = -1275 Percent = 0.608 Residual = -1425 Percent = 0.376 Residual = -1425 Percent = 0.376 Residual = -1575 Percent = 0.296 Residual = -1575 Percent = 0.296 Residual = -1725 Percent = 0.184 Residual = -1725 Percent = 0.184 Residual = -1875 Percent = 0.2 Residual = -1875 Percent = 0.2 Residual = -2025 Percent = 0.208 Residual = -2025 Percent = 0.208 Residual = -2175 Percent = 0.104 Residual = -2175 Percent = 0.104 Residual = -2325 Percent = 0.128 Residual = -2325 Percent = 0.128 Residual = -2475 Percent = 0.112 Residual = -2475 Percent = 0.112 Residual = -2625 Percent = 0.088 Residual = -2625 Percent = 0.088 Residual = -2775 Percent = 0.088 Residual = -2775 Percent = 0.088 Residual = -2925 Percent = 0.04 Residual = -2925 Percent = 0.04 Residual = -3075 Percent = 0.032 Residual = -3075 Percent = 0.032
Histogram of Residuals for Weight with normal and kernel densities overlaid

RF Plot

Residual-Fit Spread Plot for Weight

Interaction Plot

Married Mother = 1 Predicted Value = 3175.1 Smoking Mother = 1 Married Mother = 1 Predicted Value = 3454.3 Smoking Mother = 0 Married Mother = 0 Predicted Value = 3111.9 Smoking Mother = 1 Married Mother = 0 Predicted Value = 3276.3 Smoking Mother = 0
Interaction Plot for Infant Birth Weight by Smoking Mother

N-Way ANOVA: Birth Weight where Interaction Term is Significant

Least Squares Means

Adjustment for Multiple Comparisons: Tukey-Kramer

Least Squares Means

MomSmoke

Weight

LSMeans

MomSmoke Weight LSMEAN H0:LSMean1=LSMean2
Pr > |t|
0 3365.31299 <.0001
1 3143.48832  

Confidence Intervals

MomSmoke Weight LSMEAN 95% Confidence Limits
0 3365.312990 3353.513146 3377.112834
1 3143.488320 3116.951841 3170.024800

Pairwise Differences

Least Squares Means for Effect MomSmoke
i j Difference Between Means Simultaneous 95% Confidence Limits for LSMean(i)-LSMean(j)
1 2 221.824670 192.782953 250.866386

MomSmoke Mean Plot

MomSmoke = 1 LS-Mean = 3143.5 Group = 1 MomSmoke = 0 LS-Mean = 3365.3 Group = 1 MomSmoke = 1 LDL = 3117 MomSmoke = 0 LDL = 3353.5 MomSmoke = 1 LDL = 3117 MomSmoke = 0 LDL = 3353.5 MomSmoke = 1 UDL = 3170 MomSmoke = 0 UDL = 3377.1 MomSmoke = 1 UDL = 3170 MomSmoke = 0 UDL = 3377.1
Plot of Weight least-squares means for MomSmoke. With 95% confidence limits.

N-Way ANOVA: Birth Weight where Interaction Term is Significant

Least Squares Means

Adjustment for Multiple Comparisons: Tukey-Kramer

Married

Weight

LSMeans

Married Weight LSMEAN H0:LSMean1=LSMean2
Pr > |t|
0 3194.12780 <.0001
1 3314.67351  

Confidence Intervals

Married Weight LSMEAN 95% Confidence Limits
0 3194.127801 3172.707311 3215.548291
1 3314.673510 3295.062705 3334.284315

Pairwise Differences

Least Squares Means for Effect Married
i j Difference Between Means Simultaneous 95% Confidence Limits for LSMean(i)-LSMean(j)
1 2 -120.545709 -149.587425 -91.503993

Married Mean Plot

Married = 1 LS-Mean = 3314.7 Group = 1 Married = 0 LS-Mean = 3194.1 Group = 1 Married = 1 LDL = 3295.1 Married = 0 LDL = 3172.7 Married = 1 LDL = 3295.1 Married = 0 LDL = 3172.7 Married = 1 UDL = 3334.3 Married = 0 UDL = 3215.5 Married = 1 UDL = 3334.3 Married = 0 UDL = 3215.5
Plot of Weight least-squares means for Married. With 95% confidence limits.

N-Way ANOVA: Birth Weight where Interaction Term is Significant

Least Squares Means

Adjustment for Multiple Comparisons: Tukey-Kramer

MomSmoke*Married

Weight

LSMeans

MomSmoke Married Weight LSMEAN LSMEAN Number
0 0 3276.34139 1
0 1 3454.28459 2
1 0 3111.91422 3
1 1 3175.06242 4

Difference Matrix

Least Squares Means for effect MomSmoke*Married
Pr > |t| for H0: LSMean(i)=LSMean(j)

Dependent Variable: Weight
i/j 1 2 3 4
1   <.0001 <.0001 <.0001
2 <.0001   <.0001 <.0001
3 <.0001 <.0001   0.0908
4 <.0001 <.0001 0.0908  

Confidence Intervals

MomSmoke Married Weight LSMEAN 95% Confidence Limits
0 0 3276.341385 3256.032254 3296.650517
0 1 3454.284594 3442.264425 3466.304764
1 0 3111.914216 3074.193018 3149.635413
1 1 3175.062425 3137.728122 3212.396728

Pairwise Differences

Least Squares Means for Effect MomSmoke*Married
i j Difference Between Means Simultaneous 95% Confidence Limits for LSMean(i)-LSMean(j)
1 2 -177.943209 -208.877642 -147.008776
1 3 164.427170 108.271283 220.583057
1 4 101.278960 45.569089 156.988832
2 3 342.370379 290.475786 394.264971
2 4 279.222169 227.810547 330.633792
3 4 -63.148209 -132.716157 6.419739

MomSmoke*Married Mean Plot

MomSmoke*Married = 1 1 LS-Mean = 3175.1 Group = 1 MomSmoke*Married = 1 0 LS-Mean = 3111.9 Group = 1 MomSmoke*Married = 0 1 LS-Mean = 3454.3 Group = 1 MomSmoke*Married = 0 0 LS-Mean = 3276.3 Group = 1 MomSmoke*Married = 1 1 LDL = 3137.7 MomSmoke*Married = 1 0 LDL = 3074.2 MomSmoke*Married = 0 1 LDL = 3442.3 MomSmoke*Married = 0 0 LDL = 3256 MomSmoke*Married = 1 1 LDL = 3137.7 MomSmoke*Married = 1 0 LDL = 3074.2 MomSmoke*Married = 0 1 LDL = 3442.3 MomSmoke*Married = 0 0 LDL = 3256 MomSmoke*Married = 1 1 UDL = 3212.4 MomSmoke*Married = 1 0 UDL = 3149.6 MomSmoke*Married = 0 1 UDL = 3466.3 MomSmoke*Married = 0 0 UDL = 3296.7 MomSmoke*Married = 1 1 UDL = 3212.4 MomSmoke*Married = 1 0 UDL = 3149.6 MomSmoke*Married = 0 1 UDL = 3466.3 MomSmoke*Married = 0 0 UDL = 3296.7
Plot of Weight least-squares means for MomSmoke*Married. With 95% confidence limits.
  • The ANOVA table shows the F and p-values for the model as a whole, then the sum of squares, mean squares, F and p-values for each of the two factors and the interaction term. Both of the main factors are highly significant (MomSmoke and Married) and the interaction term (MomSmoke*Married where p = 0.0001) is also significant at the .05 level.
  • In this model, Babies born to mothers who smoke are approximately 221.8 grams lighter than babies born to mothers who do not smoke. Babies born from married mothers are heavier by about 120.5 grams than babies born from unmarried mothers. (Note that the 95% confidence limits [both of which are negative numbers since they are heavier] do not include 0 because the difference is significant at the .05 level.)
  • Scrolling down to the interaction tables (Least Squares Means - Adjustment for Multiple Comparisons: Tukey-Kramer), we see that nonsmoking married mothers (MomSmoke=0, Married=1, LSMEAN number identifier 2) show the heaviest birth weight, while smoking unmarried mothers (MomSmoke=1, Married=0, LSMEAN number identifier 3) show the lightest birth weight. “Looking at the last plot (LS-Means for MomSmoke * Married With 95% Confidence Limits), we see the means and confidence limits for all 4 combinations of the two factors; drawing straight lines between the means of (0 * 0) and (0 * 1), and (1 * 0) and (1 * 1) we see that there is some interaction between the two terms because there are different slopes (no interaction would show parallel lines drawn).”

Practice: Two-Way ANOVA: Weight by Gender or Cholesterol Status

SAS Code, click to expand

SAS Code:

#  (&path1 and biostats libname previously defined)
/* Practice: Two-Way Analysis of Variance - Heart / Weight - start 9.2 */
/* Model Effects Full Factorial, Type 3 Sum of Squares, Perform Multiple Comparisons default Main effects Tukey 0.05 level  Interaction plot Diagnostic plots*/
title1 "Practice: Two-Way ANOVA: Weight by Gender or Cholesterol Status Part 1";
ods noproctitle;
ods graphics / imagemap=on;
proc glm data=biostats.heart plots=none;
    class Sex Chol_Status;
    model Weight=Sex Chol_Status Sex*Chol_Status / ss3;
    lsmeans Sex Chol_Status / adjust=tukey pdiff=all alpha=0.05 cl;
quit;
title1 "Practice: Two-Way ANOVA: Weight by Gender or Cholesterol Status Part 2";
/* Collapse categories in Chol_Status and rerun */
data work.heart2;
  set biostats.heart;
  if Chol_Status EQ "Borderline" then Chol_Status2 = "Border-High"; else
  if Chol_Status EQ "High" then Chol_Status2 = "Border-High"; else
    Chol_Status2 = Chol_Status;
  run;
proc glm data=work.heart2 plots=none;
    class Sex Chol_Status2;
    model Weight=Sex Chol_Status2 Sex*Chol_Status2 / ss3;
    lsmeans Sex Chol_Status2 / adjust=tukey pdiff=all alpha=0.05 cl;
quit;

/* Running a two-way ANOVA using Weight as the dependent variable and Sex and Chol_Status (cholesterol status) as factors shows significant p-value for the model as a whole.  Both of the main factors are highly significant, but the interaction term (Sex*Chol_Status where p = 0.5409) is not significant at the .05 level.   
In this model, Females weigh about 26.2 pounds lighter.  Cholesterol Status is not as staightforward, as the Least Squares Means for effect Chol_Status table shows that differences between Borderline and Desirable, and High and Desirable are significant (p <.0001) but differences between Borderline and High are not significant (p = 0.0204) at the .05 level.
We revised the data by collapsing the Borderline and High categories of Chol_Status as Border-High, and rerun the ANOVA.  In this rerun with collapsed categories, both of the main factors remain highly significant with the interaction term (Sex*Chol_Status2 where p = 0.9869) not showing as significant at the .05 level.  Females weigh about 26.2 pounds lighter and those with Chol_Status of Border-High weigh about 5.5 pounds heavier.  */

title1;
/* Practice: Two-Way Analysis of Variance - Heart / Weight - end 9.2 */

SAS Output

Results: biostats_by_ex_SAScode.sas

Results: biostats_by_ex_SAScode.sas

Practice: Two-Way ANOVA: Weight by Gender or Cholesterol Status Part 1

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
Sex 2 Female Male
Chol_Status 3 Borderline Desirable High

Number of Observations

Number of Observations Read 5209
Number of Observations Used 5051

Practice: Two-Way ANOVA: Weight by Gender or Cholesterol Status Part 1

Dependent Variable: Weight

Analysis of Variance

Weight

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 5 905101.176 181020.235 275.54 <.0001
Error 5045 3314360.848 656.960    
Corrected Total 5050 4219462.024      

Fit Statistics

R-Square Coeff Var Root MSE Weight Mean
0.214506 16.74489 25.63122 153.0689

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
Sex 1 845072.8456 845072.8456 1286.34 <.0001
Chol_Status 2 35120.9760 17560.4880 26.73 <.0001
Sex*Chol_Status 2 807.6324 403.8162 0.61 0.5409

Practice: Two-Way ANOVA: Weight by Gender or Cholesterol Status Part 1

Least Squares Means

Adjustment for Multiple Comparisons: Tukey-Kramer

Least Squares Means

Sex

Weight

LSMeans

Sex Weight LSMEAN H0:LSMean1=LSMean2
Pr > |t|
Female 140.905421 <.0001
Male 167.155864  

Confidence Intervals

Sex Weight LSMEAN 95% Confidence Limits
Female 140.905421 139.946138 141.864705
Male 167.155864 166.088806 168.222923

Pairwise Differences

Least Squares Means for Effect Sex
i j Difference Between Means Simultaneous 95% Confidence Limits for LSMean(i)-LSMean(j)
1 2 -26.250443 -27.685309 -24.815577

Practice: Two-Way ANOVA: Weight by Gender or Cholesterol Status Part 1

Least Squares Means

Adjustment for Multiple Comparisons: Tukey-Kramer

Chol_Status

Weight

LSMeans

Chol_Status Weight LSMEAN LSMEAN Number
Borderline 154.742853 1
Desirable 150.324762 2
High 157.024313 3

Difference Matrix

Least Squares Means for effect Chol_Status
Pr > |t| for H0: LSMean(i)=LSMean(j)

Dependent Variable: Weight
i/j 1 2 3
1   <.0001 0.0204
2 <.0001   <.0001
3 0.0204 <.0001  

Confidence Intervals

Chol_Status Weight LSMEAN 95% Confidence Limits
Borderline 154.742853 153.577181 155.908525
Desirable 150.324762 148.968989 151.680536
High 157.024313 155.826200 158.222426

Pairwise Differences

Least Squares Means for Effect Chol_Status
i j Difference Between Means Simultaneous 95% Confidence Limits for LSMean(i)-LSMean(j)
1 2 4.418091 2.279913 6.556268
1 3 -2.281460 -4.280458 -0.282462
2 3 -6.699551 -8.863220 -4.535881

Practice: Two-Way ANOVA: Weight by Gender or Cholesterol Status Part 2

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
Sex 2 Female Male
Chol_Status2 2 Border-High Desirable

Number of Observations

Number of Observations Read 5209
Number of Observations Used 5051

Practice: Two-Way ANOVA: Weight by Gender or Cholesterol Status Part 2

Dependent Variable: Weight

Analysis of Variance

Weight

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 3 899243.582 299747.861 455.64 <.0001
Error 5047 3320218.442 657.860    
Corrected Total 5050 4219462.024      

Fit Statistics

R-Square Coeff Var Root MSE Weight Mean
0.213118 16.75636 25.64878 153.0689

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
Sex 1 683157.0169 683157.0169 1038.45 <.0001
Chol_Status2 1 30738.5140 30738.5140 46.73 <.0001
Sex*Chol_Status2 1 0.1763 0.1763 0.00 0.9869

Practice: Two-Way ANOVA: Weight by Gender or Cholesterol Status Part 2

Least Squares Means

Adjustment for Multiple Comparisons: Tukey-Kramer

Least Squares Means

Sex

Weight

LSMeans

Sex Weight LSMEAN H0:LSMean1=LSMean2
Pr > |t|
Female 140.008609 <.0001
Male 166.195720  

Confidence Intervals

Sex Weight LSMEAN 95% Confidence Limits
Female 140.008609 138.955753 141.061464
Male 166.195720 165.000103 167.391337

Pairwise Differences

Least Squares Means for Effect Sex
i j Difference Between Means Simultaneous 95% Confidence Limits for LSMean(i)-LSMean(j)
1 2 -26.187112 -27.780224 -24.594000

Practice: Two-Way ANOVA: Weight by Gender or Cholesterol Status Part 2

Least Squares Means

Adjustment for Multiple Comparisons: Tukey-Kramer

Chol_Status2

Weight

LSMeans

Chol_Status2 Weight LSMEAN H0:LSMean1=LSMean2
Pr > |t|
Border-High 155.879567 <.0001
Desirable 150.324762  

Confidence Intervals

Chol_Status2 Weight LSMEAN 95% Confidence Limits
Border-High 155.879567 155.044482 156.714651
Desirable 150.324762 148.968061 151.681464

Pairwise Differences

Least Squares Means for Effect Chol_Status2
i j Difference Between Means Simultaneous 95% Confidence Limits for LSMean(i)-LSMean(j)
1 2 5.554804 3.961692 7.147916
  • Running a two-way ANOVA using Weight as the dependent variable and Sex and Chol_Status (cholesterol status) as factors shows significant p-value for the model as a whole. Both of the main factors are highly significant, but the interaction term (Sex*Chol_Status where p = 0.5409) is not significant at the .05 level.
  • In this model, Females weigh about 26.2 pounds lighter. Cholesterol Status is not as staightforward, as the Least Squares Means for effect Chol_Status table shows that differences between Borderline and Desirable, and High and Desirable are significant (p <.0001) but differences between Borderline and High are not significant (p = 0.0204) at the .05 level.
  • We revised the data by collapsing the Borderline and High categories of Chol_Status as Border-High, and rerun the ANOVA. In this rerun with collapsed categories, both of the main factors remain highly significant with the interaction term (Sex*Chol_Status2 where p = 0.9869) not showing as significant at the .05 level. Females weigh about 26.2 pounds lighter and those with Chol_Status of Border-High weigh about 5.5 pounds heavier.

Chapter 10: Correlation

Correlation and Scatter Plot Matrices.

SAS Code, click to expand

SAS Code:

#  (&path1 and biostats libname previously defined)
/*** Chapter 10: Statistics Correlation ***/
/* Correlation and Scatter Plot Matrices - generated code - start */
title1 "Pearson Correlation and Scatter Plot Matrices, w/ Nonparametric Spearman";
ods noproctitle;
ods graphics / imagemap=on;
proc corr data=work.exercise pearson spearman nosimple 
        plots(maxpoints=none)=matrix(histogram);
    var Age Pushups Rest_Pulse Max_Pulse Run_Pulse;
run;

/* Pearson correlation coefficient measures the strength of the relationship between two variables.  Generate a matrix of scatter plots and include histograms on the diagonal of the matrix.  The p-value in the correlation tables is the probability that you would obtain a correlation  with an absolute value as large as or larger than the one you obtained by chance alone, given that the true population correlation between your two variables is actually 0. 
Spearman correlation is one of the most popular nonparametric alternatives to a Pearson correlation. The Spearman method substitutes ranks for the two variables and then computes a correlation on the ranks.  When there are outliers on your scatter plot, you may want to consider computing Spearman correlations. 
The relationship between Max_Pulse and Rest_Pulse is pretty strong at 0.83112, with a significant p-value of <.0001.  The inverse relationship between Age and Pushups is somewhat significant at -0.49191, with a significant p-value = 0.0003.  */ 
title1;
/* Correlation and Scatter Plot Matrices - generated code - end */

SAS Output

Results: biostats_by_ex_SAScode.sas

Results: biostats_by_ex_SAScode.sas

Pearson Correlation and Scatter Plot Matrices, w/ Nonparametric Spearman

The Corr Procedure

Variables Information

5 Variables: Age Pushups Rest_Pulse Max_Pulse Run_Pulse

Pearson Correlations

Pearson Correlation Coefficients, N = 50
Prob > |r| under H0: Rho=0
  Age Pushups Rest_Pulse Max_Pulse Run_Pulse
Age
Age
1.00000
 
-0.49191
0.0003
0.48774
0.0003
0.26582
0.0621
0.25097
0.0788
Pushups
Pushups
-0.49191
0.0003
1.00000
 
-0.49639
0.0002
-0.45010
0.0010
-0.34555
0.0140
Rest_Pulse
Rest_Pulse
0.48774
0.0003
-0.49639
0.0002
1.00000
 
0.83112
<.0001
0.76139
<.0001
Max_Pulse
Max_Pulse
0.26582
0.0621
-0.45010
0.0010
0.83112
<.0001
1.00000
 
0.93634
<.0001
Run_Pulse
Run_Pulse
0.25097
0.0788
-0.34555
0.0140
0.76139
<.0001
0.93634
<.0001
1.00000
 

Spearman Correlations

Spearman Correlation Coefficients, N = 50
Prob > |r| under H0: Rho=0
  Age Pushups Rest_Pulse Max_Pulse Run_Pulse
Age
Age
1.00000
 
-0.46625
0.0006
0.48269
0.0004
0.25725
0.0713
0.25123
0.0784
Pushups
Pushups
-0.46625
0.0006
1.00000
 
-0.48882
0.0003
-0.45181
0.0010
-0.33960
0.0158
Rest_Pulse
Rest_Pulse
0.48269
0.0004
-0.48882
0.0003
1.00000
 
0.80310
<.0001
0.70668
<.0001
Max_Pulse
Max_Pulse
0.25725
0.0713
-0.45181
0.0010
0.80310
<.0001
1.00000
 
0.91251
<.0001
Run_Pulse
Run_Pulse
0.25123
0.0784
-0.33960
0.0158
0.70668
<.0001
0.91251
<.0001
1.00000
 

Scatter Plot Matrix

Age = 84 Percent = 6 Age = 84 Percent = 6 Age = 72 Percent = 12 Age = 72 Percent = 12 Age = 60 Percent = 28 Age = 60 Percent = 28 Age = 48 Percent = 28 Age = 48 Percent = 28 Age = 36 Percent = 18 Age = 36 Percent = 18 Age = 24 Percent = 8 Age = 24 Percent = 8 Age = 79 Pushups = 10 Observation = 50 Age = 31 Pushups = 22 Observation = 49 Age = 46 Pushups = 19 Observation = 48 Age = 59 Pushups = 25 Observation = 47 Age = 31 Pushups = 48 Observation = 46 Age = 49 Pushups = 22 Observation = 45 Age = 52 Pushups = 27 Observation = 44 Age = 49 Pushups = 33 Observation = 43 Age = 34 Pushups = 38 Observation = 42 Age = 41 Pushups = 17 Observation = 41 Age = 55 Pushups = 21 Observation = 40 Age = 56 Pushups = 8 Observation = 39 Age = 31 Pushups = 30 Observation = 38 Age = 64 Pushups = 20 Observation = 37 Age = 64 Pushups = 22 Observation = 36 Age = 60 Pushups = 36 Observation = 35 Age = 69 Pushups = 26 Observation = 34 Age = 48 Pushups = 21 Observation = 33 Age = 44 Pushups = 1 Observation = 32 Age = 26 Pushups = 40 Observation = 31 Age = 23 Pushups = 30 Observation = 30 Age = 53 Pushups = 9 Observation = 29 Age = 57 Pushups = 31 Observation = 28 Age = 68 Pushups = 32 Observation = 27 Age = 43 Pushups = 33 Observation = 26 Age = 73 Pushups = 8 Observation = 25 Age = 36 Pushups = 25 Observation = 24 Age = 73 Pushups = 12 Observation = 23 Age = 84 Pushups = 11 Observation = 22 Age = 26 Pushups = 52 Observation = 21 Age = 81 Pushups = 16 Observation = 20 Age = 31 Pushups = 50 Observation = 19 Age = 43 Pushups = 29 Observation = 18 Age = 49 Pushups = 11 Observation = 17 Age = 48 Pushups = 43 Observation = 16 Age = 54 Pushups = 7 Observation = 15 Age = 51 Pushups = 23 Observation = 14 Age = 19 Pushups = 34 Observation = 13 Age = 63 Pushups = 30 Observation = 12 Age = 63 Pushups = 51 Observation = 11 Age = 49 Pushups = 9 Observation = 10 Age = 35 Pushups = 25 Observation = 9 Age = 30 Pushups = 48 Observation = 8 Age = 64 Pushups = 21 Observation = 7 Age = 57 Pushups = 14 Observation = 6 Age = 55 Pushups = 24 Observation = 5 Age = 44 Pushups = 35 Observation = 4 Age = 76 Pushups = 11 Observation = 3 Age = 64 Pushups = 36 Observation = 2 Age = 68 Pushups = 19 Observation = 1 Age = 79 Rest_Pulse = 82 Observation = 50 Age = 31 Rest_Pulse = 74 Observation = 49 Age = 46 Rest_Pulse = 84 Observation = 48 Age = 59 Rest_Pulse = 71 Observation = 47 Age = 31 Rest_Pulse = 55 Observation = 46 Age = 49 Rest_Pulse = 61 Observation = 45 Age = 52 Rest_Pulse = 52 Observation = 44 Age = 49 Rest_Pulse = 51 Observation = 43 Age = 34 Rest_Pulse = 73 Observation = 42 Age = 41 Rest_Pulse = 74 Observation = 41 Age = 55 Rest_Pulse = 71 Observation = 40 Age = 56 Rest_Pulse = 74 Observation = 39 Age = 31 Rest_Pulse = 65 Observation = 38 Age = 64 Rest_Pulse = 85 Observation = 37 Age = 64 Rest_Pulse = 78 Observation = 36 Age = 60 Rest_Pulse = 65 Observation = 35 Age = 69 Rest_Pulse = 69 Observation = 34 Age = 48 Rest_Pulse = 59 Observation = 33 Age = 44 Rest_Pulse = 59 Observation = 32 Age = 26 Rest_Pulse = 55 Observation = 31 Age = 23 Rest_Pulse = 58 Observation = 30 Age = 53 Rest_Pulse = 66 Observation = 29 Age = 57 Rest_Pulse = 67 Observation = 28 Age = 68 Rest_Pulse = 70 Observation = 27 Age = 43 Rest_Pulse = 70 Observation = 26 Age = 73 Rest_Pulse = 67 Observation = 25 Age = 36 Rest_Pulse = 66 Observation = 24 Age = 73 Rest_Pulse = 77 Observation = 23 Age = 84 Rest_Pulse = 75 Observation = 22 Age = 26 Rest_Pulse = 49 Observation = 21 Age = 81 Rest_Pulse = 86 Observation = 20 Age = 31 Rest_Pulse = 55 Observation = 19 Age = 43 Rest_Pulse = 78 Observation = 18 Age = 49 Rest_Pulse = 68 Observation = 17 Age = 48 Rest_Pulse = 77 Observation = 16 Age = 54 Rest_Pulse = 59 Observation = 15 Age = 51 Rest_Pulse = 66 Observation = 14 Age = 19 Rest_Pulse = 65 Observation = 13 Age = 63 Rest_Pulse = 73 Observation = 12 Age = 63 Rest_Pulse = 55 Observation = 11 Age = 49 Rest_Pulse = 88 Observation = 10 Age = 35 Rest_Pulse = 55 Observation = 9 Age = 30 Rest_Pulse = 60 Observation = 8 Age = 64 Rest_Pulse = 69 Observation = 7 Age = 57 Rest_Pulse = 74 Observation = 6 Age = 55 Rest_Pulse = 76 Observation = 5 Age = 44 Rest_Pulse = 59 Observation = 4 Age = 76 Rest_Pulse = 74 Observation = 3 Age = 64 Rest_Pulse = 61 Observation = 2 Age = 68 Rest_Pulse = 75 Observation = 1 Age = 79 Max_Pulse = 124 Observation = 50 Age = 31 Max_Pulse = 118 Observation = 49 Age = 46 Max_Pulse = 130 Observation = 48 Age = 59 Max_Pulse = 110 Observation = 47 Age = 31 Max_Pulse = 109 Observation = 46 Age = 49 Max_Pulse = 118 Observation = 45 Age = 52 Max_Pulse = 104 Observation = 44 Age = 49 Max_Pulse = 94 Observation = 43 Age = 34 Max_Pulse = 120 Observation = 42 Age = 41 Max_Pulse = 127 Observation = 41 Age = 55 Max_Pulse = 112 Observation = 40 Age = 56 Max_Pulse = 122 Observation = 39 Age = 31 Max_Pulse = 111 Observation = 38 Age = 64 Max_Pulse = 137 Observation = 37 Age = 64 Max_Pulse = 126 Observation = 36 Age = 60 Max_Pulse = 111 Observation = 35 Age = 69 Max_Pulse = 112 Observation = 34 Age = 48 Max_Pulse = 109 Observation = 33 Age = 44 Max_Pulse = 107 Observation = 32 Age = 26 Max_Pulse = 114 Observation = 31 Age = 23 Max_Pulse = 105 Observation = 30 Age = 53 Max_Pulse = 127 Observation = 29 Age = 57 Max_Pulse = 111 Observation = 28 Age = 68 Max_Pulse = 125 Observation = 27 Age = 43 Max_Pulse = 111 Observation = 26 Age = 73 Max_Pulse = 112 Observation = 25 Age = 36 Max_Pulse = 117 Observation = 24 Age = 73 Max_Pulse = 119 Observation = 23 Age = 84 Max_Pulse = 114 Observation = 22 Age = 26 Max_Pulse = 100 Observation = 21 Age = 81 Max_Pulse = 127 Observation = 20 Age = 31 Max_Pulse = 100 Observation = 19 Age = 43 Max_Pulse = 122 Observation = 18 Age = 49 Max_Pulse = 118 Observation = 17 Age = 48 Max_Pulse = 119 Observation = 16 Age = 54 Max_Pulse = 113 Observation = 15 Age = 51 Max_Pulse = 114 Observation = 14 Age = 19 Max_Pulse = 118 Observation = 13 Age = 63 Max_Pulse = 126 Observation = 12 Age = 63 Max_Pulse = 102 Observation = 11 Age = 49 Max_Pulse = 137 Observation = 10 Age = 35 Max_Pulse = 107 Observation = 9 Age = 30 Max_Pulse = 114 Observation = 8 Age = 64 Max_Pulse = 106 Observation = 7 Age = 57 Max_Pulse = 121 Observation = 6 Age = 55 Max_Pulse = 115 Observation = 5 Age = 44 Max_Pulse = 111 Observation = 4 Age = 76 Max_Pulse = 115 Observation = 3 Age = 64 Max_Pulse = 107 Observation = 2 Age = 68 Max_Pulse = 124 Observation = 1 Age = 79 Run_Pulse = 124 Observation = 50 Age = 31 Run_Pulse = 108 Observation = 49 Age = 46 Run_Pulse = 127 Observation = 48 Age = 59 Run_Pulse = 108 Observation = 47 Age = 31 Run_Pulse = 104 Observation = 46 Age = 49 Run_Pulse = 115 Observation = 45 Age = 52 Run_Pulse = 103 Observation = 44 Age = 49 Run_Pulse = 92 Observation = 43 Age = 34 Run_Pulse = 125 Observation = 42 Age = 41 Run_Pulse = 122 Observation = 41 Age = 55 Run_Pulse = 108 Observation = 40 Age = 56 Run_Pulse = 118 Observation = 39 Age = 31 Run_Pulse = 111 Observation = 38 Age = 64 Run_Pulse = 141 Observation = 37 Age = 64 Run_Pulse = 127 Observation = 36 Age = 60 Run_Pulse = 109 Observation = 35 Age = 69 Run_Pulse = 112 Observation = 34 Age = 48 Run_Pulse = 108 Observation = 33 Age = 44 Run_Pulse = 104 Observation = 32 Age = 26 Run_Pulse = 116 Observation = 31 Age = 23 Run_Pulse = 104 Observation = 30 Age = 53 Run_Pulse = 119 Observation = 29 Age = 57 Run_Pulse = 114 Observation = 28 Age = 68 Run_Pulse = 120 Observation = 27 Age = 43 Run_Pulse = 105 Observation = 26 Age = 73 Run_Pulse = 111 Observation = 25 Age = 36 Run_Pulse = 117 Observation = 24 Age = 73 Run_Pulse = 116 Observation = 23 Age = 84 Run_Pulse = 108 Observation = 22 Age = 26 Run_Pulse = 95 Observation = 21 Age = 81 Run_Pulse = 119 Observation = 20 Age = 31 Run_Pulse = 101 Observation = 19 Age = 43 Run_Pulse = 120 Observation = 18 Age = 49 Run_Pulse = 113 Observation = 17 Age = 48 Run_Pulse = 117 Observation = 16 Age = 54 Run_Pulse = 111 Observation = 15 Age = 51 Run_Pulse = 110 Observation = 14 Age = 19 Run_Pulse = 110 Observation = 13 Age = 63 Run_Pulse = 125 Observation = 12 Age = 63 Run_Pulse = 103 Observation = 11 Age = 49 Run_Pulse = 134 Observation = 10 Age = 35 Run_Pulse = 107 Observation = 9 Age = 30 Run_Pulse = 110 Observation = 8 Age = 64 Run_Pulse = 103 Observation = 7 Age = 57 Run_Pulse = 118 Observation = 6 Age = 55 Run_Pulse = 110 Observation = 5 Age = 44 Run_Pulse = 108 Observation = 4 Age = 76 Run_Pulse = 105 Observation = 3 Age = 64 Run_Pulse = 110 Observation = 2 Age = 68 Run_Pulse = 121 Observation = 1 Pushups = 10 Age = 79 Observation = 50 Pushups = 22 Age = 31 Observation = 49 Pushups = 19 Age = 46 Observation = 48 Pushups = 25 Age = 59 Observation = 47 Pushups = 48 Age = 31 Observation = 46 Pushups = 22 Age = 49 Observation = 45 Pushups = 27 Age = 52 Observation = 44 Pushups = 33 Age = 49 Observation = 43 Pushups = 38 Age = 34 Observation = 42 Pushups = 17 Age = 41 Observation = 41 Pushups = 21 Age = 55 Observation = 40 Pushups = 8 Age = 56 Observation = 39 Pushups = 30 Age = 31 Observation = 38 Pushups = 20 Age = 64 Observation = 37 Pushups = 22 Age = 64 Observation = 36 Pushups = 36 Age = 60 Observation = 35 Pushups = 26 Age = 69 Observation = 34 Pushups = 21 Age = 48 Observation = 33 Pushups = 1 Age = 44 Observation = 32 Pushups = 40 Age = 26 Observation = 31 Pushups = 30 Age = 23 Observation = 30 Pushups = 9 Age = 53 Observation = 29 Pushups = 31 Age = 57 Observation = 28 Pushups = 32 Age = 68 Observation = 27 Pushups = 33 Age = 43 Observation = 26 Pushups = 8 Age = 73 Observation = 25 Pushups = 25 Age = 36 Observation = 24 Pushups = 12 Age = 73 Observation = 23 Pushups = 11 Age = 84 Observation = 22 Pushups = 52 Age = 26 Observation = 21 Pushups = 16 Age = 81 Observation = 20 Pushups = 50 Age = 31 Observation = 19 Pushups = 29 Age = 43 Observation = 18 Pushups = 11 Age = 49 Observation = 17 Pushups = 43 Age = 48 Observation = 16 Pushups = 7 Age = 54 Observation = 15 Pushups = 23 Age = 51 Observation = 14 Pushups = 34 Age = 19 Observation = 13 Pushups = 30 Age = 63 Observation = 12 Pushups = 51 Age = 63 Observation = 11 Pushups = 9 Age = 49 Observation = 10 Pushups = 25 Age = 35 Observation = 9 Pushups = 48 Age = 30 Observation = 8 Pushups = 21 Age = 64 Observation = 7 Pushups = 14 Age = 57 Observation = 6 Pushups = 24 Age = 55 Observation = 5 Pushups = 35 Age = 44 Observation = 4 Pushups = 11 Age = 76 Observation = 3 Pushups = 36 Age = 64 Observation = 2 Pushups = 19 Age = 68 Observation = 1 Pushups = 50 Percent = 10 Pushups = 50 Percent = 10 Pushups = 40 Percent = 12 Pushups = 40 Percent = 12 Pushups = 30 Percent = 28 Pushups = 30 Percent = 28 Pushups = 20 Percent = 26 Pushups = 20 Percent = 26 Pushups = 10 Percent = 22 Pushups = 10 Percent = 22 Pushups = 0 Percent = 2 Pushups = 0 Percent = 2 Pushups = 10 Rest_Pulse = 82 Observation = 50 Pushups = 22 Rest_Pulse = 74 Observation = 49 Pushups = 19 Rest_Pulse = 84 Observation = 48 Pushups = 25 Rest_Pulse = 71 Observation = 47 Pushups = 48 Rest_Pulse = 55 Observation = 46 Pushups = 22 Rest_Pulse = 61 Observation = 45 Pushups = 27 Rest_Pulse = 52 Observation = 44 Pushups = 33 Rest_Pulse = 51 Observation = 43 Pushups = 38 Rest_Pulse = 73 Observation = 42 Pushups = 17 Rest_Pulse = 74 Observation = 41 Pushups = 21 Rest_Pulse = 71 Observation = 40 Pushups = 8 Rest_Pulse = 74 Observation = 39 Pushups = 30 Rest_Pulse = 65 Observation = 38 Pushups = 20 Rest_Pulse = 85 Observation = 37 Pushups = 22 Rest_Pulse = 78 Observation = 36 Pushups = 36 Rest_Pulse = 65 Observation = 35 Pushups = 26 Rest_Pulse = 69 Observation = 34 Pushups = 21 Rest_Pulse = 59 Observation = 33 Pushups = 1 Rest_Pulse = 59 Observation = 32 Pushups = 40 Rest_Pulse = 55 Observation = 31 Pushups = 30 Rest_Pulse = 58 Observation = 30 Pushups = 9 Rest_Pulse = 66 Observation = 29 Pushups = 31 Rest_Pulse = 67 Observation = 28 Pushups = 32 Rest_Pulse = 70 Observation = 27 Pushups = 33 Rest_Pulse = 70 Observation = 26 Pushups = 8 Rest_Pulse = 67 Observation = 25 Pushups = 25 Rest_Pulse = 66 Observation = 24 Pushups = 12 Rest_Pulse = 77 Observation = 23 Pushups = 11 Rest_Pulse = 75 Observation = 22 Pushups = 52 Rest_Pulse = 49 Observation = 21 Pushups = 16 Rest_Pulse = 86 Observation = 20 Pushups = 50 Rest_Pulse = 55 Observation = 19 Pushups = 29 Rest_Pulse = 78 Observation = 18 Pushups = 11 Rest_Pulse = 68 Observation = 17 Pushups = 43 Rest_Pulse = 77 Observation = 16 Pushups = 7 Rest_Pulse = 59 Observation = 15 Pushups = 23 Rest_Pulse = 66 Observation = 14 Pushups = 34 Rest_Pulse = 65 Observation = 13 Pushups = 30 Rest_Pulse = 73 Observation = 12 Pushups = 51 Rest_Pulse = 55 Observation = 11 Pushups = 9 Rest_Pulse = 88 Observation = 10 Pushups = 25 Rest_Pulse = 55 Observation = 9 Pushups = 48 Rest_Pulse = 60 Observation = 8 Pushups = 21 Rest_Pulse = 69 Observation = 7 Pushups = 14 Rest_Pulse = 74 Observation = 6 Pushups = 24 Rest_Pulse = 76 Observation = 5 Pushups = 35 Rest_Pulse = 59 Observation = 4 Pushups = 11 Rest_Pulse = 74 Observation = 3 Pushups = 36 Rest_Pulse = 61 Observation = 2 Pushups = 19 Rest_Pulse = 75 Observation = 1 Pushups = 10 Max_Pulse = 124 Observation = 50 Pushups = 22 Max_Pulse = 118 Observation = 49 Pushups = 19 Max_Pulse = 130 Observation = 48 Pushups = 25 Max_Pulse = 110 Observation = 47 Pushups = 48 Max_Pulse = 109 Observation = 46 Pushups = 22 Max_Pulse = 118 Observation = 45 Pushups = 27 Max_Pulse = 104 Observation = 44 Pushups = 33 Max_Pulse = 94 Observation = 43 Pushups = 38 Max_Pulse = 120 Observation = 42 Pushups = 17 Max_Pulse = 127 Observation = 41 Pushups = 21 Max_Pulse = 112 Observation = 40 Pushups = 8 Max_Pulse = 122 Observation = 39 Pushups = 30 Max_Pulse = 111 Observation = 38 Pushups = 20 Max_Pulse = 137 Observation = 37 Pushups = 22 Max_Pulse = 126 Observation = 36 Pushups = 36 Max_Pulse = 111 Observation = 35 Pushups = 26 Max_Pulse = 112 Observation = 34 Pushups = 21 Max_Pulse = 109 Observation = 33 Pushups = 1 Max_Pulse = 107 Observation = 32 Pushups = 40 Max_Pulse = 114 Observation = 31 Pushups = 30 Max_Pulse = 105 Observation = 30 Pushups = 9 Max_Pulse = 127 Observation = 29 Pushups = 31 Max_Pulse = 111 Observation = 28 Pushups = 32 Max_Pulse = 125 Observation = 27 Pushups = 33 Max_Pulse = 111 Observation = 26 Pushups = 8 Max_Pulse = 112 Observation = 25 Pushups = 25 Max_Pulse = 117 Observation = 24 Pushups = 12 Max_Pulse = 119 Observation = 23 Pushups = 11 Max_Pulse = 114 Observation = 22 Pushups = 52 Max_Pulse = 100 Observation = 21 Pushups = 16 Max_Pulse = 127 Observation = 20 Pushups = 50 Max_Pulse = 100 Observation = 19 Pushups = 29 Max_Pulse = 122 Observation = 18 Pushups = 11 Max_Pulse = 118 Observation = 17 Pushups = 43 Max_Pulse = 119 Observation = 16 Pushups = 7 Max_Pulse = 113 Observation = 15 Pushups = 23 Max_Pulse = 114 Observation = 14 Pushups = 34 Max_Pulse = 118 Observation = 13 Pushups = 30 Max_Pulse = 126 Observation = 12 Pushups = 51 Max_Pulse = 102 Observation = 11 Pushups = 9 Max_Pulse = 137 Observation = 10 Pushups = 25 Max_Pulse = 107 Observation = 9 Pushups = 48 Max_Pulse = 114 Observation = 8 Pushups = 21 Max_Pulse = 106 Observation = 7 Pushups = 14 Max_Pulse = 121 Observation = 6 Pushups = 24 Max_Pulse = 115 Observation = 5 Pushups = 35 Max_Pulse = 111 Observation = 4 Pushups = 11 Max_Pulse = 115 Observation = 3 Pushups = 36 Max_Pulse = 107 Observation = 2 Pushups = 19 Max_Pulse = 124 Observation = 1 Pushups = 10 Run_Pulse = 124 Observation = 50 Pushups = 22 Run_Pulse = 108 Observation = 49 Pushups = 19 Run_Pulse = 127 Observation = 48 Pushups = 25 Run_Pulse = 108 Observation = 47 Pushups = 48 Run_Pulse = 104 Observation = 46 Pushups = 22 Run_Pulse = 115 Observation = 45 Pushups = 27 Run_Pulse = 103 Observation = 44 Pushups = 33 Run_Pulse = 92 Observation = 43 Pushups = 38 Run_Pulse = 125 Observation = 42 Pushups = 17 Run_Pulse = 122 Observation = 41 Pushups = 21 Run_Pulse = 108 Observation = 40 Pushups = 8 Run_Pulse = 118 Observation = 39 Pushups = 30 Run_Pulse = 111 Observation = 38 Pushups = 20 Run_Pulse = 141 Observation = 37 Pushups = 22 Run_Pulse = 127 Observation = 36 Pushups = 36 Run_Pulse = 109 Observation = 35 Pushups = 26 Run_Pulse = 112 Observation = 34 Pushups = 21 Run_Pulse = 108 Observation = 33 Pushups = 1 Run_Pulse = 104 Observation = 32 Pushups = 40 Run_Pulse = 116 Observation = 31 Pushups = 30 Run_Pulse = 104 Observation = 30 Pushups = 9 Run_Pulse = 119 Observation = 29 Pushups = 31 Run_Pulse = 114 Observation = 28 Pushups = 32 Run_Pulse = 120 Observation = 27 Pushups = 33 Run_Pulse = 105 Observation = 26 Pushups = 8 Run_Pulse = 111 Observation = 25 Pushups = 25 Run_Pulse = 117 Observation = 24 Pushups = 12 Run_Pulse = 116 Observation = 23 Pushups = 11 Run_Pulse = 108 Observation = 22 Pushups = 52 Run_Pulse = 95 Observation = 21 Pushups = 16 Run_Pulse = 119 Observation = 20 Pushups = 50 Run_Pulse = 101 Observation = 19 Pushups = 29 Run_Pulse = 120 Observation = 18 Pushups = 11 Run_Pulse = 113 Observation = 17 Pushups = 43 Run_Pulse = 117 Observation = 16 Pushups = 7 Run_Pulse = 111 Observation = 15 Pushups = 23 Run_Pulse = 110 Observation = 14 Pushups = 34 Run_Pulse = 110 Observation = 13 Pushups = 30 Run_Pulse = 125 Observation = 12 Pushups = 51 Run_Pulse = 103 Observation = 11 Pushups = 9 Run_Pulse = 134 Observation = 10 Pushups = 25 Run_Pulse = 107 Observation = 9 Pushups = 48 Run_Pulse = 110 Observation = 8 Pushups = 21 Run_Pulse = 103 Observation = 7 Pushups = 14 Run_Pulse = 118 Observation = 6 Pushups = 24 Run_Pulse = 110 Observation = 5 Pushups = 35 Run_Pulse = 108 Observation = 4 Pushups = 11 Run_Pulse = 105 Observation = 3 Pushups = 36 Run_Pulse = 110 Observation = 2 Pushups = 19 Run_Pulse = 121 Observation = 1 Rest_Pulse = 82 Age = 79 Observation = 50 Rest_Pulse = 74 Age = 31 Observation = 49 Rest_Pulse = 84 Age = 46 Observation = 48 Rest_Pulse = 71 Age = 59 Observation = 47 Rest_Pulse = 55 Age = 31 Observation = 46 Rest_Pulse = 61 Age = 49 Observation = 45 Rest_Pulse = 52 Age = 52 Observation = 44 Rest_Pulse = 51 Age = 49 Observation = 43 Rest_Pulse = 73 Age = 34 Observation = 42 Rest_Pulse = 74 Age = 41 Observation = 41 Rest_Pulse = 71 Age = 55 Observation = 40 Rest_Pulse = 74 Age = 56 Observation = 39 Rest_Pulse = 65 Age = 31 Observation = 38 Rest_Pulse = 85 Age = 64 Observation = 37 Rest_Pulse = 78 Age = 64 Observation = 36 Rest_Pulse = 65 Age = 60 Observation = 35 Rest_Pulse = 69 Age = 69 Observation = 34 Rest_Pulse = 59 Age = 48 Observation = 33 Rest_Pulse = 59 Age = 44 Observation = 32 Rest_Pulse = 55 Age = 26 Observation = 31 Rest_Pulse = 58 Age = 23 Observation = 30 Rest_Pulse = 66 Age = 53 Observation = 29 Rest_Pulse = 67 Age = 57 Observation = 28 Rest_Pulse = 70 Age = 68 Observation = 27 Rest_Pulse = 70 Age = 43 Observation = 26 Rest_Pulse = 67 Age = 73 Observation = 25 Rest_Pulse = 66 Age = 36 Observation = 24 Rest_Pulse = 77 Age = 73 Observation = 23 Rest_Pulse = 75 Age = 84 Observation = 22 Rest_Pulse = 49 Age = 26 Observation = 21 Rest_Pulse = 86 Age = 81 Observation = 20 Rest_Pulse = 55 Age = 31 Observation = 19 Rest_Pulse = 78 Age = 43 Observation = 18 Rest_Pulse = 68 Age = 49 Observation = 17 Rest_Pulse = 77 Age = 48 Observation = 16 Rest_Pulse = 59 Age = 54 Observation = 15 Rest_Pulse = 66 Age = 51 Observation = 14 Rest_Pulse = 65 Age = 19 Observation = 13 Rest_Pulse = 73 Age = 63 Observation = 12 Rest_Pulse = 55 Age = 63 Observation = 11 Rest_Pulse = 88 Age = 49 Observation = 10 Rest_Pulse = 55 Age = 35 Observation = 9 Rest_Pulse = 60 Age = 30 Observation = 8 Rest_Pulse = 69 Age = 64 Observation = 7 Rest_Pulse = 74 Age = 57 Observation = 6 Rest_Pulse = 76 Age = 55 Observation = 5 Rest_Pulse = 59 Age = 44 Observation = 4 Rest_Pulse = 74 Age = 76 Observation = 3 Rest_Pulse = 61 Age = 64 Observation = 2 Rest_Pulse = 75 Age = 68 Observation = 1 Rest_Pulse = 82 Pushups = 10 Observation = 50 Rest_Pulse = 74 Pushups = 22 Observation = 49 Rest_Pulse = 84 Pushups = 19 Observation = 48 Rest_Pulse = 71 Pushups = 25 Observation = 47 Rest_Pulse = 55 Pushups = 48 Observation = 46 Rest_Pulse = 61 Pushups = 22 Observation = 45 Rest_Pulse = 52 Pushups = 27 Observation = 44 Rest_Pulse = 51 Pushups = 33 Observation = 43 Rest_Pulse = 73 Pushups = 38 Observation = 42 Rest_Pulse = 74 Pushups = 17 Observation = 41 Rest_Pulse = 71 Pushups = 21 Observation = 40 Rest_Pulse = 74 Pushups = 8 Observation = 39 Rest_Pulse = 65 Pushups = 30 Observation = 38 Rest_Pulse = 85 Pushups = 20 Observation = 37 Rest_Pulse = 78 Pushups = 22 Observation = 36 Rest_Pulse = 65 Pushups = 36 Observation = 35 Rest_Pulse = 69 Pushups = 26 Observation = 34 Rest_Pulse = 59 Pushups = 21 Observation = 33 Rest_Pulse = 59 Pushups = 1 Observation = 32 Rest_Pulse = 55 Pushups = 40 Observation = 31 Rest_Pulse = 58 Pushups = 30 Observation = 30 Rest_Pulse = 66 Pushups = 9 Observation = 29 Rest_Pulse = 67 Pushups = 31 Observation = 28 Rest_Pulse = 70 Pushups = 32 Observation = 27 Rest_Pulse = 70 Pushups = 33 Observation = 26 Rest_Pulse = 67 Pushups = 8 Observation = 25 Rest_Pulse = 66 Pushups = 25 Observation = 24 Rest_Pulse = 77 Pushups = 12 Observation = 23 Rest_Pulse = 75 Pushups = 11 Observation = 22 Rest_Pulse = 49 Pushups = 52 Observation = 21 Rest_Pulse = 86 Pushups = 16 Observation = 20 Rest_Pulse = 55 Pushups = 50 Observation = 19 Rest_Pulse = 78 Pushups = 29 Observation = 18 Rest_Pulse = 68 Pushups = 11 Observation = 17 Rest_Pulse = 77 Pushups = 43 Observation = 16 Rest_Pulse = 59 Pushups = 7 Observation = 15 Rest_Pulse = 66 Pushups = 23 Observation = 14 Rest_Pulse = 65 Pushups = 34 Observation = 13 Rest_Pulse = 73 Pushups = 30 Observation = 12 Rest_Pulse = 55 Pushups = 51 Observation = 11 Rest_Pulse = 88 Pushups = 9 Observation = 10 Rest_Pulse = 55 Pushups = 25 Observation = 9 Rest_Pulse = 60 Pushups = 48 Observation = 8 Rest_Pulse = 69 Pushups = 21 Observation = 7 Rest_Pulse = 74 Pushups = 14 Observation = 6 Rest_Pulse = 76 Pushups = 24 Observation = 5 Rest_Pulse = 59 Pushups = 35 Observation = 4 Rest_Pulse = 74 Pushups = 11 Observation = 3 Rest_Pulse = 61 Pushups = 36 Observation = 2 Rest_Pulse = 75 Pushups = 19 Observation = 1 Rest_Pulse = 87 Percent = 8 Rest_Pulse = 87 Percent = 8 Rest_Pulse = 81 Percent = 6 Rest_Pulse = 81 Percent = 6 Rest_Pulse = 75 Percent = 24 Rest_Pulse = 75 Percent = 24 Rest_Pulse = 69 Percent = 24 Rest_Pulse = 69 Percent = 24 Rest_Pulse = 63 Percent = 12 Rest_Pulse = 63 Percent = 12 Rest_Pulse = 57 Percent = 20 Rest_Pulse = 57 Percent = 20 Rest_Pulse = 51 Percent = 6 Rest_Pulse = 51 Percent = 6 Rest_Pulse = 82 Max_Pulse = 124 Observation = 50 Rest_Pulse = 74 Max_Pulse = 118 Observation = 49 Rest_Pulse = 84 Max_Pulse = 130 Observation = 48 Rest_Pulse = 71 Max_Pulse = 110 Observation = 47 Rest_Pulse = 55 Max_Pulse = 109 Observation = 46 Rest_Pulse = 61 Max_Pulse = 118 Observation = 45 Rest_Pulse = 52 Max_Pulse = 104 Observation = 44 Rest_Pulse = 51 Max_Pulse = 94 Observation = 43 Rest_Pulse = 73 Max_Pulse = 120 Observation = 42 Rest_Pulse = 74 Max_Pulse = 127 Observation = 41 Rest_Pulse = 71 Max_Pulse = 112 Observation = 40 Rest_Pulse = 74 Max_Pulse = 122 Observation = 39 Rest_Pulse = 65 Max_Pulse = 111 Observation = 38 Rest_Pulse = 85 Max_Pulse = 137 Observation = 37 Rest_Pulse = 78 Max_Pulse = 126 Observation = 36 Rest_Pulse = 65 Max_Pulse = 111 Observation = 35 Rest_Pulse = 69 Max_Pulse = 112 Observation = 34 Rest_Pulse = 59 Max_Pulse = 109 Observation = 33 Rest_Pulse = 59 Max_Pulse = 107 Observation = 32 Rest_Pulse = 55 Max_Pulse = 114 Observation = 31 Rest_Pulse = 58 Max_Pulse = 105 Observation = 30 Rest_Pulse = 66 Max_Pulse = 127 Observation = 29 Rest_Pulse = 67 Max_Pulse = 111 Observation = 28 Rest_Pulse = 70 Max_Pulse = 125 Observation = 27 Rest_Pulse = 70 Max_Pulse = 111 Observation = 26 Rest_Pulse = 67 Max_Pulse = 112 Observation = 25 Rest_Pulse = 66 Max_Pulse = 117 Observation = 24 Rest_Pulse = 77 Max_Pulse = 119 Observation = 23 Rest_Pulse = 75 Max_Pulse = 114 Observation = 22 Rest_Pulse = 49 Max_Pulse = 100 Observation = 21 Rest_Pulse = 86 Max_Pulse = 127 Observation = 20 Rest_Pulse = 55 Max_Pulse = 100 Observation = 19 Rest_Pulse = 78 Max_Pulse = 122 Observation = 18 Rest_Pulse = 68 Max_Pulse = 118 Observation = 17 Rest_Pulse = 77 Max_Pulse = 119 Observation = 16 Rest_Pulse = 59 Max_Pulse = 113 Observation = 15 Rest_Pulse = 66 Max_Pulse = 114 Observation = 14 Rest_Pulse = 65 Max_Pulse = 118 Observation = 13 Rest_Pulse = 73 Max_Pulse = 126 Observation = 12 Rest_Pulse = 55 Max_Pulse = 102 Observation = 11 Rest_Pulse = 88 Max_Pulse = 137 Observation = 10 Rest_Pulse = 55 Max_Pulse = 107 Observation = 9 Rest_Pulse = 60 Max_Pulse = 114 Observation = 8 Rest_Pulse = 69 Max_Pulse = 106 Observation = 7 Rest_Pulse = 74 Max_Pulse = 121 Observation = 6 Rest_Pulse = 76 Max_Pulse = 115 Observation = 5 Rest_Pulse = 59 Max_Pulse = 111 Observation = 4 Rest_Pulse = 74 Max_Pulse = 115 Observation = 3 Rest_Pulse = 61 Max_Pulse = 107 Observation = 2 Rest_Pulse = 75 Max_Pulse = 124 Observation = 1 Rest_Pulse = 82 Run_Pulse = 124 Observation = 50 Rest_Pulse = 74 Run_Pulse = 108 Observation = 49 Rest_Pulse = 84 Run_Pulse = 127 Observation = 48 Rest_Pulse = 71 Run_Pulse = 108 Observation = 47 Rest_Pulse = 55 Run_Pulse = 104 Observation = 46 Rest_Pulse = 61 Run_Pulse = 115 Observation = 45 Rest_Pulse = 52 Run_Pulse = 103 Observation = 44 Rest_Pulse = 51 Run_Pulse = 92 Observation = 43 Rest_Pulse = 73 Run_Pulse = 125 Observation = 42 Rest_Pulse = 74 Run_Pulse = 122 Observation = 41 Rest_Pulse = 71 Run_Pulse = 108 Observation = 40 Rest_Pulse = 74 Run_Pulse = 118 Observation = 39 Rest_Pulse = 65 Run_Pulse = 111 Observation = 38 Rest_Pulse = 85 Run_Pulse = 141 Observation = 37 Rest_Pulse = 78 Run_Pulse = 127 Observation = 36 Rest_Pulse = 65 Run_Pulse = 109 Observation = 35 Rest_Pulse = 69 Run_Pulse = 112 Observation = 34 Rest_Pulse = 59 Run_Pulse = 108 Observation = 33 Rest_Pulse = 59 Run_Pulse = 104 Observation = 32 Rest_Pulse = 55 Run_Pulse = 116 Observation = 31 Rest_Pulse = 58 Run_Pulse = 104 Observation = 30 Rest_Pulse = 66 Run_Pulse = 119 Observation = 29 Rest_Pulse = 67 Run_Pulse = 114 Observation = 28 Rest_Pulse = 70 Run_Pulse = 120 Observation = 27 Rest_Pulse = 70 Run_Pulse = 105 Observation = 26 Rest_Pulse = 67 Run_Pulse = 111 Observation = 25 Rest_Pulse = 66 Run_Pulse = 117 Observation = 24 Rest_Pulse = 77 Run_Pulse = 116 Observation = 23 Rest_Pulse = 75 Run_Pulse = 108 Observation = 22 Rest_Pulse = 49 Run_Pulse = 95 Observation = 21 Rest_Pulse = 86 Run_Pulse = 119 Observation = 20 Rest_Pulse = 55 Run_Pulse = 101 Observation = 19 Rest_Pulse = 78 Run_Pulse = 120 Observation = 18 Rest_Pulse = 68 Run_Pulse = 113 Observation = 17 Rest_Pulse = 77 Run_Pulse = 117 Observation = 16 Rest_Pulse = 59 Run_Pulse = 111 Observation = 15 Rest_Pulse = 66 Run_Pulse = 110 Observation = 14 Rest_Pulse = 65 Run_Pulse = 110 Observation = 13 Rest_Pulse = 73 Run_Pulse = 125 Observation = 12 Rest_Pulse = 55 Run_Pulse = 103 Observation = 11 Rest_Pulse = 88 Run_Pulse = 134 Observation = 10 Rest_Pulse = 55 Run_Pulse = 107 Observation = 9 Rest_Pulse = 60 Run_Pulse = 110 Observation = 8 Rest_Pulse = 69 Run_Pulse = 103 Observation = 7 Rest_Pulse = 74 Run_Pulse = 118 Observation = 6 Rest_Pulse = 76 Run_Pulse = 110 Observation = 5 Rest_Pulse = 59 Run_Pulse = 108 Observation = 4 Rest_Pulse = 74 Run_Pulse = 105 Observation = 3 Rest_Pulse = 61 Run_Pulse = 110 Observation = 2 Rest_Pulse = 75 Run_Pulse = 121 Observation = 1 Max_Pulse = 124 Age = 79 Observation = 50 Max_Pulse = 118 Age = 31 Observation = 49 Max_Pulse = 130 Age = 46 Observation = 48 Max_Pulse = 110 Age = 59 Observation = 47 Max_Pulse = 109 Age = 31 Observation = 46 Max_Pulse = 118 Age = 49 Observation = 45 Max_Pulse = 104 Age = 52 Observation = 44 Max_Pulse = 94 Age = 49 Observation = 43 Max_Pulse = 120 Age = 34 Observation = 42 Max_Pulse = 127 Age = 41 Observation = 41 Max_Pulse = 112 Age = 55 Observation = 40 Max_Pulse = 122 Age = 56 Observation = 39 Max_Pulse = 111 Age = 31 Observation = 38 Max_Pulse = 137 Age = 64 Observation = 37 Max_Pulse = 126 Age = 64 Observation = 36 Max_Pulse = 111 Age = 60 Observation = 35 Max_Pulse = 112 Age = 69 Observation = 34 Max_Pulse = 109 Age = 48 Observation = 33 Max_Pulse = 107 Age = 44 Observation = 32 Max_Pulse = 114 Age = 26 Observation = 31 Max_Pulse = 105 Age = 23 Observation = 30 Max_Pulse = 127 Age = 53 Observation = 29 Max_Pulse = 111 Age = 57 Observation = 28 Max_Pulse = 125 Age = 68 Observation = 27 Max_Pulse = 111 Age = 43 Observation = 26 Max_Pulse = 112 Age = 73 Observation = 25 Max_Pulse = 117 Age = 36 Observation = 24 Max_Pulse = 119 Age = 73 Observation = 23 Max_Pulse = 114 Age = 84 Observation = 22 Max_Pulse = 100 Age = 26 Observation = 21 Max_Pulse = 127 Age = 81 Observation = 20 Max_Pulse = 100 Age = 31 Observation = 19 Max_Pulse = 122 Age = 43 Observation = 18 Max_Pulse = 118 Age = 49 Observation = 17 Max_Pulse = 119 Age = 48 Observation = 16 Max_Pulse = 113 Age = 54 Observation = 15 Max_Pulse = 114 Age = 51 Observation = 14 Max_Pulse = 118 Age = 19 Observation = 13 Max_Pulse = 126 Age = 63 Observation = 12 Max_Pulse = 102 Age = 63 Observation = 11 Max_Pulse = 137 Age = 49 Observation = 10 Max_Pulse = 107 Age = 35 Observation = 9 Max_Pulse = 114 Age = 30 Observation = 8 Max_Pulse = 106 Age = 64 Observation = 7 Max_Pulse = 121 Age = 57 Observation = 6 Max_Pulse = 115 Age = 55 Observation = 5 Max_Pulse = 111 Age = 44 Observation = 4 Max_Pulse = 115 Age = 76 Observation = 3 Max_Pulse = 107 Age = 64 Observation = 2 Max_Pulse = 124 Age = 68 Observation = 1 Max_Pulse = 124 Pushups = 10 Observation = 50 Max_Pulse = 118 Pushups = 22 Observation = 49 Max_Pulse = 130 Pushups = 19 Observation = 48 Max_Pulse = 110 Pushups = 25 Observation = 47 Max_Pulse = 109 Pushups = 48 Observation = 46 Max_Pulse = 118 Pushups = 22 Observation = 45 Max_Pulse = 104 Pushups = 27 Observation = 44 Max_Pulse = 94 Pushups = 33 Observation = 43 Max_Pulse = 120 Pushups = 38 Observation = 42 Max_Pulse = 127 Pushups = 17 Observation = 41 Max_Pulse = 112 Pushups = 21 Observation = 40 Max_Pulse = 122 Pushups = 8 Observation = 39 Max_Pulse = 111 Pushups = 30 Observation = 38 Max_Pulse = 137 Pushups = 20 Observation = 37 Max_Pulse = 126 Pushups = 22 Observation = 36 Max_Pulse = 111 Pushups = 36 Observation = 35 Max_Pulse = 112 Pushups = 26 Observation = 34 Max_Pulse = 109 Pushups = 21 Observation = 33 Max_Pulse = 107 Pushups = 1 Observation = 32 Max_Pulse = 114 Pushups = 40 Observation = 31 Max_Pulse = 105 Pushups = 30 Observation = 30 Max_Pulse = 127 Pushups = 9 Observation = 29 Max_Pulse = 111 Pushups = 31 Observation = 28 Max_Pulse = 125 Pushups = 32 Observation = 27 Max_Pulse = 111 Pushups = 33 Observation = 26 Max_Pulse = 112 Pushups = 8 Observation = 25 Max_Pulse = 117 Pushups = 25 Observation = 24 Max_Pulse = 119 Pushups = 12 Observation = 23 Max_Pulse = 114 Pushups = 11 Observation = 22 Max_Pulse = 100 Pushups = 52 Observation = 21 Max_Pulse = 127 Pushups = 16 Observation = 20 Max_Pulse = 100 Pushups = 50 Observation = 19 Max_Pulse = 122 Pushups = 29 Observation = 18 Max_Pulse = 118 Pushups = 11 Observation = 17 Max_Pulse = 119 Pushups = 43 Observation = 16 Max_Pulse = 113 Pushups = 7 Observation = 15 Max_Pulse = 114 Pushups = 23 Observation = 14 Max_Pulse = 118 Pushups = 34 Observation = 13 Max_Pulse = 126 Pushups = 30 Observation = 12 Max_Pulse = 102 Pushups = 51 Observation = 11 Max_Pulse = 137 Pushups = 9 Observation = 10 Max_Pulse = 107 Pushups = 25 Observation = 9 Max_Pulse = 114 Pushups = 48 Observation = 8 Max_Pulse = 106 Pushups = 21 Observation = 7 Max_Pulse = 121 Pushups = 14 Observation = 6 Max_Pulse = 115 Pushups = 24 Observation = 5 Max_Pulse = 111 Pushups = 35 Observation = 4 Max_Pulse = 115 Pushups = 11 Observation = 3 Max_Pulse = 107 Pushups = 36 Observation = 2 Max_Pulse = 124 Pushups = 19 Observation = 1 Max_Pulse = 124 Rest_Pulse = 82 Observation = 50 Max_Pulse = 118 Rest_Pulse = 74 Observation = 49 Max_Pulse = 130 Rest_Pulse = 84 Observation = 48 Max_Pulse = 110 Rest_Pulse = 71 Observation = 47 Max_Pulse = 109 Rest_Pulse = 55 Observation = 46 Max_Pulse = 118 Rest_Pulse = 61 Observation = 45 Max_Pulse = 104 Rest_Pulse = 52 Observation = 44 Max_Pulse = 94 Rest_Pulse = 51 Observation = 43 Max_Pulse = 120 Rest_Pulse = 73 Observation = 42 Max_Pulse = 127 Rest_Pulse = 74 Observation = 41 Max_Pulse = 112 Rest_Pulse = 71 Observation = 40 Max_Pulse = 122 Rest_Pulse = 74 Observation = 39 Max_Pulse = 111 Rest_Pulse = 65 Observation = 38 Max_Pulse = 137 Rest_Pulse = 85 Observation = 37 Max_Pulse = 126 Rest_Pulse = 78 Observation = 36 Max_Pulse = 111 Rest_Pulse = 65 Observation = 35 Max_Pulse = 112 Rest_Pulse = 69 Observation = 34 Max_Pulse = 109 Rest_Pulse = 59 Observation = 33 Max_Pulse = 107 Rest_Pulse = 59 Observation = 32 Max_Pulse = 114 Rest_Pulse = 55 Observation = 31 Max_Pulse = 105 Rest_Pulse = 58 Observation = 30 Max_Pulse = 127 Rest_Pulse = 66 Observation = 29 Max_Pulse = 111 Rest_Pulse = 67 Observation = 28 Max_Pulse = 125 Rest_Pulse = 70 Observation = 27 Max_Pulse = 111 Rest_Pulse = 70 Observation = 26 Max_Pulse = 112 Rest_Pulse = 67 Observation = 25 Max_Pulse = 117 Rest_Pulse = 66 Observation = 24 Max_Pulse = 119 Rest_Pulse = 77 Observation = 23 Max_Pulse = 114 Rest_Pulse = 75 Observation = 22 Max_Pulse = 100 Rest_Pulse = 49 Observation = 21 Max_Pulse = 127 Rest_Pulse = 86 Observation = 20 Max_Pulse = 100 Rest_Pulse = 55 Observation = 19 Max_Pulse = 122 Rest_Pulse = 78 Observation = 18 Max_Pulse = 118 Rest_Pulse = 68 Observation = 17 Max_Pulse = 119 Rest_Pulse = 77 Observation = 16 Max_Pulse = 113 Rest_Pulse = 59 Observation = 15 Max_Pulse = 114 Rest_Pulse = 66 Observation = 14 Max_Pulse = 118 Rest_Pulse = 65 Observation = 13 Max_Pulse = 126 Rest_Pulse = 73 Observation = 12 Max_Pulse = 102 Rest_Pulse = 55 Observation = 11 Max_Pulse = 137 Rest_Pulse = 88 Observation = 10 Max_Pulse = 107 Rest_Pulse = 55 Observation = 9 Max_Pulse = 114 Rest_Pulse = 60 Observation = 8 Max_Pulse = 106 Rest_Pulse = 69 Observation = 7 Max_Pulse = 121 Rest_Pulse = 74 Observation = 6 Max_Pulse = 115 Rest_Pulse = 76 Observation = 5 Max_Pulse = 111 Rest_Pulse = 59 Observation = 4 Max_Pulse = 115 Rest_Pulse = 74 Observation = 3 Max_Pulse = 107 Rest_Pulse = 61 Observation = 2 Max_Pulse = 124 Rest_Pulse = 75 Observation = 1 Max_Pulse = 136 Percent = 4 Max_Pulse = 136 Percent = 4 Max_Pulse = 128 Percent = 18 Max_Pulse = 128 Percent = 18 Max_Pulse = 120 Percent = 22 Max_Pulse = 120 Percent = 22 Max_Pulse = 112 Percent = 36 Max_Pulse = 112 Percent = 36 Max_Pulse = 104 Percent = 18 Max_Pulse = 104 Percent = 18 Max_Pulse = 96 Percent = 2 Max_Pulse = 96 Percent = 2 Max_Pulse = 124 Run_Pulse = 124 Observation = 50 Max_Pulse = 118 Run_Pulse = 108 Observation = 49 Max_Pulse = 130 Run_Pulse = 127 Observation = 48 Max_Pulse = 110 Run_Pulse = 108 Observation = 47 Max_Pulse = 109 Run_Pulse = 104 Observation = 46 Max_Pulse = 118 Run_Pulse = 115 Observation = 45 Max_Pulse = 104 Run_Pulse = 103 Observation = 44 Max_Pulse = 94 Run_Pulse = 92 Observation = 43 Max_Pulse = 120 Run_Pulse = 125 Observation = 42 Max_Pulse = 127 Run_Pulse = 122 Observation = 41 Max_Pulse = 112 Run_Pulse = 108 Observation = 40 Max_Pulse = 122 Run_Pulse = 118 Observation = 39 Max_Pulse = 111 Run_Pulse = 111 Observation = 38 Max_Pulse = 137 Run_Pulse = 141 Observation = 37 Max_Pulse = 126 Run_Pulse = 127 Observation = 36 Max_Pulse = 111 Run_Pulse = 109 Observation = 35 Max_Pulse = 112 Run_Pulse = 112 Observation = 34 Max_Pulse = 109 Run_Pulse = 108 Observation = 33 Max_Pulse = 107 Run_Pulse = 104 Observation = 32 Max_Pulse = 114 Run_Pulse = 116 Observation = 31 Max_Pulse = 105 Run_Pulse = 104 Observation = 30 Max_Pulse = 127 Run_Pulse = 119 Observation = 29 Max_Pulse = 111 Run_Pulse = 114 Observation = 28 Max_Pulse = 125 Run_Pulse = 120 Observation = 27 Max_Pulse = 111 Run_Pulse = 105 Observation = 26 Max_Pulse = 112 Run_Pulse = 111 Observation = 25 Max_Pulse = 117 Run_Pulse = 117 Observation = 24 Max_Pulse = 119 Run_Pulse = 116 Observation = 23 Max_Pulse = 114 Run_Pulse = 108 Observation = 22 Max_Pulse = 100 Run_Pulse = 95 Observation = 21 Max_Pulse = 127 Run_Pulse = 119 Observation = 20 Max_Pulse = 100 Run_Pulse = 101 Observation = 19 Max_Pulse = 122 Run_Pulse = 120 Observation = 18 Max_Pulse = 118 Run_Pulse = 113 Observation = 17 Max_Pulse = 119 Run_Pulse = 117 Observation = 16 Max_Pulse = 113 Run_Pulse = 111 Observation = 15 Max_Pulse = 114 Run_Pulse = 110 Observation = 14 Max_Pulse = 118 Run_Pulse = 110 Observation = 13 Max_Pulse = 126 Run_Pulse = 125 Observation = 12 Max_Pulse = 102 Run_Pulse = 103 Observation = 11 Max_Pulse = 137 Run_Pulse = 134 Observation = 10 Max_Pulse = 107 Run_Pulse = 107 Observation = 9 Max_Pulse = 114 Run_Pulse = 110 Observation = 8 Max_Pulse = 106 Run_Pulse = 103 Observation = 7 Max_Pulse = 121 Run_Pulse = 118 Observation = 6 Max_Pulse = 115 Run_Pulse = 110 Observation = 5 Max_Pulse = 111 Run_Pulse = 108 Observation = 4 Max_Pulse = 115 Run_Pulse = 105 Observation = 3 Max_Pulse = 107 Run_Pulse = 110 Observation = 2 Max_Pulse = 124 Run_Pulse = 121 Observation = 1 Run_Pulse = 124 Age = 79 Observation = 50 Run_Pulse = 108 Age = 31 Observation = 49 Run_Pulse = 127 Age = 46 Observation = 48 Run_Pulse = 108 Age = 59 Observation = 47 Run_Pulse = 104 Age = 31 Observation = 46 Run_Pulse = 115 Age = 49 Observation = 45 Run_Pulse = 103 Age = 52 Observation = 44 Run_Pulse = 92 Age = 49 Observation = 43 Run_Pulse = 125 Age = 34 Observation = 42 Run_Pulse = 122 Age = 41 Observation = 41 Run_Pulse = 108 Age = 55 Observation = 40 Run_Pulse = 118 Age = 56 Observation = 39 Run_Pulse = 111 Age = 31 Observation = 38 Run_Pulse = 141 Age = 64 Observation = 37 Run_Pulse = 127 Age = 64 Observation = 36 Run_Pulse = 109 Age = 60 Observation = 35 Run_Pulse = 112 Age = 69 Observation = 34 Run_Pulse = 108 Age = 48 Observation = 33 Run_Pulse = 104 Age = 44 Observation = 32 Run_Pulse = 116 Age = 26 Observation = 31 Run_Pulse = 104 Age = 23 Observation = 30 Run_Pulse = 119 Age = 53 Observation = 29 Run_Pulse = 114 Age = 57 Observation = 28 Run_Pulse = 120 Age = 68 Observation = 27 Run_Pulse = 105 Age = 43 Observation = 26 Run_Pulse = 111 Age = 73 Observation = 25 Run_Pulse = 117 Age = 36 Observation = 24 Run_Pulse = 116 Age = 73 Observation = 23 Run_Pulse = 108 Age = 84 Observation = 22 Run_Pulse = 95 Age = 26 Observation = 21 Run_Pulse = 119 Age = 81 Observation = 20 Run_Pulse = 101 Age = 31 Observation = 19 Run_Pulse = 120 Age = 43 Observation = 18 Run_Pulse = 113 Age = 49 Observation = 17 Run_Pulse = 117 Age = 48 Observation = 16 Run_Pulse = 111 Age = 54 Observation = 15 Run_Pulse = 110 Age = 51 Observation = 14 Run_Pulse = 110 Age = 19 Observation = 13 Run_Pulse = 125 Age = 63 Observation = 12 Run_Pulse = 103 Age = 63 Observation = 11 Run_Pulse = 134 Age = 49 Observation = 10 Run_Pulse = 107 Age = 35 Observation = 9 Run_Pulse = 110 Age = 30 Observation = 8 Run_Pulse = 103 Age = 64 Observation = 7 Run_Pulse = 118 Age = 57 Observation = 6 Run_Pulse = 110 Age = 55 Observation = 5 Run_Pulse = 108 Age = 44 Observation = 4 Run_Pulse = 105 Age = 76 Observation = 3 Run_Pulse = 110 Age = 64 Observation = 2 Run_Pulse = 121 Age = 68 Observation = 1 Run_Pulse = 124 Pushups = 10 Observation = 50 Run_Pulse = 108 Pushups = 22 Observation = 49 Run_Pulse = 127 Pushups = 19 Observation = 48 Run_Pulse = 108 Pushups = 25 Observation = 47 Run_Pulse = 104 Pushups = 48 Observation = 46 Run_Pulse = 115 Pushups = 22 Observation = 45 Run_Pulse = 103 Pushups = 27 Observation = 44 Run_Pulse = 92 Pushups = 33 Observation = 43 Run_Pulse = 125 Pushups = 38 Observation = 42 Run_Pulse = 122 Pushups = 17 Observation = 41 Run_Pulse = 108 Pushups = 21 Observation = 40 Run_Pulse = 118 Pushups = 8 Observation = 39 Run_Pulse = 111 Pushups = 30 Observation = 38 Run_Pulse = 141 Pushups = 20 Observation = 37 Run_Pulse = 127 Pushups = 22 Observation = 36 Run_Pulse = 109 Pushups = 36 Observation = 35 Run_Pulse = 112 Pushups = 26 Observation = 34 Run_Pulse = 108 Pushups = 21 Observation = 33 Run_Pulse = 104 Pushups = 1 Observation = 32 Run_Pulse = 116 Pushups = 40 Observation = 31 Run_Pulse = 104 Pushups = 30 Observation = 30 Run_Pulse = 119 Pushups = 9 Observation = 29 Run_Pulse = 114 Pushups = 31 Observation = 28 Run_Pulse = 120 Pushups = 32 Observation = 27 Run_Pulse = 105 Pushups = 33 Observation = 26 Run_Pulse = 111 Pushups = 8 Observation = 25 Run_Pulse = 117 Pushups = 25 Observation = 24 Run_Pulse = 116 Pushups = 12 Observation = 23 Run_Pulse = 108 Pushups = 11 Observation = 22 Run_Pulse = 95 Pushups = 52 Observation = 21 Run_Pulse = 119 Pushups = 16 Observation = 20 Run_Pulse = 101 Pushups = 50 Observation = 19 Run_Pulse = 120 Pushups = 29 Observation = 18 Run_Pulse = 113 Pushups = 11 Observation = 17 Run_Pulse = 117 Pushups = 43 Observation = 16 Run_Pulse = 111 Pushups = 7 Observation = 15 Run_Pulse = 110 Pushups = 23 Observation = 14 Run_Pulse = 110 Pushups = 34 Observation = 13 Run_Pulse = 125 Pushups = 30 Observation = 12 Run_Pulse = 103 Pushups = 51 Observation = 11 Run_Pulse = 134 Pushups = 9 Observation = 10 Run_Pulse = 107 Pushups = 25 Observation = 9 Run_Pulse = 110 Pushups = 48 Observation = 8 Run_Pulse = 103 Pushups = 21 Observation = 7 Run_Pulse = 118 Pushups = 14 Observation = 6 Run_Pulse = 110 Pushups = 24 Observation = 5 Run_Pulse = 108 Pushups = 35 Observation = 4 Run_Pulse = 105 Pushups = 11 Observation = 3 Run_Pulse = 110 Pushups = 36 Observation = 2 Run_Pulse = 121 Pushups = 19 Observation = 1 Run_Pulse = 124 Rest_Pulse = 82 Observation = 50 Run_Pulse = 108 Rest_Pulse = 74 Observation = 49 Run_Pulse = 127 Rest_Pulse = 84 Observation = 48 Run_Pulse = 108 Rest_Pulse = 71 Observation = 47 Run_Pulse = 104 Rest_Pulse = 55 Observation = 46 Run_Pulse = 115 Rest_Pulse = 61 Observation = 45 Run_Pulse = 103 Rest_Pulse = 52 Observation = 44 Run_Pulse = 92 Rest_Pulse = 51 Observation = 43 Run_Pulse = 125 Rest_Pulse = 73 Observation = 42 Run_Pulse = 122 Rest_Pulse = 74 Observation = 41 Run_Pulse = 108 Rest_Pulse = 71 Observation = 40 Run_Pulse = 118 Rest_Pulse = 74 Observation = 39 Run_Pulse = 111 Rest_Pulse = 65 Observation = 38 Run_Pulse = 141 Rest_Pulse = 85 Observation = 37 Run_Pulse = 127 Rest_Pulse = 78 Observation = 36 Run_Pulse = 109 Rest_Pulse = 65 Observation = 35 Run_Pulse = 112 Rest_Pulse = 69 Observation = 34 Run_Pulse = 108 Rest_Pulse = 59 Observation = 33 Run_Pulse = 104 Rest_Pulse = 59 Observation = 32 Run_Pulse = 116 Rest_Pulse = 55 Observation = 31 Run_Pulse = 104 Rest_Pulse = 58 Observation = 30 Run_Pulse = 119 Rest_Pulse = 66 Observation = 29 Run_Pulse = 114 Rest_Pulse = 67 Observation = 28 Run_Pulse = 120 Rest_Pulse = 70 Observation = 27 Run_Pulse = 105 Rest_Pulse = 70 Observation = 26 Run_Pulse = 111 Rest_Pulse = 67 Observation = 25 Run_Pulse = 117 Rest_Pulse = 66 Observation = 24 Run_Pulse = 116 Rest_Pulse = 77 Observation = 23 Run_Pulse = 108 Rest_Pulse = 75 Observation = 22 Run_Pulse = 95 Rest_Pulse = 49 Observation = 21 Run_Pulse = 119 Rest_Pulse = 86 Observation = 20 Run_Pulse = 101 Rest_Pulse = 55 Observation = 19 Run_Pulse = 120 Rest_Pulse = 78 Observation = 18 Run_Pulse = 113 Rest_Pulse = 68 Observation = 17 Run_Pulse = 117 Rest_Pulse = 77 Observation = 16 Run_Pulse = 111 Rest_Pulse = 59 Observation = 15 Run_Pulse = 110 Rest_Pulse = 66 Observation = 14 Run_Pulse = 110 Rest_Pulse = 65 Observation = 13 Run_Pulse = 125 Rest_Pulse = 73 Observation = 12 Run_Pulse = 103 Rest_Pulse = 55 Observation = 11 Run_Pulse = 134 Rest_Pulse = 88 Observation = 10 Run_Pulse = 107 Rest_Pulse = 55 Observation = 9 Run_Pulse = 110 Rest_Pulse = 60 Observation = 8 Run_Pulse = 103 Rest_Pulse = 69 Observation = 7 Run_Pulse = 118 Rest_Pulse = 74 Observation = 6 Run_Pulse = 110 Rest_Pulse = 76 Observation = 5 Run_Pulse = 108 Rest_Pulse = 59 Observation = 4 Run_Pulse = 105 Rest_Pulse = 74 Observation = 3 Run_Pulse = 110 Rest_Pulse = 61 Observation = 2 Run_Pulse = 121 Rest_Pulse = 75 Observation = 1 Run_Pulse = 124 Max_Pulse = 124 Observation = 50 Run_Pulse = 108 Max_Pulse = 118 Observation = 49 Run_Pulse = 127 Max_Pulse = 130 Observation = 48 Run_Pulse = 108 Max_Pulse = 110 Observation = 47 Run_Pulse = 104 Max_Pulse = 109 Observation = 46 Run_Pulse = 115 Max_Pulse = 118 Observation = 45 Run_Pulse = 103 Max_Pulse = 104 Observation = 44 Run_Pulse = 92 Max_Pulse = 94 Observation = 43 Run_Pulse = 125 Max_Pulse = 120 Observation = 42 Run_Pulse = 122 Max_Pulse = 127 Observation = 41 Run_Pulse = 108 Max_Pulse = 112 Observation = 40 Run_Pulse = 118 Max_Pulse = 122 Observation = 39 Run_Pulse = 111 Max_Pulse = 111 Observation = 38 Run_Pulse = 141 Max_Pulse = 137 Observation = 37 Run_Pulse = 127 Max_Pulse = 126 Observation = 36 Run_Pulse = 109 Max_Pulse = 111 Observation = 35 Run_Pulse = 112 Max_Pulse = 112 Observation = 34 Run_Pulse = 108 Max_Pulse = 109 Observation = 33 Run_Pulse = 104 Max_Pulse = 107 Observation = 32 Run_Pulse = 116 Max_Pulse = 114 Observation = 31 Run_Pulse = 104 Max_Pulse = 105 Observation = 30 Run_Pulse = 119 Max_Pulse = 127 Observation = 29 Run_Pulse = 114 Max_Pulse = 111 Observation = 28 Run_Pulse = 120 Max_Pulse = 125 Observation = 27 Run_Pulse = 105 Max_Pulse = 111 Observation = 26 Run_Pulse = 111 Max_Pulse = 112 Observation = 25 Run_Pulse = 117 Max_Pulse = 117 Observation = 24 Run_Pulse = 116 Max_Pulse = 119 Observation = 23 Run_Pulse = 108 Max_Pulse = 114 Observation = 22 Run_Pulse = 95 Max_Pulse = 100 Observation = 21 Run_Pulse = 119 Max_Pulse = 127 Observation = 20 Run_Pulse = 101 Max_Pulse = 100 Observation = 19 Run_Pulse = 120 Max_Pulse = 122 Observation = 18 Run_Pulse = 113 Max_Pulse = 118 Observation = 17 Run_Pulse = 117 Max_Pulse = 119 Observation = 16 Run_Pulse = 111 Max_Pulse = 113 Observation = 15 Run_Pulse = 110 Max_Pulse = 114 Observation = 14 Run_Pulse = 110 Max_Pulse = 118 Observation = 13 Run_Pulse = 125 Max_Pulse = 126 Observation = 12 Run_Pulse = 103 Max_Pulse = 102 Observation = 11 Run_Pulse = 134 Max_Pulse = 137 Observation = 10 Run_Pulse = 107 Max_Pulse = 107 Observation = 9 Run_Pulse = 110 Max_Pulse = 114 Observation = 8 Run_Pulse = 103 Max_Pulse = 106 Observation = 7 Run_Pulse = 118 Max_Pulse = 121 Observation = 6 Run_Pulse = 110 Max_Pulse = 115 Observation = 5 Run_Pulse = 108 Max_Pulse = 111 Observation = 4 Run_Pulse = 105 Max_Pulse = 115 Observation = 3 Run_Pulse = 110 Max_Pulse = 107 Observation = 2 Run_Pulse = 121 Max_Pulse = 124 Observation = 1 Run_Pulse = 140 Percent = 2 Run_Pulse = 140 Percent = 2 Run_Pulse = 132 Percent = 2 Run_Pulse = 132 Percent = 2 Run_Pulse = 124 Percent = 18 Run_Pulse = 124 Percent = 18 Run_Pulse = 116 Percent = 24 Run_Pulse = 116 Percent = 24 Run_Pulse = 108 Percent = 42 Run_Pulse = 108 Percent = 42 Run_Pulse = 100 Percent = 8 Run_Pulse = 100 Percent = 8 Run_Pulse = 92 Percent = 4 Run_Pulse = 92 Percent = 4
Scatter Plot Matrix
  • Pearson correlation coefficient measures the strength of the relationship between two variables. Generate a matrix of scatter plots and include histograms on the diagonal of the matrix. The p-value in the correlation tables is the probability that you would obtain a correlation with an absolute value as large as or larger than the one you obtained by chance alone, given that the true population correlation between your two variables is actually 0.
  • Spearman correlation is one of the most popular nonparametric alternatives to a Pearson correlation. The Spearman method substitutes ranks for the two variables and then computes a correlation on the ranks. When there are outliers on your scatter plot, you may want to consider computing Spearman correlations.
  • The relationship between Max_Pulse and Rest_Pulse is pretty strong at 0.83112, with a significant p-value of <.0001. The inverse relationship between Age and Pushups is somewhat significant at -0.49191, with a significant p-value = 0.0003.

Practice: Correlation and Scatter Plot Matrices - Height / Weight / Cholesterol

SAS Code, click to expand

SAS Code:

#  (&path1 and biostats libname previously defined)
/* Practice: Correlation and Scatter Plot Matrices - Heart / Weight - start 10.2 */
title1 "Practice: Correlation and Scatter Plot Matrices - Heart / Weight";
proc corr data=biostats.heart pearson spearman nosimple 
        plots(maxpoints=none)=matrix(histogram);
    var Height Weight Cholesterol;
run;

/* We see some relationship between Height and Weight, but not much for Height and Cholesterol, or Weight and Cholesterol. */
title1;
/* Practice: Correlation and Scatter Plot Matrices - Heart / Weight - end 10.2 */

SAS Output

Results: biostats_by_ex_SAScode.sas

Results: biostats_by_ex_SAScode.sas

Practice: Correlation and Scatter Plot Matrices - Heart / Weight

The Corr Procedure

Variables Information

3 Variables: Height Weight Cholesterol

Pearson Correlations

Pearson Correlation Coefficients
Prob > |r| under H0: Rho=0
Number of Observations
  Height Weight Cholesterol
Height
1.00000
 
5203
0.51739
<.0001
5199
-0.07959
<.0001
5051
Weight
0.51739
<.0001
5199
1.00000
 
5203
0.07243
<.0001
5051
Cholesterol
-0.07959
<.0001
5051
0.07243
<.0001
5051
1.00000
 
5057

Spearman Correlations

Spearman Correlation Coefficients
Prob > |r| under H0: Rho=0
Number of Observations
  Height Weight Cholesterol
Height
1.00000
 
5203
0.52969
<.0001
5199
-0.07054
<.0001
5051
Weight
0.52969
<.0001
5199
1.00000
 
5203
0.09730
<.0001
5051
Cholesterol
-0.07054
<.0001
5051
0.09730
<.0001
5051
1.00000
 
5057

Scatter Plot Matrix

Height = 76.5 Percent = 0.0577 Height = 76.5 Percent = 0.0577 Height = 75.5 Percent = 0.0961 Height = 75.5 Percent = 0.0961 Height = 74.5 Percent = 0.2691 Height = 74.5 Percent = 0.2691 Height = 73.5 Percent = 0.7303 Height = 73.5 Percent = 0.7303 Height = 72.5 Percent = 1.7298 Height = 72.5 Percent = 1.7298 Height = 71.5 Percent = 2.4601 Height = 71.5 Percent = 2.4601 Height = 70.5 Percent = 3.6902 Height = 70.5 Percent = 3.6902 Height = 69.5 Percent = 5.5545 Height = 69.5 Percent = 5.5545 Height = 68.5 Percent = 6.8999 Height = 68.5 Percent = 6.8999 Height = 67.5 Percent = 8.0915 Height = 67.5 Percent = 8.0915 Height = 66.5 Percent = 7.8032 Height = 66.5 Percent = 7.8032 Height = 65.5 Percent = 10.398 Height = 65.5 Percent = 10.398 Height = 64.5 Percent = 9.8597 Height = 64.5 Percent = 9.8597 Height = 63.5 Percent = 9.9558 Height = 63.5 Percent = 9.9558 Height = 62.5 Percent = 10.974 Height = 62.5 Percent = 10.974 Height = 61.5 Percent = 8.1299 Height = 61.5 Percent = 8.1299 Height = 60.5 Percent = 5.9773 Height = 60.5 Percent = 5.9773 Height = 59.5 Percent = 3.9593 Height = 59.5 Percent = 3.9593 Height = 58.5 Percent = 1.9988 Height = 58.5 Percent = 1.9988 Height = 57.5 Percent = 0.615 Height = 57.5 Percent = 0.615 Height = 56.5 Percent = 0.5574 Height = 56.5 Percent = 0.5574 Height = 55.5 Percent = 0.1153 Height = 55.5 Percent = 0.1153 Height = 54.5 Percent = 0.0384 Height = 54.5 Percent = 0.0384 Height = 53.5 Percent = 0.0192 Height = 53.5 Percent = 0.0192 Height = 52.5 Percent = 0 Height = 52.5 Percent = 0 Height = 51.5 Percent = 0.0192 Height = 51.5 Percent = 0.0192 Weight = 300 Percent = 0.0384 Weight = 300 Percent = 0.0384 Weight = 290 Percent = 0.0192 Weight = 290 Percent = 0.0192 Weight = 280 Percent = 0.0577 Weight = 280 Percent = 0.0577 Weight = 270 Percent = 0.0577 Weight = 270 Percent = 0.0577 Weight = 260 Percent = 0.0769 Weight = 260 Percent = 0.0769 Weight = 250 Percent = 0.1153 Weight = 250 Percent = 0.1153 Weight = 240 Percent = 0.4805 Weight = 240 Percent = 0.4805 Weight = 230 Percent = 0.6342 Weight = 230 Percent = 0.6342 Weight = 220 Percent = 1.134 Weight = 220 Percent = 1.134 Weight = 210 Percent = 2.0757 Weight = 210 Percent = 2.0757 Weight = 200 Percent = 3.4019 Weight = 200 Percent = 3.4019 Weight = 190 Percent = 5.9004 Weight = 190 Percent = 5.9004 Weight = 180 Percent = 8.745 Weight = 180 Percent = 8.745 Weight = 170 Percent = 10.263 Weight = 170 Percent = 10.263 Weight = 160 Percent = 10.936 Weight = 160 Percent = 10.936 Weight = 150 Percent = 13.761 Weight = 150 Percent = 13.761 Weight = 140 Percent = 14.472 Weight = 140 Percent = 14.472 Weight = 130 Percent = 11.935 Weight = 130 Percent = 11.935 Weight = 120 Percent = 8.6873 Weight = 120 Percent = 8.6873 Weight = 110 Percent = 4.9202 Weight = 110 Percent = 4.9202 Weight = 100 Percent = 1.7682 Weight = 100 Percent = 1.7682 Weight = 90 Percent = 0.4228 Weight = 90 Percent = 0.4228 Weight = 80 Percent = 0.0384 Weight = 80 Percent = 0.0384 Weight = 70 Percent = 0.0577 Weight = 70 Percent = 0.0577 Cholesterol = 560 Percent = 0.0198 Cholesterol = 560 Percent = 0.0198 Cholesterol = 540 Percent = 0.0198 Cholesterol = 540 Percent = 0.0198 Cholesterol = 520 Percent = 0 Cholesterol = 520 Percent = 0 Cholesterol = 500 Percent = 0.0395 Cholesterol = 500 Percent = 0.0395 Cholesterol = 480 Percent = 0.0198 Cholesterol = 480 Percent = 0.0198 Cholesterol = 460 Percent = 0 Cholesterol = 460 Percent = 0 Cholesterol = 440 Percent = 0.0395 Cholesterol = 440 Percent = 0.0395 Cholesterol = 420 Percent = 0.0791 Cholesterol = 420 Percent = 0.0791 Cholesterol = 400 Percent = 0.0791 Cholesterol = 400 Percent = 0.0791 Cholesterol = 380 Percent = 0.178 Cholesterol = 380 Percent = 0.178 Cholesterol = 360 Percent = 0.5932 Cholesterol = 360 Percent = 0.5932 Cholesterol = 340 Percent = 1.2062 Cholesterol = 340 Percent = 1.2062 Cholesterol = 320 Percent = 2.1752 Cholesterol = 320 Percent = 2.1752 Cholesterol = 300 Percent = 4.4691 Cholesterol = 300 Percent = 4.4691 Cholesterol = 280 Percent = 7.5934 Cholesterol = 280 Percent = 7.5934 Cholesterol = 260 Percent = 11.232 Cholesterol = 260 Percent = 11.232 Cholesterol = 240 Percent = 16.789 Cholesterol = 240 Percent = 16.789 Cholesterol = 220 Percent = 17.876 Cholesterol = 220 Percent = 17.876 Cholesterol = 200 Percent = 18.193 Cholesterol = 200 Percent = 18.193 Cholesterol = 180 Percent = 11.865 Cholesterol = 180 Percent = 11.865 Cholesterol = 160 Percent = 6.1103 Cholesterol = 160 Percent = 6.1103 Cholesterol = 140 Percent = 1.1865 Cholesterol = 140 Percent = 1.1865 Cholesterol = 120 Percent = 0.2175 Cholesterol = 120 Percent = 0.2175 Cholesterol = 100 Percent = 0.0198 Cholesterol = 100 Percent = 0.0198
Scatter Plot Matrix
  • We see some relationship between Height and Weight, but not much for Height and Cholesterol, or Weight and Cholesterol.

Chapter 11: Simple and Multiple Regression

Simple Linear Regression.

SAS Code, click to expand

SAS Code:

#  (&path1 and biostats libname previously defined)
/*** Chapter 11: Simple and Multiple Regression ***/

/* Simple Linear Regression - generated code - start */
ods noproctitle;
ods graphics / imagemap=on;
title1 "Simple Linear Regression"; 
proc reg data=work.exercise alpha=0.05 
  plots(only)=(diagnostics(unpack) residuals(unpack) fitplot observedbypredicted);
  model Run_Pulse=Rest_Pulse /;
  run;
quit;

/* "The mean square due to the model is much larger than the mean square due to error, yielding a very large F-value and a low p-value.  The mean of the dependent variable Run_Pulse is 112.92, and the adjusted R-square is .5710.  (The addition of independent variables in a model causes the value of R-square to increase even if independent variables are only randomly 
correlated with the dependent variable; Adj R-Sq adjusts for the number of independent variables in the model and is a way to compare models with different numbers of independent variables.)"  
  
The model is: Run_Pulse = 63.15163 + (.73297 * Rest_Pulse).  

"The Residual by Predicted for Run_Pulse plot shows points that seem mostly random.  The spread of the points around 0 does not tend to increase or decrease with different values of Run_Pulse."  

"The Cook's D for Run_Pulse plot shows the Cook's D value for each observation, where larger values indicates the more influential points."

"The Q-Q Plot of Residuals for Run_Pulse shows the distribution of the residuals, where the points fall very closely around the straight line."

"The shaded portion of the Fit plot for Run_Pulse graph represents the 95% confidence limit for the prediction of Run_Pulse for any given value of Rest_Pulse.  The other, wider confidence limits marked with dashed lines are for individual data points.  Given a value of Rest_Pulse, you are 95% confident that a random data point will be within these limits."  */

title1; 
/* Simple Linear Regression - generated code - end */

SAS Output

Results: biostats_by_ex_SAScode.sas

Results: biostats_by_ex_SAScode.sas

Simple Linear Regression

Model: MODEL1

Dependent Variable: Run_Pulse Run_Pulse

The Reg Procedure

MODEL1

Fit

Run_Pulse

Number of Observations

Number of Observations Read 50
Number of Observations Used 50

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 1 2484.46062 2484.46062 66.21 <.0001
Error 48 1801.21938 37.52540    
Corrected Total 49 4285.68000      

Fit Statistics

Root MSE 6.12580 R-Square 0.5797
Dependent Mean 112.92000 Adj R-Sq 0.5710
Coeff Var 5.42490    

Parameter Estimates

Parameter Estimates
Variable Label DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
Intercept Intercept 1 63.15163 6.17751 10.22 <.0001
Rest_Pulse Rest_Pulse 1 0.73297 0.09008 8.14 <.0001

Simple Linear Regression

Model: MODEL1

Dependent Variable: Run_Pulse Run_Pulse

Observation-wise Statistics

Run_Pulse

Diagnostic Plots

Residual Histogram

Residual = 21.221 Percent = 0.0658 Residual = 21.003 Percent = 0.0847 Residual = 21.003 Percent = 0.0847 Residual = 20.785 Percent = 0.108 Residual = 20.785 Percent = 0.108 Residual = 20.566 Percent = 0.1364 Residual = 20.566 Percent = 0.1364 Residual = 20.348 Percent = 0.1707 Residual = 20.348 Percent = 0.1707 Residual = 20.13 Percent = 0.2115 Residual = 20.13 Percent = 0.2115 Residual = 19.912 Percent = 0.2597 Residual = 19.912 Percent = 0.2597 Residual = 19.693 Percent = 0.3158 Residual = 19.693 Percent = 0.3158 Residual = 19.475 Percent = 0.3805 Residual = 19.475 Percent = 0.3805 Residual = 19.257 Percent = 0.4543 Residual = 19.257 Percent = 0.4543 Residual = 19.038 Percent = 0.5374 Residual = 19.038 Percent = 0.5374 Residual = 18.82 Percent = 0.6299 Residual = 18.82 Percent = 0.6299 Residual = 18.602 Percent = 0.7317 Residual = 18.602 Percent = 0.7317 Residual = 18.384 Percent = 0.8425 Residual = 18.384 Percent = 0.8425 Residual = 18.165 Percent = 0.9616 Residual = 18.165 Percent = 0.9616 Residual = 17.947 Percent = 1.0882 Residual = 17.947 Percent = 1.0882 Residual = 17.729 Percent = 1.2211 Residual = 17.729 Percent = 1.2211 Residual = 16.856 Percent = 1.7856 Residual = 16.856 Percent = 1.7856 Residual = 16.419 Percent = 2.0637 Residual = 16.419 Percent = 2.0637 Residual = 16.201 Percent = 2.1956 Residual = 16.201 Percent = 2.1956 Residual = 15.983 Percent = 2.3207 Residual = 15.983 Percent = 2.3207 Residual = 15.765 Percent = 2.438 Residual = 15.765 Percent = 2.438 Residual = 15.546 Percent = 2.5463 Residual = 15.546 Percent = 2.5463 Residual = 15.328 Percent = 2.645 Residual = 15.328 Percent = 2.645 Residual = 15.11 Percent = 2.734 Residual = 15.11 Percent = 2.734 Residual = 14.892 Percent = 2.8132 Residual = 14.892 Percent = 2.8132 Residual = 14.673 Percent = 2.8832 Residual = 14.673 Percent = 2.8832 Residual = 14.455 Percent = 2.9447 Residual = 14.455 Percent = 2.9447 Residual = 14.237 Percent = 2.9991 Residual = 14.237 Percent = 2.9991 Residual = 14.018 Percent = 3.0481 Residual = 14.018 Percent = 3.0481 Residual = 13.582 Percent = 3.1384 Residual = 13.582 Percent = 3.1384 Residual = 13.364 Percent = 3.1852 Residual = 13.364 Percent = 3.1852 Residual = 13.145 Percent = 3.2374 Residual = 13.145 Percent = 3.2374 Residual = 12.927 Percent = 3.299 Residual = 12.927 Percent = 3.299 Residual = 12.709 Percent = 3.374 Residual = 12.709 Percent = 3.374 Residual = 12.491 Percent = 3.4669 Residual = 12.491 Percent = 3.4669 Residual = 12.272 Percent = 3.5826 Residual = 12.272 Percent = 3.5826 Residual = 12.054 Percent = 3.7259 Residual = 12.054 Percent = 3.7259 Residual = 11.836 Percent = 3.9018 Residual = 11.836 Percent = 3.9018 Residual = 11.618 Percent = 4.115 Residual = 11.618 Percent = 4.115 Residual = 11.399 Percent = 4.3701 Residual = 11.399 Percent = 4.3701 Residual = 11.181 Percent = 4.6708 Residual = 11.181 Percent = 4.6708 Residual = 10.963 Percent = 5.0205 Residual = 10.963 Percent = 5.0205 Residual = 10.745 Percent = 5.4215 Residual = 10.745 Percent = 5.4215 Residual = 10.526 Percent = 5.8748 Residual = 10.526 Percent = 5.8748 Residual = 10.308 Percent = 6.3805 Residual = 10.308 Percent = 6.3805 Residual = 10.09 Percent = 6.9373 Residual = 10.09 Percent = 6.9373 Residual = 9.8715 Percent = 7.5424 Residual = 9.8715 Percent = 7.5424 Residual = 9.6532 Percent = 8.192 Residual = 9.6532 Percent = 8.192 Residual = 9.435 Percent = 8.8807 Residual = 9.435 Percent = 8.8807 Residual = 9.2167 Percent = 9.6022 Residual = 9.2167 Percent = 9.6022 Residual = 8.1254 Percent = 13.439 Residual = 8.1254 Percent = 13.439 Residual = 7.6889 Percent = 14.939 Residual = 7.6889 Percent = 14.939 Residual = 7.4706 Percent = 15.658 Residual = 7.4706 Percent = 15.658 Residual = 7.2524 Percent = 16.351 Residual = 7.2524 Percent = 16.351 Residual = 7.0341 Percent = 17.017 Residual = 7.0341 Percent = 17.017 Residual = 6.8159 Percent = 17.656 Residual = 6.8159 Percent = 17.656 Residual = 6.5976 Percent = 18.271 Residual = 6.5976 Percent = 18.271 Residual = 6.3793 Percent = 18.865 Residual = 6.3793 Percent = 18.865 Residual = 5.7246 Percent = 20.579 Residual = 5.7246 Percent = 20.579 Residual = 5.288 Percent = 21.734 Residual = 5.288 Percent = 21.734 Residual = 5.0698 Percent = 22.337 Residual = 5.0698 Percent = 22.337 Residual = 4.8515 Percent = 22.967 Residual = 4.8515 Percent = 22.967 Residual = 4.6332 Percent = 23.628 Residual = 4.6332 Percent = 23.628 Residual = 4.415 Percent = 24.324 Residual = 4.415 Percent = 24.324 Residual = 4.1967 Percent = 25.058 Residual = 4.1967 Percent = 25.058 Residual = 3.9785 Percent = 25.829 Residual = 3.9785 Percent = 25.829 Residual = 2.4506 Percent = 31.86 Residual = 2.4506 Percent = 31.86 Residual = 2.2324 Percent = 32.701 Residual = 2.2324 Percent = 32.701 Residual = 2.0141 Percent = 33.499 Residual = 2.0141 Percent = 33.499 Residual = 1.7959 Percent = 34.242 Residual = 1.7959 Percent = 34.242 Residual = 1.5776 Percent = 34.917 Residual = 1.5776 Percent = 34.917 Residual = 1.3593 Percent = 35.511 Residual = 1.3593 Percent = 35.511 Residual = 1.1411 Percent = 36.013 Residual = 1.1411 Percent = 36.013 Residual = 0.9228 Percent = 36.414 Residual = 0.9228 Percent = 36.414 Residual = 0.7046 Percent = 36.704 Residual = 0.7046 Percent = 36.704 Residual = 0.4863 Percent = 36.876 Residual = 0.4863 Percent = 36.876 Residual = 0.268 Percent = 36.925 Residual = 0.268 Percent = 36.925 Residual = 0.0498 Percent = 36.846 Residual = 0.0498 Percent = 36.846 Residual = -0.168 Percent = 36.637 Residual = -0.168 Percent = 36.637 Residual = -0.387 Percent = 36.299 Residual = -0.387 Percent = 36.299 Residual = -0.605 Percent = 35.831 Residual = -0.605 Percent = 35.831 Residual = -0.823 Percent = 35.238 Residual = -0.823 Percent = 35.238 Residual = -1.042 Percent = 34.523 Residual = -1.042 Percent = 34.523 Residual = -1.26 Percent = 33.695 Residual = -1.26 Percent = 33.695 Residual = -1.478 Percent = 32.76 Residual = -1.478 Percent = 32.76 Residual = -1.696 Percent = 31.73 Residual = -1.696 Percent = 31.73 Residual = -1.915 Percent = 30.616 Residual = -1.915 Percent = 30.616 Residual = -2.133 Percent = 29.431 Residual = -2.133 Percent = 29.431 Residual = -2.351 Percent = 28.19 Residual = -2.351 Percent = 28.19 Residual = -3.006 Percent = 24.3 Residual = -3.006 Percent = 24.3 Residual = -3.442 Percent = 21.739 Residual = -3.442 Percent = 21.739 Residual = -3.661 Percent = 20.522 Residual = -3.661 Percent = 20.522 Residual = -3.879 Percent = 19.368 Residual = -3.879 Percent = 19.368 Residual = -4.097 Percent = 18.292 Residual = -4.097 Percent = 18.292 Residual = -4.315 Percent = 17.307 Residual = -4.315 Percent = 17.307 Residual = -4.534 Percent = 16.424 Residual = -4.534 Percent = 16.424 Residual = -4.752 Percent = 15.65 Residual = -4.752 Percent = 15.65 Residual = -4.97 Percent = 14.992 Residual = -4.97 Percent = 14.992 Residual = -5.188 Percent = 14.451 Residual = -5.188 Percent = 14.451 Residual = -5.407 Percent = 14.027 Residual = -5.407 Percent = 14.027 Residual = -5.625 Percent = 13.717 Residual = -5.625 Percent = 13.717 Residual = -5.843 Percent = 13.514 Residual = -5.843 Percent = 13.514 Residual = -6.062 Percent = 13.41 Residual = -6.062 Percent = 13.41 Residual = -6.28 Percent = 13.394 Residual = -6.28 Percent = 13.394 Residual = -6.498 Percent = 13.452 Residual = -6.498 Percent = 13.452 Residual = -6.716 Percent = 13.572 Residual = -6.716 Percent = 13.572 Residual = -6.935 Percent = 13.738 Residual = -6.935 Percent = 13.738 Residual = -7.153 Percent = 13.934 Residual = -7.153 Percent = 13.934 Residual = -7.589 Percent = 14.353 Residual = -7.589 Percent = 14.353 Residual = -7.808 Percent = 14.547 Residual = -7.808 Percent = 14.547 Residual = -8.026 Percent = 14.713 Residual = -8.026 Percent = 14.713 Residual = -8.244 Percent = 14.837 Residual = -8.244 Percent = 14.837 Residual = -8.462 Percent = 14.911 Residual = -8.462 Percent = 14.911 Residual = -8.681 Percent = 14.927 Residual = -8.681 Percent = 14.927 Residual = -8.899 Percent = 14.877 Residual = -8.899 Percent = 14.877 Residual = -9.117 Percent = 14.759 Residual = -9.117 Percent = 14.759 Residual = -9.335 Percent = 14.57 Residual = -9.335 Percent = 14.57 Residual = -9.554 Percent = 14.311 Residual = -9.554 Percent = 14.311 Residual = -9.772 Percent = 13.983 Residual = -9.772 Percent = 13.983 Residual = -9.99 Percent = 13.59 Residual = -9.99 Percent = 13.59 Residual = -10.21 Percent = 13.137 Residual = -10.21 Percent = 13.137 Residual = -10.43 Percent = 12.63 Residual = -10.43 Percent = 12.63 Residual = -10.65 Percent = 12.076 Residual = -10.65 Percent = 12.076 Residual = -10.86 Percent = 11.484 Residual = -10.86 Percent = 11.484 Residual = -11.08 Percent = 10.861 Residual = -11.08 Percent = 10.861 Residual = -11.95 Percent = 8.2272 Residual = -11.95 Percent = 8.2272 Residual = -12.39 Percent = 6.9299 Residual = -12.39 Percent = 6.9299 Residual = -12.61 Percent = 6.3081 Residual = -12.61 Percent = 6.3081 Residual = -12.83 Percent = 5.7106 Residual = -12.83 Percent = 5.7106 Residual = -13.05 Percent = 5.1411 Residual = -13.05 Percent = 5.1411 Residual = -13.26 Percent = 4.6026 Residual = -13.26 Percent = 4.6026 Residual = -13.48 Percent = 4.0972 Residual = -13.48 Percent = 4.0972 Residual = -13.7 Percent = 3.6264 Residual = -13.7 Percent = 3.6264 Residual = -13.92 Percent = 3.191 Residual = -13.92 Percent = 3.191 Residual = -14.14 Percent = 2.7912 Residual = -14.14 Percent = 2.7912 Residual = -14.36 Percent = 2.4267 Residual = -14.36 Percent = 2.4267 Residual = -14.57 Percent = 2.0968 Residual = -14.57 Percent = 2.0968 Residual = -14.79 Percent = 1.8003 Residual = -14.79 Percent = 1.8003 Residual = -15.01 Percent = 1.5357 Residual = -15.01 Percent = 1.5357 Residual = -15.23 Percent = 1.3013 Residual = -15.23 Percent = 1.3013 Residual = -15.45 Percent = 1.0952 Residual = -15.45 Percent = 1.0952 Residual = -15.67 Percent = 0.9153 Residual = -15.67 Percent = 0.9153 Residual = -15.88 Percent = 0.7596 Residual = -15.88 Percent = 0.7596 Residual = -16.1 Percent = 0.6257 Residual = -16.1 Percent = 0.6257 Residual = -16.32 Percent = 0.5117 Residual = -16.32 Percent = 0.5117 Residual = -16.54 Percent = 0.4152 Residual = -16.54 Percent = 0.4152 Residual = -16.76 Percent = 0.3343 Residual = -16.76 Percent = 0.3343 Residual = -16.97 Percent = 0.2671 Residual = -16.97 Percent = 0.2671 Residual = -17.19 Percent = 0.2117 Residual = -17.19 Percent = 0.2117 Residual = -17.41 Percent = 0.1664 Residual = -17.41 Percent = 0.1664 Residual = -17.63 Percent = 0.1297 Residual = -17.63 Percent = 0.1297 Residual = -17.85 Percent = 0.1003 Residual = -17.85 Percent = 0.1003 Residual = -18.07 Percent = 0.0769 Residual = 18.189 Percent = 0.3655 Residual = 18.005 Percent = 0.4001 Residual = 18.005 Percent = 0.4001 Residual = 17.821 Percent = 0.4376 Residual = 17.821 Percent = 0.4376 Residual = 17.638 Percent = 0.4781 Residual = 17.638 Percent = 0.4781 Residual = 17.454 Percent = 0.5219 Residual = 17.454 Percent = 0.5219 Residual = 17.27 Percent = 0.5692 Residual = 17.27 Percent = 0.5692 Residual = 17.087 Percent = 0.6203 Residual = 17.087 Percent = 0.6203 Residual = 16.903 Percent = 0.6753 Residual = 16.903 Percent = 0.6753 Residual = 16.719 Percent = 0.7344 Residual = 16.719 Percent = 0.7344 Residual = 16.535 Percent = 0.7981 Residual = 16.535 Percent = 0.7981 Residual = 16.352 Percent = 0.8664 Residual = 16.352 Percent = 0.8664 Residual = 16.168 Percent = 0.9398 Residual = 16.168 Percent = 0.9398 Residual = 15.984 Percent = 1.0184 Residual = 15.984 Percent = 1.0184 Residual = 15.8 Percent = 1.1026 Residual = 15.8 Percent = 1.1026 Residual = 15.617 Percent = 1.1927 Residual = 15.617 Percent = 1.1927 Residual = 15.433 Percent = 1.2889 Residual = 15.433 Percent = 1.2889 Residual = 15.249 Percent = 1.3916 Residual = 15.249 Percent = 1.3916 Residual = 15.066 Percent = 1.5012 Residual = 15.066 Percent = 1.5012 Residual = 14.882 Percent = 1.6178 Residual = 14.882 Percent = 1.6178 Residual = 14.698 Percent = 1.7419 Residual = 14.698 Percent = 1.7419 Residual = 14.514 Percent = 1.8739 Residual = 14.514 Percent = 1.8739 Residual = 14.331 Percent = 2.0139 Residual = 14.331 Percent = 2.0139 Residual = 14.147 Percent = 2.1625 Residual = 14.147 Percent = 2.1625 Residual = 13.963 Percent = 2.3198 Residual = 13.963 Percent = 2.3198 Residual = 13.779 Percent = 2.4864 Residual = 13.779 Percent = 2.4864 Residual = 13.596 Percent = 2.6624 Residual = 13.596 Percent = 2.6624 Residual = 13.412 Percent = 2.8483 Residual = 13.412 Percent = 2.8483 Residual = 13.228 Percent = 3.0444 Residual = 13.228 Percent = 3.0444 Residual = 13.045 Percent = 3.251 Residual = 13.045 Percent = 3.251 Residual = 12.861 Percent = 3.4684 Residual = 12.861 Percent = 3.4684 Residual = 12.677 Percent = 3.697 Residual = 12.677 Percent = 3.697 Residual = 12.493 Percent = 3.937 Residual = 12.493 Percent = 3.937 Residual = 12.31 Percent = 4.1888 Residual = 12.31 Percent = 4.1888 Residual = 12.126 Percent = 4.4525 Residual = 12.126 Percent = 4.4525 Residual = 11.942 Percent = 4.7285 Residual = 11.942 Percent = 4.7285 Residual = 11.758 Percent = 5.0171 Residual = 11.758 Percent = 5.0171 Residual = 11.575 Percent = 5.3183 Residual = 11.575 Percent = 5.3183 Residual = 11.391 Percent = 5.6325 Residual = 11.391 Percent = 5.6325 Residual = 11.207 Percent = 5.9597 Residual = 11.207 Percent = 5.9597 Residual = 11.024 Percent = 6.3002 Residual = 11.024 Percent = 6.3002 Residual = 10.84 Percent = 6.654 Residual = 10.84 Percent = 6.654 Residual = 10.656 Percent = 7.0212 Residual = 10.656 Percent = 7.0212 Residual = 10.472 Percent = 7.4019 Residual = 10.472 Percent = 7.4019 Residual = 10.289 Percent = 7.796 Residual = 10.289 Percent = 7.796 Residual = 10.105 Percent = 8.2037 Residual = 10.105 Percent = 8.2037 Residual = 9.9212 Percent = 8.6247 Residual = 9.9212 Percent = 8.6247 Residual = 9.5538 Percent = 9.5064 Residual = 9.5538 Percent = 9.5064 Residual = 9.1863 Percent = 10.44 Residual = 9.1863 Percent = 10.44 Residual = 8.8189 Percent = 11.423 Residual = 8.8189 Percent = 11.423 Residual = 8.4514 Percent = 12.453 Residual = 8.4514 Percent = 12.453 Residual = 8.084 Percent = 13.526 Residual = 8.084 Percent = 13.526 Residual = 5.3281 Percent = 22.361 Residual = 5.3281 Percent = 22.361 Residual = 4.7769 Percent = 24.121 Residual = 4.7769 Percent = 24.121 Residual = 4.4094 Percent = 25.255 Residual = 4.4094 Percent = 25.255 Residual = 4.042 Percent = 26.344 Residual = 4.042 Percent = 26.344 Residual = 3.6745 Percent = 27.38 Residual = 3.6745 Percent = 27.38 Residual = 3.4908 Percent = 27.875 Residual = 3.4908 Percent = 27.875 Residual = 3.3071 Percent = 28.352 Residual = 3.3071 Percent = 28.352 Residual = 3.1233 Percent = 28.812 Residual = 3.1233 Percent = 28.812 Residual = 2.9396 Percent = 29.252 Residual = 2.9396 Percent = 29.252 Residual = 2.7559 Percent = 29.671 Residual = 2.7559 Percent = 29.671 Residual = 2.5722 Percent = 30.069 Residual = 2.5722 Percent = 30.069 Residual = 2.3884 Percent = 30.444 Residual = 2.3884 Percent = 30.444 Residual = 2.2047 Percent = 30.795 Residual = 2.2047 Percent = 30.795 Residual = 2.021 Percent = 31.122 Residual = 2.021 Percent = 31.122 Residual = 1.8373 Percent = 31.424 Residual = 1.8373 Percent = 31.424 Residual = 1.6535 Percent = 31.699 Residual = 1.6535 Percent = 31.699 Residual = 1.4698 Percent = 31.947 Residual = 1.4698 Percent = 31.947 Residual = 1.2861 Percent = 32.168 Residual = 1.2861 Percent = 32.168 Residual = 1.1024 Percent = 32.361 Residual = 1.1024 Percent = 32.361 Residual = 0.9186 Percent = 32.524 Residual = 0.9186 Percent = 32.524 Residual = 0.7349 Percent = 32.659 Residual = 0.7349 Percent = 32.659 Residual = 0.5512 Percent = 32.764 Residual = 0.5512 Percent = 32.764 Residual = 0.3675 Percent = 32.84 Residual = 0.3675 Percent = 32.84 Residual = 0.1837 Percent = 32.885 Residual = 0.1837 Percent = 32.885 Residual = 11E-15 Percent = 32.9 Residual = 11E-15 Percent = 32.9 Residual = -0.184 Percent = 32.885 Residual = -0.184 Percent = 32.885 Residual = -0.367 Percent = 32.84 Residual = -0.367 Percent = 32.84 Residual = -0.551 Percent = 32.764 Residual = -0.551 Percent = 32.764 Residual = -0.735 Percent = 32.659 Residual = -0.735 Percent = 32.659 Residual = -0.919 Percent = 32.524 Residual = -0.919 Percent = 32.524 Residual = -1.102 Percent = 32.361 Residual = -1.102 Percent = 32.361 Residual = -1.286 Percent = 32.168 Residual = -1.286 Percent = 32.168 Residual = -1.47 Percent = 31.947 Residual = -1.47 Percent = 31.947 Residual = -1.654 Percent = 31.699 Residual = -1.654 Percent = 31.699 Residual = -1.837 Percent = 31.424 Residual = -1.837 Percent = 31.424 Residual = -2.021 Percent = 31.122 Residual = -2.021 Percent = 31.122 Residual = -2.205 Percent = 30.795 Residual = -2.205 Percent = 30.795 Residual = -2.388 Percent = 30.444 Residual = -2.388 Percent = 30.444 Residual = -2.572 Percent = 30.069 Residual = -2.572 Percent = 30.069 Residual = -2.756 Percent = 29.671 Residual = -2.756 Percent = 29.671 Residual = -2.94 Percent = 29.252 Residual = -2.94 Percent = 29.252 Residual = -3.123 Percent = 28.812 Residual = -3.123 Percent = 28.812 Residual = -3.307 Percent = 28.352 Residual = -3.307 Percent = 28.352 Residual = -3.491 Percent = 27.875 Residual = -3.491 Percent = 27.875 Residual = -3.675 Percent = 27.38 Residual = -3.675 Percent = 27.38 Residual = -4.042 Percent = 26.344 Residual = -4.042 Percent = 26.344 Residual = -4.409 Percent = 25.255 Residual = -4.409 Percent = 25.255 Residual = -6.614 Percent = 18.146 Residual = -6.614 Percent = 18.146 Residual = -7.349 Percent = 15.782 Residual = -7.349 Percent = 15.782 Residual = -7.9 Percent = 14.077 Residual = -7.9 Percent = 14.077 Residual = -8.268 Percent = 12.984 Residual = -8.268 Percent = 12.984 Residual = -8.635 Percent = 11.932 Residual = -8.635 Percent = 11.932 Residual = -9.003 Percent = 10.925 Residual = -9.003 Percent = 10.925 Residual = -9.37 Percent = 9.9668 Residual = -9.37 Percent = 9.9668 Residual = -9.737 Percent = 9.059 Residual = -9.737 Percent = 9.059 Residual = -9.921 Percent = 8.6247 Residual = -9.921 Percent = 8.6247 Residual = -10.1 Percent = 8.2037 Residual = -10.1 Percent = 8.2037 Residual = -10.29 Percent = 7.796 Residual = -10.29 Percent = 7.796 Residual = -10.47 Percent = 7.4019 Residual = -10.47 Percent = 7.4019 Residual = -10.66 Percent = 7.0212 Residual = -10.66 Percent = 7.0212 Residual = -10.84 Percent = 6.654 Residual = -10.84 Percent = 6.654 Residual = -11.02 Percent = 6.3002 Residual = -11.02 Percent = 6.3002 Residual = -11.21 Percent = 5.9597 Residual = -11.21 Percent = 5.9597 Residual = -11.39 Percent = 5.6325 Residual = -11.39 Percent = 5.6325 Residual = -11.57 Percent = 5.3183 Residual = -11.57 Percent = 5.3183 Residual = -11.76 Percent = 5.0171 Residual = -11.76 Percent = 5.0171 Residual = -11.94 Percent = 4.7285 Residual = -11.94 Percent = 4.7285 Residual = -12.13 Percent = 4.4525 Residual = -12.13 Percent = 4.4525 Residual = -12.31 Percent = 4.1888 Residual = -12.31 Percent = 4.1888 Residual = -12.49 Percent = 3.937 Residual = -12.49 Percent = 3.937 Residual = -12.68 Percent = 3.697 Residual = -12.68 Percent = 3.697 Residual = -12.86 Percent = 3.4684 Residual = -12.86 Percent = 3.4684 Residual = -13.04 Percent = 3.251 Residual = -13.04 Percent = 3.251 Residual = -13.23 Percent = 3.0444 Residual = -13.23 Percent = 3.0444 Residual = -13.41 Percent = 2.8483 Residual = -13.41 Percent = 2.8483 Residual = -13.6 Percent = 2.6624 Residual = -13.6 Percent = 2.6624 Residual = -13.78 Percent = 2.4864 Residual = -13.78 Percent = 2.4864 Residual = -13.96 Percent = 2.3198 Residual = -13.96 Percent = 2.3198 Residual = -14.15 Percent = 2.1625 Residual = -14.15 Percent = 2.1625 Residual = -14.33 Percent = 2.0139 Residual = -14.33 Percent = 2.0139 Residual = -14.51 Percent = 1.8739 Residual = -14.51 Percent = 1.8739 Residual = -14.7 Percent = 1.7419 Residual = -14.7 Percent = 1.7419 Residual = -14.88 Percent = 1.6178 Residual = -14.88 Percent = 1.6178 Residual = -15.07 Percent = 1.5012 Residual = -15.07 Percent = 1.5012 Residual = -15.25 Percent = 1.3916 Residual = -15.25 Percent = 1.3916 Residual = -15.43 Percent = 1.2889 Residual = -15.43 Percent = 1.2889 Residual = -15.62 Percent = 1.1927 Residual = -15.62 Percent = 1.1927 Residual = -15.8 Percent = 1.1026 Residual = -15.8 Percent = 1.1026 Residual = -15.98 Percent = 1.0184 Residual = -15.98 Percent = 1.0184 Residual = -16.17 Percent = 0.9398 Residual = -16.17 Percent = 0.9398 Residual = -16.35 Percent = 0.8664 Residual = -16.35 Percent = 0.8664 Residual = -16.54 Percent = 0.7981 Residual = -16.54 Percent = 0.7981 Residual = -16.72 Percent = 0.7344 Residual = -16.72 Percent = 0.7344 Residual = -16.9 Percent = 0.6753 Residual = -16.9 Percent = 0.6753 Residual = -17.09 Percent = 0.6203 Residual = -17.09 Percent = 0.6203 Residual = -17.27 Percent = 0.5692 Residual = -17.27 Percent = 0.5692 Residual = -17.45 Percent = 0.5219 Residual = -17.45 Percent = 0.5219 Residual = -17.64 Percent = 0.4781 Residual = -17.64 Percent = 0.4781 Residual = -17.82 Percent = 0.4376 Residual = -17.82 Percent = 0.4376 Residual = -18.01 Percent = 0.4001 Residual = -18.01 Percent = 0.4001 Residual = -18.19 Percent = 0.3655 Residual = 15 Percent = 4 Residual = 15 Percent = 4 Residual = 10 Percent = 4 Residual = 10 Percent = 4 Residual = 5 Percent = 22 Residual = 5 Percent = 22 Residual = 0 Percent = 44 Residual = 0 Percent = 44 Residual = -5 Percent = 12 Residual = -5 Percent = 12 Residual = -10 Percent = 14 Residual = -10 Percent = 14
Histogram of residuals for Run_Pulse with normal and kernel densities overlaid.

Residual by Predicted

Residual = 0.7452 Predicted Value = 123.25 Observation Number = 50 Residual = -9.391 Predicted Value = 117.39 Observation Number = 49 Residual = 2.2793 Predicted Value = 124.72 Observation Number = 48 Residual = -7.192 Predicted Value = 115.19 Observation Number = 47 Residual = 0.5353 Predicted Value = 103.46 Observation Number = 46 Residual = 7.1375 Predicted Value = 107.86 Observation Number = 45 Residual = 1.7342 Predicted Value = 101.27 Observation Number = 44 Residual = -8.533 Predicted Value = 100.53 Observation Number = 43 Residual = 8.3419 Predicted Value = 116.66 Observation Number = 42 Residual = 4.6089 Predicted Value = 117.39 Observation Number = 41 Residual = -7.192 Predicted Value = 115.19 Observation Number = 40 Residual = 0.6089 Predicted Value = 117.39 Observation Number = 39 Residual = 0.2056 Predicted Value = 110.79 Observation Number = 38 Residual = 15.546 Predicted Value = 125.45 Observation Number = 37 Residual = 6.677 Predicted Value = 120.32 Observation Number = 36 Residual = -1.794 Predicted Value = 110.79 Observation Number = 35 Residual = -1.726 Predicted Value = 113.73 Observation Number = 34 Residual = 1.6034 Predicted Value = 106.4 Observation Number = 33 Residual = -2.397 Predicted Value = 106.4 Observation Number = 32 Residual = 12.535 Predicted Value = 103.46 Observation Number = 31 Residual = -1.664 Predicted Value = 105.66 Observation Number = 30 Residual = 7.4726 Predicted Value = 111.53 Observation Number = 29 Residual = 1.7397 Predicted Value = 112.26 Observation Number = 28 Residual = 5.5408 Predicted Value = 114.46 Observation Number = 27 Residual = -9.459 Predicted Value = 114.46 Observation Number = 26 Residual = -1.26 Predicted Value = 112.26 Observation Number = 25 Residual = 5.4726 Predicted Value = 111.53 Observation Number = 24 Residual = -3.59 Predicted Value = 119.59 Observation Number = 23 Residual = -10.12 Predicted Value = 118.12 Observation Number = 22 Residual = -4.067 Predicted Value = 99.067 Observation Number = 21 Residual = -7.187 Predicted Value = 126.19 Observation Number = 20 Residual = -2.465 Predicted Value = 103.46 Observation Number = 19 Residual = -0.323 Predicted Value = 120.32 Observation Number = 18 Residual = 0.0067 Predicted Value = 112.99 Observation Number = 17 Residual = -2.59 Predicted Value = 119.59 Observation Number = 16 Residual = 4.6034 Predicted Value = 106.4 Observation Number = 15 Residual = -1.527 Predicted Value = 111.53 Observation Number = 14 Residual = -0.794 Predicted Value = 110.79 Observation Number = 13 Residual = 8.3419 Predicted Value = 116.66 Observation Number = 12 Residual = -0.465 Predicted Value = 103.46 Observation Number = 11 Residual = 6.3474 Predicted Value = 127.65 Observation Number = 10 Residual = 3.5353 Predicted Value = 103.46 Observation Number = 9 Residual = 2.8704 Predicted Value = 107.13 Observation Number = 8 Residual = -10.73 Predicted Value = 113.73 Observation Number = 7 Residual = 0.6089 Predicted Value = 117.39 Observation Number = 6 Residual = -8.857 Predicted Value = 118.86 Observation Number = 5 Residual = 1.6034 Predicted Value = 106.4 Observation Number = 4 Residual = -12.39 Predicted Value = 117.39 Observation Number = 3 Residual = 2.1375 Predicted Value = 107.86 Observation Number = 2 Residual = 2.8759 Predicted Value = 118.12 Observation Number = 1 Y = 0
Scatter plot of residuals by predicted values for Run_Pulse.

RStudent by Predicted

RStudent = 0.1244 Predicted Value = 123.25 Observation Number = 50 RStudent = -1.579 Predicted Value = 117.39 Observation Number = 49 RStudent = 0.3836 Predicted Value = 124.72 Observation Number = 48 RStudent = -1.192 Predicted Value = 115.19 Observation Number = 47 RStudent = 0.089 Predicted Value = 103.46 Observation Number = 46 RStudent = 1.1883 Predicted Value = 107.86 Observation Number = 45 RStudent = 0.2915 Predicted Value = 101.27 Observation Number = 44 RStudent = -1.471 Predicted Value = 100.53 Observation Number = 43 RStudent = 1.393 Predicted Value = 116.66 Observation Number = 42 RStudent = 0.7598 Predicted Value = 117.39 Observation Number = 41 RStudent = -1.192 Predicted Value = 115.19 Observation Number = 40 RStudent = 0.0998 Predicted Value = 117.39 Observation Number = 39 RStudent = 0.0336 Predicted Value = 110.79 Observation Number = 38 RStudent = 2.8387 Predicted Value = 125.45 Observation Number = 37 RStudent = 1.1165 Predicted Value = 120.32 Observation Number = 36 RStudent = -0.293 Predicted Value = 110.79 Observation Number = 35 RStudent = -0.282 Predicted Value = 113.73 Observation Number = 34 RStudent = 0.2641 Predicted Value = 106.4 Observation Number = 33 RStudent = -0.395 Predicted Value = 106.4 Observation Number = 32 RStudent = 2.1876 Predicted Value = 103.46 Observation Number = 31 RStudent = -0.275 Predicted Value = 105.66 Observation Number = 30 RStudent = 1.2396 Predicted Value = 111.53 Observation Number = 29 RStudent = 0.2841 Predicted Value = 112.26 Observation Number = 28 RStudent = 0.9125 Predicted Value = 114.46 Observation Number = 27 RStudent = -1.585 Predicted Value = 114.46 Observation Number = 26 RStudent = -0.206 Predicted Value = 112.26 Observation Number = 25 RStudent = 0.901 Predicted Value = 111.53 Observation Number = 24 RStudent = -0.593 Predicted Value = 119.59 Observation Number = 23 RStudent = -1.712 Predicted Value = 118.12 Observation Number = 22 RStudent = -0.695 Predicted Value = 99.067 Observation Number = 21 RStudent = -1.237 Predicted Value = 126.19 Observation Number = 20 RStudent = -0.411 Predicted Value = 103.46 Observation Number = 19 RStudent = -0.053 Predicted Value = 120.32 Observation Number = 18 RStudent = 0.0011 Predicted Value = 112.99 Observation Number = 17 RStudent = -0.427 Predicted Value = 119.59 Observation Number = 16 RStudent = 0.7625 Predicted Value = 106.4 Observation Number = 15 RStudent = -0.249 Predicted Value = 111.53 Observation Number = 14 RStudent = -0.13 Predicted Value = 110.79 Observation Number = 13 RStudent = 1.393 Predicted Value = 116.66 Observation Number = 12 RStudent = -0.077 Predicted Value = 103.46 Observation Number = 11 RStudent = 1.0991 Predicted Value = 127.65 Observation Number = 10 RStudent = 0.5899 Predicted Value = 103.46 Observation Number = 9 RStudent = 0.4728 Predicted Value = 107.13 Observation Number = 8 RStudent = -1.811 Predicted Value = 113.73 Observation Number = 7 RStudent = 0.0998 Predicted Value = 117.39 Observation Number = 6 RStudent = -1.49 Predicted Value = 118.86 Observation Number = 5 RStudent = 0.2641 Predicted Value = 106.4 Observation Number = 4 RStudent = -2.126 Predicted Value = 117.39 Observation Number = 3 RStudent = 0.3511 Predicted Value = 107.86 Observation Number = 2 RStudent = 0.473 Predicted Value = 118.12 Observation Number = 1 Y = 2 Y = -2
Scatter plot of studentized residuals (RSTUDENT) by predicted values for Run_Pulse.

Observed by Predicted

Run_Pulse = 124 Predicted Value = 123.25 Observation Number = 50 Run_Pulse = 108 Predicted Value = 117.39 Observation Number = 49 Run_Pulse = 127 Predicted Value = 124.72 Observation Number = 48 Run_Pulse = 108 Predicted Value = 115.19 Observation Number = 47 Run_Pulse = 104 Predicted Value = 103.46 Observation Number = 46 Run_Pulse = 115 Predicted Value = 107.86 Observation Number = 45 Run_Pulse = 103 Predicted Value = 101.27 Observation Number = 44 Run_Pulse = 92 Predicted Value = 100.53 Observation Number = 43 Run_Pulse = 125 Predicted Value = 116.66 Observation Number = 42 Run_Pulse = 122 Predicted Value = 117.39 Observation Number = 41 Run_Pulse = 108 Predicted Value = 115.19 Observation Number = 40 Run_Pulse = 118 Predicted Value = 117.39 Observation Number = 39 Run_Pulse = 111 Predicted Value = 110.79 Observation Number = 38 Run_Pulse = 141 Predicted Value = 125.45 Observation Number = 37 Run_Pulse = 127 Predicted Value = 120.32 Observation Number = 36 Run_Pulse = 109 Predicted Value = 110.79 Observation Number = 35 Run_Pulse = 112 Predicted Value = 113.73 Observation Number = 34 Run_Pulse = 108 Predicted Value = 106.4 Observation Number = 33 Run_Pulse = 104 Predicted Value = 106.4 Observation Number = 32 Run_Pulse = 116 Predicted Value = 103.46 Observation Number = 31 Run_Pulse = 104 Predicted Value = 105.66 Observation Number = 30 Run_Pulse = 119 Predicted Value = 111.53 Observation Number = 29 Run_Pulse = 114 Predicted Value = 112.26 Observation Number = 28 Run_Pulse = 120 Predicted Value = 114.46 Observation Number = 27 Run_Pulse = 105 Predicted Value = 114.46 Observation Number = 26 Run_Pulse = 111 Predicted Value = 112.26 Observation Number = 25 Run_Pulse = 117 Predicted Value = 111.53 Observation Number = 24 Run_Pulse = 116 Predicted Value = 119.59 Observation Number = 23 Run_Pulse = 108 Predicted Value = 118.12 Observation Number = 22 Run_Pulse = 95 Predicted Value = 99.067 Observation Number = 21 Run_Pulse = 119 Predicted Value = 126.19 Observation Number = 20 Run_Pulse = 101 Predicted Value = 103.46 Observation Number = 19 Run_Pulse = 120 Predicted Value = 120.32 Observation Number = 18 Run_Pulse = 113 Predicted Value = 112.99 Observation Number = 17 Run_Pulse = 117 Predicted Value = 119.59 Observation Number = 16 Run_Pulse = 111 Predicted Value = 106.4 Observation Number = 15 Run_Pulse = 110 Predicted Value = 111.53 Observation Number = 14 Run_Pulse = 110 Predicted Value = 110.79 Observation Number = 13 Run_Pulse = 125 Predicted Value = 116.66 Observation Number = 12 Run_Pulse = 103 Predicted Value = 103.46 Observation Number = 11 Run_Pulse = 134 Predicted Value = 127.65 Observation Number = 10 Run_Pulse = 107 Predicted Value = 103.46 Observation Number = 9 Run_Pulse = 110 Predicted Value = 107.13 Observation Number = 8 Run_Pulse = 103 Predicted Value = 113.73 Observation Number = 7 Run_Pulse = 118 Predicted Value = 117.39 Observation Number = 6 Run_Pulse = 110 Predicted Value = 118.86 Observation Number = 5 Run_Pulse = 108 Predicted Value = 106.4 Observation Number = 4 Run_Pulse = 105 Predicted Value = 117.39 Observation Number = 3 Run_Pulse = 110 Predicted Value = 107.86 Observation Number = 2 Run_Pulse = 121 Predicted Value = 118.12 Observation Number = 1 Slope = 1 Y = 0
Scatter plot of observed by predicted values for Run_Pulse.

Cook's D

Cook's D = .00053 Observation Number = 50 Cook's D = 0.0349 Observation Number = 49 Cook's D = 0.0062 Observation Number = 48 Cook's D = 0.0159 Observation Number = 47 Cook's D = .00024 Observation Number = 46 Cook's D = 0.0219 Observation Number = 45 Cook's D = 0.0035 Observation Number = 44 Cook's D = 0.0941 Observation Number = 43 Cook's D = 0.025 Observation Number = 42 Cook's D = 0.0084 Observation Number = 41 Cook's D = 0.0159 Observation Number = 40 Cook's D = .00015 Observation Number = 39 Cook's D = 1.3E-5 Observation Number = 38 Cook's D = 0.3189 Observation Number = 37 Cook's D = 0.0272 Observation Number = 36 Cook's D = .00098 Observation Number = 35 Cook's D = .00084 Observation Number = 34 Cook's D = 0.0014 Observation Number = 33 Cook's D = 0.0031 Observation Number = 32 Cook's D = 0.1315 Observation Number = 31 Cook's D = 0.0017 Observation Number = 30 Cook's D = 0.0161 Observation Number = 29 Cook's D = .00085 Observation Number = 28 Cook's D = 0.0089 Observation Number = 27 Cook's D = 0.0261 Observation Number = 26 Cook's D = .00044 Observation Number = 25 Cook's D = 0.0086 Observation Number = 24 Cook's D = 0.007 Observation Number = 23 Cook's D = 0.0449 Observation Number = 22 Cook's D = 0.0263 Observation Number = 21 Cook's D = 0.0756 Observation Number = 20 Cook's D = 0.0051 Observation Number = 19 Cook's D = 6.4E-5 Observation Number = 18 Cook's D = 1.2E-8 Observation Number = 17 Cook's D = 0.0037 Observation Number = 16 Cook's D = 0.0113 Observation Number = 15 Cook's D = .00067 Observation Number = 14 Cook's D = .00019 Observation Number = 13 Cook's D = 0.025 Observation Number = 12 Cook's D = .00018 Observation Number = 11 Cook's D = 0.0723 Observation Number = 10 Cook's D = 0.0105 Observation Number = 9 Cook's D = 0.0039 Observation Number = 8 Cook's D = 0.0324 Observation Number = 7 Cook's D = .00015 Observation Number = 6 Cook's D = 0.0383 Observation Number = 5 Cook's D = 0.0014 Observation Number = 4 Cook's D = 0.0607 Observation Number = 3 Cook's D = 0.002 Observation Number = 2 Cook's D = 0.0036 Observation Number = 1 Cook's D = .00053 Observation Number = 50 Cook's D = 0.0349 Observation Number = 49 Cook's D = 0.0062 Observation Number = 48 Cook's D = 0.0159 Observation Number = 47 Cook's D = .00024 Observation Number = 46 Cook's D = 0.0219 Observation Number = 45 Cook's D = 0.0035 Observation Number = 44 Cook's D = 0.0941 Observation Number = 43 Cook's D = 0.025 Observation Number = 42 Cook's D = 0.0084 Observation Number = 41 Cook's D = 0.0159 Observation Number = 40 Cook's D = .00015 Observation Number = 39 Cook's D = 1.3E-5 Observation Number = 38 Cook's D = 0.3189 Observation Number = 37 Cook's D = 0.0272 Observation Number = 36 Cook's D = .00098 Observation Number = 35 Cook's D = .00084 Observation Number = 34 Cook's D = 0.0014 Observation Number = 33 Cook's D = 0.0031 Observation Number = 32 Cook's D = 0.1315 Observation Number = 31 Cook's D = 0.0017 Observation Number = 30 Cook's D = 0.0161 Observation Number = 29 Cook's D = .00085 Observation Number = 28 Cook's D = 0.0089 Observation Number = 27 Cook's D = 0.0261 Observation Number = 26 Cook's D = .00044 Observation Number = 25 Cook's D = 0.0086 Observation Number = 24 Cook's D = 0.007 Observation Number = 23 Cook's D = 0.0449 Observation Number = 22 Cook's D = 0.0263 Observation Number = 21 Cook's D = 0.0756 Observation Number = 20 Cook's D = 0.0051 Observation Number = 19 Cook's D = 6.4E-5 Observation Number = 18 Cook's D = 1.2E-8 Observation Number = 17 Cook's D = 0.0037 Observation Number = 16 Cook's D = 0.0113 Observation Number = 15 Cook's D = .00067 Observation Number = 14 Cook's D = .00019 Observation Number = 13 Cook's D = 0.025 Observation Number = 12 Cook's D = .00018 Observation Number = 11 Cook's D = 0.0723 Observation Number = 10 Cook's D = 0.0105 Observation Number = 9 Cook's D = 0.0039 Observation Number = 8 Cook's D = 0.0324 Observation Number = 7 Cook's D = .00015 Observation Number = 6 Cook's D = 0.0383 Observation Number = 5 Cook's D = 0.0014 Observation Number = 4 Cook's D = 0.0607 Observation Number = 3 Cook's D = 0.002 Observation Number = 2 Cook's D = 0.0036 Observation Number = 1 Y = 0.08
Needle plot of Cook's D statistic by observation for Run_Pulse.

RStudent by Leverage

RStudent = -1.471 Hat Diagonal = 0.0818 Observation Number = 43 RStudent = 2.8387 Hat Diagonal = 0.0832 Observation Number = 37 RStudent = 2.1876 Hat Diagonal = 0.056 Observation Number = 31 RStudent = -0.695 Hat Diagonal = 0.0972 Observation Number = 21 RStudent = -1.237 Hat Diagonal = 0.0908 Observation Number = 20 RStudent = 1.0991 Hat Diagonal = 0.1074 Observation Number = 10 RStudent = -2.126 Hat Diagonal = 0.028 Observation Number = 3 RStudent = 0.1244 Hat Diagonal = 0.063 Observation Number = 50 RStudent = -1.579 Hat Diagonal = 0.028 Observation Number = 49 RStudent = 0.3836 Hat Diagonal = 0.0761 Observation Number = 48 RStudent = -1.192 Hat Diagonal = 0.0221 Observation Number = 47 RStudent = 0.089 Hat Diagonal = 0.056 Observation Number = 46 RStudent = 1.1883 Hat Diagonal = 0.0303 Observation Number = 45 RStudent = 0.2915 Hat Diagonal = 0.0747 Observation Number = 44 RStudent = 1.393 Hat Diagonal = 0.0256 Observation Number = 42 RStudent = 0.7598 Hat Diagonal = 0.028 Observation Number = 41 RStudent = -1.192 Hat Diagonal = 0.0221 Observation Number = 40 RStudent = 0.0998 Hat Diagonal = 0.028 Observation Number = 39 RStudent = 0.0336 Hat Diagonal = 0.0218 Observation Number = 38 RStudent = 1.1165 Hat Diagonal = 0.0421 Observation Number = 36 RStudent = -0.293 Hat Diagonal = 0.0218 Observation Number = 35 RStudent = -0.282 Hat Diagonal = 0.0203 Observation Number = 34 RStudent = 0.2641 Hat Diagonal = 0.0371 Observation Number = 33 RStudent = -0.395 Hat Diagonal = 0.0371 Observation Number = 32 RStudent = -0.275 Hat Diagonal = 0.0412 Observation Number = 30 RStudent = 1.2396 Hat Diagonal = 0.0208 Observation Number = 29 RStudent = 0.2841 Hat Diagonal = 0.0202 Observation Number = 28 RStudent = 0.9125 Hat Diagonal = 0.021 Observation Number = 27 RStudent = -1.585 Hat Diagonal = 0.021 Observation Number = 26 RStudent = -0.206 Hat Diagonal = 0.0202 Observation Number = 25 RStudent = 0.901 Hat Diagonal = 0.0208 Observation Number = 24 RStudent = -0.593 Hat Diagonal = 0.0379 Observation Number = 23 RStudent = -1.712 Hat Diagonal = 0.0309 Observation Number = 22 RStudent = -0.411 Hat Diagonal = 0.056 Observation Number = 19 RStudent = -0.053 Hat Diagonal = 0.0421 Observation Number = 18 RStudent = 0.0011 Hat Diagonal = 0.02 Observation Number = 17 RStudent = -0.427 Hat Diagonal = 0.0379 Observation Number = 16 RStudent = 0.7625 Hat Diagonal = 0.0371 Observation Number = 15 RStudent = -0.249 Hat Diagonal = 0.0208 Observation Number = 14 RStudent = -0.13 Hat Diagonal = 0.0218 Observation Number = 13 RStudent = 1.393 Hat Diagonal = 0.0256 Observation Number = 12 RStudent = -0.077 Hat Diagonal = 0.056 Observation Number = 11 RStudent = 0.5899 Hat Diagonal = 0.056 Observation Number = 9 RStudent = 0.4728 Hat Diagonal = 0.0335 Observation Number = 8 RStudent = -1.811 Hat Diagonal = 0.0203 Observation Number = 7 RStudent = 0.0998 Hat Diagonal = 0.028 Observation Number = 6 RStudent = -1.49 Hat Diagonal = 0.0342 Observation Number = 5 RStudent = 0.2641 Hat Diagonal = 0.0371 Observation Number = 4 RStudent = 0.3511 Hat Diagonal = 0.0303 Observation Number = 2 RStudent = 0.473 Hat Diagonal = 0.0309 Observation Number = 1 X = 0.08 Y = -2 Y = 2
Scatter plot of studentized residuals (RSTUDENT) by leverage for Run_Pulse.

Q-Q Plot

Quantile = 2.2433 Residual = 15.546 Quantile = 1.8475 Residual = 12.535 Quantile = 1.6235 Residual = 8.3419 Quantile = 1.46 Residual = 8.3419 Quantile = 1.3283 Residual = 7.4726 Quantile = 1.2163 Residual = 7.1375 Quantile = 1.1177 Residual = 6.677 Quantile = 1.029 Residual = 6.3474 Quantile = 0.9477 Residual = 5.5408 Quantile = 0.8722 Residual = 5.4726 Quantile = 0.8014 Residual = 4.6089 Quantile = 0.7344 Residual = 4.6034 Quantile = 0.6706 Residual = 3.5353 Quantile = 0.6094 Residual = 2.8759 Quantile = 0.5503 Residual = 2.8704 Quantile = 0.4932 Residual = 2.2793 Quantile = 0.4376 Residual = 2.1375 Quantile = 0.3833 Residual = 1.7397 Quantile = 0.3301 Residual = 1.7342 Quantile = 0.2779 Residual = 1.6034 Quantile = 0.2264 Residual = 1.6034 Quantile = 0.1755 Residual = 0.7452 Quantile = 0.125 Residual = 0.6089 Quantile = 0.0749 Residual = 0.6089 Quantile = 0.0249 Residual = 0.5353 Quantile = -0.025 Residual = 0.2056 Quantile = -0.075 Residual = 0.0067 Quantile = -0.125 Residual = -0.323 Quantile = -0.175 Residual = -0.465 Quantile = -0.226 Residual = -0.794 Quantile = -0.278 Residual = -1.26 Quantile = -0.33 Residual = -1.527 Quantile = -0.383 Residual = -1.664 Quantile = -0.438 Residual = -1.726 Quantile = -0.493 Residual = -1.794 Quantile = -0.55 Residual = -2.397 Quantile = -0.609 Residual = -2.465 Quantile = -0.671 Residual = -2.59 Quantile = -0.734 Residual = -3.59 Quantile = -0.801 Residual = -4.067 Quantile = -0.872 Residual = -7.187 Quantile = -0.948 Residual = -7.192 Quantile = -1.029 Residual = -7.192 Quantile = -1.118 Residual = -8.533 Quantile = -1.216 Residual = -8.857 Quantile = -1.328 Residual = -9.391 Quantile = -1.46 Residual = -9.459 Quantile = -1.624 Residual = -10.12 Quantile = -1.847 Residual = -10.73 Quantile = -2.243 Residual = -12.39 Slope = 6.063 Y = -3E-16
Q-Q plot of residuals for Run_Pulse.

RF Plot

Proportion Less = 0.9876 Fit-Mean = 14.733 Proportion Less = 0.9677 Fit-Mean = 13.267 Proportion Less = 0.9478 Fit-Mean = 12.534 Proportion Less = 0.9279 Fit-Mean = 11.801 Proportion Less = 0.908 Fit-Mean = 10.335 Proportion Less = 0.8881 Fit-Mean = 7.403 Proportion Less = 0.8682 Fit-Mean = 7.403 Proportion Less = 0.8483 Fit-Mean = 6.67 Proportion Less = 0.8284 Fit-Mean = 6.67 Proportion Less = 0.8085 Fit-Mean = 5.937 Proportion Less = 0.7886 Fit-Mean = 5.2041 Proportion Less = 0.7687 Fit-Mean = 5.2041 Proportion Less = 0.7488 Fit-Mean = 4.4711 Proportion Less = 0.7289 Fit-Mean = 4.4711 Proportion Less = 0.709 Fit-Mean = 4.4711 Proportion Less = 0.6891 Fit-Mean = 4.4711 Proportion Less = 0.6692 Fit-Mean = 4.4711 Proportion Less = 0.6493 Fit-Mean = 3.7381 Proportion Less = 0.6294 Fit-Mean = 3.7381 Proportion Less = 0.6095 Fit-Mean = 2.2722 Proportion Less = 0.5896 Fit-Mean = 2.2722 Proportion Less = 0.5697 Fit-Mean = 1.5392 Proportion Less = 0.5498 Fit-Mean = 1.5392 Proportion Less = 0.5299 Fit-Mean = 0.8063 Proportion Less = 0.51 Fit-Mean = 0.8063 Proportion Less = 0.49 Fit-Mean = 0.0733 Proportion Less = 0.4701 Fit-Mean = -0.66 Proportion Less = 0.4502 Fit-Mean = -0.66 Proportion Less = 0.4303 Fit-Mean = -1.393 Proportion Less = 0.4104 Fit-Mean = -1.393 Proportion Less = 0.3905 Fit-Mean = -1.393 Proportion Less = 0.3706 Fit-Mean = -2.126 Proportion Less = 0.3507 Fit-Mean = -2.126 Proportion Less = 0.3308 Fit-Mean = -2.126 Proportion Less = 0.3109 Fit-Mean = -5.057 Proportion Less = 0.291 Fit-Mean = -5.057 Proportion Less = 0.2711 Fit-Mean = -5.79 Proportion Less = 0.2512 Fit-Mean = -6.523 Proportion Less = 0.2313 Fit-Mean = -6.523 Proportion Less = 0.2114 Fit-Mean = -6.523 Proportion Less = 0.1915 Fit-Mean = -6.523 Proportion Less = 0.1716 Fit-Mean = -7.256 Proportion Less = 0.1517 Fit-Mean = -9.455 Proportion Less = 0.1318 Fit-Mean = -9.455 Proportion Less = 0.1119 Fit-Mean = -9.455 Proportion Less = 0.092 Fit-Mean = -9.455 Proportion Less = 0.0721 Fit-Mean = -9.455 Proportion Less = 0.0522 Fit-Mean = -11.65 Proportion Less = 0.0323 Fit-Mean = -12.39 Proportion Less = 0.0124 Fit-Mean = -13.85 Proportion Less = 0.9876 Residual = 15.546 Proportion Less = 0.9677 Residual = 12.535 Proportion Less = 0.9478 Residual = 8.3419 Proportion Less = 0.9279 Residual = 8.3419 Proportion Less = 0.908 Residual = 7.4726 Proportion Less = 0.8881 Residual = 7.1375 Proportion Less = 0.8682 Residual = 6.677 Proportion Less = 0.8483 Residual = 6.3474 Proportion Less = 0.8284 Residual = 5.5408 Proportion Less = 0.8085 Residual = 5.4726 Proportion Less = 0.7886 Residual = 4.6089 Proportion Less = 0.7687 Residual = 4.6034 Proportion Less = 0.7488 Residual = 3.5353 Proportion Less = 0.7289 Residual = 2.8759 Proportion Less = 0.709 Residual = 2.8704 Proportion Less = 0.6891 Residual = 2.2793 Proportion Less = 0.6692 Residual = 2.1375 Proportion Less = 0.6493 Residual = 1.7397 Proportion Less = 0.6294 Residual = 1.7342 Proportion Less = 0.6095 Residual = 1.6034 Proportion Less = 0.5896 Residual = 1.6034 Proportion Less = 0.5697 Residual = 0.7452 Proportion Less = 0.5498 Residual = 0.6089 Proportion Less = 0.5299 Residual = 0.6089 Proportion Less = 0.51 Residual = 0.5353 Proportion Less = 0.49 Residual = 0.2056 Proportion Less = 0.4701 Residual = 0.0067 Proportion Less = 0.4502 Residual = -0.323 Proportion Less = 0.4303 Residual = -0.465 Proportion Less = 0.4104 Residual = -0.794 Proportion Less = 0.3905 Residual = -1.26 Proportion Less = 0.3706 Residual = -1.527 Proportion Less = 0.3507 Residual = -1.664 Proportion Less = 0.3308 Residual = -1.726 Proportion Less = 0.3109 Residual = -1.794 Proportion Less = 0.291 Residual = -2.397 Proportion Less = 0.2711 Residual = -2.465 Proportion Less = 0.2512 Residual = -2.59 Proportion Less = 0.2313 Residual = -3.59 Proportion Less = 0.2114 Residual = -4.067 Proportion Less = 0.1915 Residual = -7.187 Proportion Less = 0.1716 Residual = -7.192 Proportion Less = 0.1517 Residual = -7.192 Proportion Less = 0.1318 Residual = -8.533 Proportion Less = 0.1119 Residual = -8.857 Proportion Less = 0.092 Residual = -9.391 Proportion Less = 0.0721 Residual = -9.459 Proportion Less = 0.0522 Residual = -10.12 Proportion Less = 0.0323 Residual = -10.73 Proportion Less = 0.0124 Residual = -12.39
Residual-Fit spread plot for Run_Pulse. This plot consists of two side-by-side plots that show the spread in the fitted values about their mean and the spread in the residuals respectively.

Residual Plots

Rest_Pulse

Residual = 0.7452 Rest_Pulse = 82 Observation Number = 50 Residual = -9.391 Rest_Pulse = 74 Observation Number = 49 Residual = 2.2793 Rest_Pulse = 84 Observation Number = 48 Residual = -7.192 Rest_Pulse = 71 Observation Number = 47 Residual = 0.5353 Rest_Pulse = 55 Observation Number = 46 Residual = 7.1375 Rest_Pulse = 61 Observation Number = 45 Residual = 1.7342 Rest_Pulse = 52 Observation Number = 44 Residual = -8.533 Rest_Pulse = 51 Observation Number = 43 Residual = 8.3419 Rest_Pulse = 73 Observation Number = 42 Residual = 4.6089 Rest_Pulse = 74 Observation Number = 41 Residual = -7.192 Rest_Pulse = 71 Observation Number = 40 Residual = 0.6089 Rest_Pulse = 74 Observation Number = 39 Residual = 0.2056 Rest_Pulse = 65 Observation Number = 38 Residual = 15.546 Rest_Pulse = 85 Observation Number = 37 Residual = 6.677 Rest_Pulse = 78 Observation Number = 36 Residual = -1.794 Rest_Pulse = 65 Observation Number = 35 Residual = -1.726 Rest_Pulse = 69 Observation Number = 34 Residual = 1.6034 Rest_Pulse = 59 Observation Number = 33 Residual = -2.397 Rest_Pulse = 59 Observation Number = 32 Residual = 12.535 Rest_Pulse = 55 Observation Number = 31 Residual = -1.664 Rest_Pulse = 58 Observation Number = 30 Residual = 7.4726 Rest_Pulse = 66 Observation Number = 29 Residual = 1.7397 Rest_Pulse = 67 Observation Number = 28 Residual = 5.5408 Rest_Pulse = 70 Observation Number = 27 Residual = -9.459 Rest_Pulse = 70 Observation Number = 26 Residual = -1.26 Rest_Pulse = 67 Observation Number = 25 Residual = 5.4726 Rest_Pulse = 66 Observation Number = 24 Residual = -3.59 Rest_Pulse = 77 Observation Number = 23 Residual = -10.12 Rest_Pulse = 75 Observation Number = 22 Residual = -4.067 Rest_Pulse = 49 Observation Number = 21 Residual = -7.187 Rest_Pulse = 86 Observation Number = 20 Residual = -2.465 Rest_Pulse = 55 Observation Number = 19 Residual = -0.323 Rest_Pulse = 78 Observation Number = 18 Residual = 0.0067 Rest_Pulse = 68 Observation Number = 17 Residual = -2.59 Rest_Pulse = 77 Observation Number = 16 Residual = 4.6034 Rest_Pulse = 59 Observation Number = 15 Residual = -1.527 Rest_Pulse = 66 Observation Number = 14 Residual = -0.794 Rest_Pulse = 65 Observation Number = 13 Residual = 8.3419 Rest_Pulse = 73 Observation Number = 12 Residual = -0.465 Rest_Pulse = 55 Observation Number = 11 Residual = 6.3474 Rest_Pulse = 88 Observation Number = 10 Residual = 3.5353 Rest_Pulse = 55 Observation Number = 9 Residual = 2.8704 Rest_Pulse = 60 Observation Number = 8 Residual = -10.73 Rest_Pulse = 69 Observation Number = 7 Residual = 0.6089 Rest_Pulse = 74 Observation Number = 6 Residual = -8.857 Rest_Pulse = 76 Observation Number = 5 Residual = 1.6034 Rest_Pulse = 59 Observation Number = 4 Residual = -12.39 Rest_Pulse = 74 Observation Number = 3 Residual = 2.1375 Rest_Pulse = 61 Observation Number = 2 Residual = 2.8759 Rest_Pulse = 75 Observation Number = 1 Y = 0
Scatter plot of residuals by Rest_Pulse for Run_Pulse.

Fit Plot

Rest_Pulse = 88 Predicted Value = 127.65 Rest_Pulse = 86 Predicted Value = 126.19 Rest_Pulse = 86 Predicted Value = 126.19 Rest_Pulse = 85 Predicted Value = 125.45 Rest_Pulse = 85 Predicted Value = 125.45 Rest_Pulse = 84 Predicted Value = 124.72 Rest_Pulse = 84 Predicted Value = 124.72 Rest_Pulse = 82 Predicted Value = 123.25 Rest_Pulse = 82 Predicted Value = 123.25 Rest_Pulse = 78 Predicted Value = 120.32 Rest_Pulse = 78 Predicted Value = 120.32 Rest_Pulse = 78 Predicted Value = 120.32 Rest_Pulse = 78 Predicted Value = 120.32 Rest_Pulse = 77 Predicted Value = 119.59 Rest_Pulse = 77 Predicted Value = 119.59 Rest_Pulse = 77 Predicted Value = 119.59 Rest_Pulse = 77 Predicted Value = 119.59 Rest_Pulse = 76 Predicted Value = 118.86 Rest_Pulse = 76 Predicted Value = 118.86 Rest_Pulse = 75 Predicted Value = 118.12 Rest_Pulse = 75 Predicted Value = 118.12 Rest_Pulse = 75 Predicted Value = 118.12 Rest_Pulse = 75 Predicted Value = 118.12 Rest_Pulse = 74 Predicted Value = 117.39 Rest_Pulse = 74 Predicted Value = 117.39 Rest_Pulse = 74 Predicted Value = 117.39 Rest_Pulse = 74 Predicted Value = 117.39 Rest_Pulse = 74 Predicted Value = 117.39 Rest_Pulse = 74 Predicted Value = 117.39 Rest_Pulse = 74 Predicted Value = 117.39 Rest_Pulse = 74 Predicted Value = 117.39 Rest_Pulse = 74 Predicted Value = 117.39 Rest_Pulse = 74 Predicted Value = 117.39 Rest_Pulse = 73 Predicted Value = 116.66 Rest_Pulse = 73 Predicted Value = 116.66 Rest_Pulse = 73 Predicted Value = 116.66 Rest_Pulse = 73 Predicted Value = 116.66 Rest_Pulse = 71 Predicted Value = 115.19 Rest_Pulse = 71 Predicted Value = 115.19 Rest_Pulse = 71 Predicted Value = 115.19 Rest_Pulse = 71 Predicted Value = 115.19 Rest_Pulse = 70 Predicted Value = 114.46 Rest_Pulse = 70 Predicted Value = 114.46 Rest_Pulse = 70 Predicted Value = 114.46 Rest_Pulse = 70 Predicted Value = 114.46 Rest_Pulse = 69 Predicted Value = 113.73 Rest_Pulse = 69 Predicted Value = 113.73 Rest_Pulse = 69 Predicted Value = 113.73 Rest_Pulse = 69 Predicted Value = 113.73 Rest_Pulse = 68 Predicted Value = 112.99 Rest_Pulse = 68 Predicted Value = 112.99 Rest_Pulse = 67 Predicted Value = 112.26 Rest_Pulse = 67 Predicted Value = 112.26 Rest_Pulse = 67 Predicted Value = 112.26 Rest_Pulse = 67 Predicted Value = 112.26 Rest_Pulse = 66 Predicted Value = 111.53 Rest_Pulse = 66 Predicted Value = 111.53 Rest_Pulse = 66 Predicted Value = 111.53 Rest_Pulse = 66 Predicted Value = 111.53 Rest_Pulse = 66 Predicted Value = 111.53 Rest_Pulse = 66 Predicted Value = 111.53 Rest_Pulse = 65 Predicted Value = 110.79 Rest_Pulse = 65 Predicted Value = 110.79 Rest_Pulse = 65 Predicted Value = 110.79 Rest_Pulse = 65 Predicted Value = 110.79 Rest_Pulse = 65 Predicted Value = 110.79 Rest_Pulse = 65 Predicted Value = 110.79 Rest_Pulse = 61 Predicted Value = 107.86 Rest_Pulse = 61 Predicted Value = 107.86 Rest_Pulse = 61 Predicted Value = 107.86 Rest_Pulse = 61 Predicted Value = 107.86 Rest_Pulse = 60 Predicted Value = 107.13 Rest_Pulse = 60 Predicted Value = 107.13 Rest_Pulse = 59 Predicted Value = 106.4 Rest_Pulse = 59 Predicted Value = 106.4 Rest_Pulse = 59 Predicted Value = 106.4 Rest_Pulse = 59 Predicted Value = 106.4 Rest_Pulse = 59 Predicted Value = 106.4 Rest_Pulse = 59 Predicted Value = 106.4 Rest_Pulse = 59 Predicted Value = 106.4 Rest_Pulse = 59 Predicted Value = 106.4 Rest_Pulse = 58 Predicted Value = 105.66 Rest_Pulse = 58 Predicted Value = 105.66 Rest_Pulse = 55 Predicted Value = 103.46 Rest_Pulse = 55 Predicted Value = 103.46 Rest_Pulse = 55 Predicted Value = 103.46 Rest_Pulse = 55 Predicted Value = 103.46 Rest_Pulse = 55 Predicted Value = 103.46 Rest_Pulse = 55 Predicted Value = 103.46 Rest_Pulse = 55 Predicted Value = 103.46 Rest_Pulse = 55 Predicted Value = 103.46 Rest_Pulse = 55 Predicted Value = 103.46 Rest_Pulse = 55 Predicted Value = 103.46 Rest_Pulse = 52 Predicted Value = 101.27 Rest_Pulse = 52 Predicted Value = 101.27 Rest_Pulse = 51 Predicted Value = 100.53 Rest_Pulse = 51 Predicted Value = 100.53 Rest_Pulse = 49 Predicted Value = 99.067 Run_Pulse = 124 Rest_Pulse = 82 Observation Number = 50 Run_Pulse = 108 Rest_Pulse = 74 Observation Number = 49 Run_Pulse = 127 Rest_Pulse = 84 Observation Number = 48 Run_Pulse = 108 Rest_Pulse = 71 Observation Number = 47 Run_Pulse = 104 Rest_Pulse = 55 Observation Number = 46 Run_Pulse = 115 Rest_Pulse = 61 Observation Number = 45 Run_Pulse = 103 Rest_Pulse = 52 Observation Number = 44 Run_Pulse = 92 Rest_Pulse = 51 Observation Number = 43 Run_Pulse = 125 Rest_Pulse = 73 Observation Number = 42 Run_Pulse = 122 Rest_Pulse = 74 Observation Number = 41 Run_Pulse = 108 Rest_Pulse = 71 Observation Number = 40 Run_Pulse = 118 Rest_Pulse = 74 Observation Number = 39 Run_Pulse = 111 Rest_Pulse = 65 Observation Number = 38 Run_Pulse = 141 Rest_Pulse = 85 Observation Number = 37 Run_Pulse = 127 Rest_Pulse = 78 Observation Number = 36 Run_Pulse = 109 Rest_Pulse = 65 Observation Number = 35 Run_Pulse = 112 Rest_Pulse = 69 Observation Number = 34 Run_Pulse = 108 Rest_Pulse = 59 Observation Number = 33 Run_Pulse = 104 Rest_Pulse = 59 Observation Number = 32 Run_Pulse = 116 Rest_Pulse = 55 Observation Number = 31 Run_Pulse = 104 Rest_Pulse = 58 Observation Number = 30 Run_Pulse = 119 Rest_Pulse = 66 Observation Number = 29 Run_Pulse = 114 Rest_Pulse = 67 Observation Number = 28 Run_Pulse = 120 Rest_Pulse = 70 Observation Number = 27 Run_Pulse = 105 Rest_Pulse = 70 Observation Number = 26 Run_Pulse = 111 Rest_Pulse = 67 Observation Number = 25 Run_Pulse = 117 Rest_Pulse = 66 Observation Number = 24 Run_Pulse = 116 Rest_Pulse = 77 Observation Number = 23 Run_Pulse = 108 Rest_Pulse = 75 Observation Number = 22 Run_Pulse = 95 Rest_Pulse = 49 Observation Number = 21 Run_Pulse = 119 Rest_Pulse = 86 Observation Number = 20 Run_Pulse = 101 Rest_Pulse = 55 Observation Number = 19 Run_Pulse = 120 Rest_Pulse = 78 Observation Number = 18 Run_Pulse = 113 Rest_Pulse = 68 Observation Number = 17 Run_Pulse = 117 Rest_Pulse = 77 Observation Number = 16 Run_Pulse = 111 Rest_Pulse = 59 Observation Number = 15 Run_Pulse = 110 Rest_Pulse = 66 Observation Number = 14 Run_Pulse = 110 Rest_Pulse = 65 Observation Number = 13 Run_Pulse = 125 Rest_Pulse = 73 Observation Number = 12 Run_Pulse = 103 Rest_Pulse = 55 Observation Number = 11 Run_Pulse = 134 Rest_Pulse = 88 Observation Number = 10 Run_Pulse = 107 Rest_Pulse = 55 Observation Number = 9 Run_Pulse = 110 Rest_Pulse = 60 Observation Number = 8 Run_Pulse = 103 Rest_Pulse = 69 Observation Number = 7 Run_Pulse = 118 Rest_Pulse = 74 Observation Number = 6 Run_Pulse = 110 Rest_Pulse = 76 Observation Number = 5 Run_Pulse = 108 Rest_Pulse = 59 Observation Number = 4 Run_Pulse = 105 Rest_Pulse = 74 Observation Number = 3 Run_Pulse = 110 Rest_Pulse = 61 Observation Number = 2 Run_Pulse = 121 Rest_Pulse = 75 Observation Number = 1 Rest_Pulse = 88 Upper 95% CL Predict = 140.61 Lower 95% CL Predict = 114.69 Rest_Pulse = 86 Upper 95% CL Predict = 139.05 Lower 95% CL Predict = 113.32 Rest_Pulse = 88 Upper 95% CL Predict = 140.61 Lower 95% CL Predict = 114.69 Rest_Pulse = 86 Upper 95% CL Predict = 139.05 Lower 95% CL Predict = 113.32 Rest_Pulse = 86 Upper 95% CL Predict = 139.05 Lower 95% CL Predict = 113.32 Rest_Pulse = 85 Upper 95% CL Predict = 138.27 Lower 95% CL Predict = 112.63 Rest_Pulse = 86 Upper 95% CL Predict = 139.05 Lower 95% CL Predict = 113.32 Rest_Pulse = 85 Upper 95% CL Predict = 138.27 Lower 95% CL Predict = 112.63 Rest_Pulse = 85 Upper 95% CL Predict = 138.27 Lower 95% CL Predict = 112.63 Rest_Pulse = 84 Upper 95% CL Predict = 137.5 Lower 95% CL Predict = 111.94 Rest_Pulse = 85 Upper 95% CL Predict = 138.27 Lower 95% CL Predict = 112.63 Rest_Pulse = 84 Upper 95% CL Predict = 137.5 Lower 95% CL Predict = 111.94 Rest_Pulse = 84 Upper 95% CL Predict = 137.5 Lower 95% CL Predict = 111.94 Rest_Pulse = 82 Upper 95% CL Predict = 135.95 Lower 95% CL Predict = 110.56 Rest_Pulse = 84 Upper 95% CL Predict = 137.5 Lower 95% CL Predict = 111.94 Rest_Pulse = 82 Upper 95% CL Predict = 135.95 Lower 95% CL Predict = 110.56 Rest_Pulse = 82 Upper 95% CL Predict = 135.95 Lower 95% CL Predict = 110.56 Rest_Pulse = 78 Upper 95% CL Predict = 132.9 Lower 95% CL Predict = 107.75 Rest_Pulse = 82 Upper 95% CL Predict = 135.95 Lower 95% CL Predict = 110.56 Rest_Pulse = 78 Upper 95% CL Predict = 132.9 Lower 95% CL Predict = 107.75 Rest_Pulse = 78 Upper 95% CL Predict = 132.9 Lower 95% CL Predict = 107.75 Rest_Pulse = 78 Upper 95% CL Predict = 132.9 Lower 95% CL Predict = 107.75 Rest_Pulse = 78 Upper 95% CL Predict = 132.9 Lower 95% CL Predict = 107.75 Rest_Pulse = 78 Upper 95% CL Predict = 132.9 Lower 95% CL Predict = 107.75 Rest_Pulse = 78 Upper 95% CL Predict = 132.9 Lower 95% CL Predict = 107.75 Rest_Pulse = 77 Upper 95% CL Predict = 132.14 Lower 95% CL Predict = 107.04 Rest_Pulse = 78 Upper 95% CL Predict = 132.9 Lower 95% CL Predict = 107.75 Rest_Pulse = 77 Upper 95% CL Predict = 132.14 Lower 95% CL Predict = 107.04 Rest_Pulse = 77 Upper 95% CL Predict = 132.14 Lower 95% CL Predict = 107.04 Rest_Pulse = 77 Upper 95% CL Predict = 132.14 Lower 95% CL Predict = 107.04 Rest_Pulse = 77 Upper 95% CL Predict = 132.14 Lower 95% CL Predict = 107.04 Rest_Pulse = 77 Upper 95% CL Predict = 132.14 Lower 95% CL Predict = 107.04 Rest_Pulse = 77 Upper 95% CL Predict = 132.14 Lower 95% CL Predict = 107.04 Rest_Pulse = 76 Upper 95% CL Predict = 131.38 Lower 95% CL Predict = 106.33 Rest_Pulse = 77 Upper 95% CL Predict = 132.14 Lower 95% CL Predict = 107.04 Rest_Pulse = 76 Upper 95% CL Predict = 131.38 Lower 95% CL Predict = 106.33 Rest_Pulse = 76 Upper 95% CL Predict = 131.38 Lower 95% CL Predict = 106.33 Rest_Pulse = 75 Upper 95% CL Predict = 130.63 Lower 95% CL Predict = 105.62 Rest_Pulse = 76 Upper 95% CL Predict = 131.38 Lower 95% CL Predict = 106.33 Rest_Pulse = 75 Upper 95% CL Predict = 130.63 Lower 95% CL Predict = 105.62 Rest_Pulse = 75 Upper 95% CL Predict = 130.63 Lower 95% CL Predict = 105.62 Rest_Pulse = 75 Upper 95% CL Predict = 130.63 Lower 95% CL Predict = 105.62 Rest_Pulse = 75 Upper 95% CL Predict = 130.63 Lower 95% CL Predict = 105.62 Rest_Pulse = 75 Upper 95% CL Predict = 130.63 Lower 95% CL Predict = 105.62 Rest_Pulse = 75 Upper 95% CL Predict = 130.63 Lower 95% CL Predict = 105.62 Rest_Pulse = 74 Upper 95% CL Predict = 129.88 Lower 95% CL Predict = 104.9 Rest_Pulse = 75 Upper 95% CL Predict = 130.63 Lower 95% CL Predict = 105.62 Rest_Pulse = 74 Upper 95% CL Predict = 129.88 Lower 95% CL Predict = 104.9 Rest_Pulse = 74 Upper 95% CL Predict = 129.88 Lower 95% CL Predict = 104.9 Rest_Pulse = 74 Upper 95% CL Predict = 129.88 Lower 95% CL Predict = 104.9 Rest_Pulse = 74 Upper 95% CL Predict = 129.88 Lower 95% CL Predict = 104.9 Rest_Pulse = 74 Upper 95% CL Predict = 129.88 Lower 95% CL Predict = 104.9 Rest_Pulse = 74 Upper 95% CL Predict = 129.88 Lower 95% CL Predict = 104.9 Rest_Pulse = 74 Upper 95% CL Predict = 129.88 Lower 95% CL Predict = 104.9 Rest_Pulse = 74 Upper 95% CL Predict = 129.88 Lower 95% CL Predict = 104.9 Rest_Pulse = 74 Upper 95% CL Predict = 129.88 Lower 95% CL Predict = 104.9 Rest_Pulse = 74 Upper 95% CL Predict = 129.88 Lower 95% CL Predict = 104.9 Rest_Pulse = 74 Upper 95% CL Predict = 129.88 Lower 95% CL Predict = 104.9 Rest_Pulse = 74 Upper 95% CL Predict = 129.88 Lower 95% CL Predict = 104.9 Rest_Pulse = 74 Upper 95% CL Predict = 129.88 Lower 95% CL Predict = 104.9 Rest_Pulse = 74 Upper 95% CL Predict = 129.88 Lower 95% CL Predict = 104.9 Rest_Pulse = 74 Upper 95% CL Predict = 129.88 Lower 95% CL Predict = 104.9 Rest_Pulse = 74 Upper 95% CL Predict = 129.88 Lower 95% CL Predict = 104.9 Rest_Pulse = 74 Upper 95% CL Predict = 129.88 Lower 95% CL Predict = 104.9 Rest_Pulse = 74 Upper 95% CL Predict = 129.88 Lower 95% CL Predict = 104.9 Rest_Pulse = 73 Upper 95% CL Predict = 129.13 Lower 95% CL Predict = 104.18 Rest_Pulse = 74 Upper 95% CL Predict = 129.88 Lower 95% CL Predict = 104.9 Rest_Pulse = 73 Upper 95% CL Predict = 129.13 Lower 95% CL Predict = 104.18 Rest_Pulse = 73 Upper 95% CL Predict = 129.13 Lower 95% CL Predict = 104.18 Rest_Pulse = 73 Upper 95% CL Predict = 129.13 Lower 95% CL Predict = 104.18 Rest_Pulse = 73 Upper 95% CL Predict = 129.13 Lower 95% CL Predict = 104.18 Rest_Pulse = 73 Upper 95% CL Predict = 129.13 Lower 95% CL Predict = 104.18 Rest_Pulse = 73 Upper 95% CL Predict = 129.13 Lower 95% CL Predict = 104.18 Rest_Pulse = 71 Upper 95% CL Predict = 127.64 Lower 95% CL Predict = 102.74 Rest_Pulse = 73 Upper 95% CL Predict = 129.13 Lower 95% CL Predict = 104.18 Rest_Pulse = 71 Upper 95% CL Predict = 127.64 Lower 95% CL Predict = 102.74 Rest_Pulse = 71 Upper 95% CL Predict = 127.64 Lower 95% CL Predict = 102.74 Rest_Pulse = 71 Upper 95% CL Predict = 127.64 Lower 95% CL Predict = 102.74 Rest_Pulse = 71 Upper 95% CL Predict = 127.64 Lower 95% CL Predict = 102.74 Rest_Pulse = 71 Upper 95% CL Predict = 127.64 Lower 95% CL Predict = 102.74 Rest_Pulse = 71 Upper 95% CL Predict = 127.64 Lower 95% CL Predict = 102.74 Rest_Pulse = 70 Upper 95% CL Predict = 126.9 Lower 95% CL Predict = 102.01 Rest_Pulse = 71 Upper 95% CL Predict = 127.64 Lower 95% CL Predict = 102.74 Rest_Pulse = 70 Upper 95% CL Predict = 126.9 Lower 95% CL Predict = 102.01 Rest_Pulse = 70 Upper 95% CL Predict = 126.9 Lower 95% CL Predict = 102.01 Rest_Pulse = 70 Upper 95% CL Predict = 126.9 Lower 95% CL Predict = 102.01 Rest_Pulse = 70 Upper 95% CL Predict = 126.9 Lower 95% CL Predict = 102.01 Rest_Pulse = 70 Upper 95% CL Predict = 126.9 Lower 95% CL Predict = 102.01 Rest_Pulse = 70 Upper 95% CL Predict = 126.9 Lower 95% CL Predict = 102.01 Rest_Pulse = 69 Upper 95% CL Predict = 126.17 Lower 95% CL Predict = 101.29 Rest_Pulse = 70 Upper 95% CL Predict = 126.9 Lower 95% CL Predict = 102.01 Rest_Pulse = 69 Upper 95% CL Predict = 126.17 Lower 95% CL Predict = 101.29 Rest_Pulse = 69 Upper 95% CL Predict = 126.17 Lower 95% CL Predict = 101.29 Rest_Pulse = 69 Upper 95% CL Predict = 126.17 Lower 95% CL Predict = 101.29 Rest_Pulse = 69 Upper 95% CL Predict = 126.17 Lower 95% CL Predict = 101.29 Rest_Pulse = 69 Upper 95% CL Predict = 126.17 Lower 95% CL Predict = 101.29 Rest_Pulse = 69 Upper 95% CL Predict = 126.17 Lower 95% CL Predict = 101.29 Rest_Pulse = 68 Upper 95% CL Predict = 125.43 Lower 95% CL Predict = 100.55 Rest_Pulse = 69 Upper 95% CL Predict = 126.17 Lower 95% CL Predict = 101.29 Rest_Pulse = 68 Upper 95% CL Predict = 125.43 Lower 95% CL Predict = 100.55 Rest_Pulse = 68 Upper 95% CL Predict = 125.43 Lower 95% CL Predict = 100.55 Rest_Pulse = 67 Upper 95% CL Predict = 124.7 Lower 95% CL Predict = 99.82 Rest_Pulse = 68 Upper 95% CL Predict = 125.43 Lower 95% CL Predict = 100.55 Rest_Pulse = 67 Upper 95% CL Predict = 124.7 Lower 95% CL Predict = 99.82 Rest_Pulse = 67 Upper 95% CL Predict = 124.7 Lower 95% CL Predict = 99.82 Rest_Pulse = 67 Upper 95% CL Predict = 124.7 Lower 95% CL Predict = 99.82 Rest_Pulse = 67 Upper 95% CL Predict = 124.7 Lower 95% CL Predict = 99.82 Rest_Pulse = 67 Upper 95% CL Predict = 124.7 Lower 95% CL Predict = 99.82 Rest_Pulse = 67 Upper 95% CL Predict = 124.7 Lower 95% CL Predict = 99.82 Rest_Pulse = 66 Upper 95% CL Predict = 123.97 Lower 95% CL Predict = 99.083 Rest_Pulse = 67 Upper 95% CL Predict = 124.7 Lower 95% CL Predict = 99.82 Rest_Pulse = 66 Upper 95% CL Predict = 123.97 Lower 95% CL Predict = 99.083 Rest_Pulse = 66 Upper 95% CL Predict = 123.97 Lower 95% CL Predict = 99.083 Rest_Pulse = 66 Upper 95% CL Predict = 123.97 Lower 95% CL Predict = 99.083 Rest_Pulse = 66 Upper 95% CL Predict = 123.97 Lower 95% CL Predict = 99.083 Rest_Pulse = 66 Upper 95% CL Predict = 123.97 Lower 95% CL Predict = 99.083 Rest_Pulse = 66 Upper 95% CL Predict = 123.97 Lower 95% CL Predict = 99.083 Rest_Pulse = 66 Upper 95% CL Predict = 123.97 Lower 95% CL Predict = 99.083 Rest_Pulse = 66 Upper 95% CL Predict = 123.97 Lower 95% CL Predict = 99.083 Rest_Pulse = 66 Upper 95% CL Predict = 123.97 Lower 95% CL Predict = 99.083 Rest_Pulse = 66 Upper 95% CL Predict = 123.97 Lower 95% CL Predict = 99.083 Rest_Pulse = 65 Upper 95% CL Predict = 123.24 Lower 95% CL Predict = 98.344 Rest_Pulse = 66 Upper 95% CL Predict = 123.97 Lower 95% CL Predict = 99.083 Rest_Pulse = 65 Upper 95% CL Predict = 123.24 Lower 95% CL Predict = 98.344 Rest_Pulse = 65 Upper 95% CL Predict = 123.24 Lower 95% CL Predict = 98.344 Rest_Pulse = 65 Upper 95% CL Predict = 123.24 Lower 95% CL Predict = 98.344 Rest_Pulse = 65 Upper 95% CL Predict = 123.24 Lower 95% CL Predict = 98.344 Rest_Pulse = 65 Upper 95% CL Predict = 123.24 Lower 95% CL Predict = 98.344 Rest_Pulse = 65 Upper 95% CL Predict = 123.24 Lower 95% CL Predict = 98.344 Rest_Pulse = 65 Upper 95% CL Predict = 123.24 Lower 95% CL Predict = 98.344 Rest_Pulse = 65 Upper 95% CL Predict = 123.24 Lower 95% CL Predict = 98.344 Rest_Pulse = 65 Upper 95% CL Predict = 123.24 Lower 95% CL Predict = 98.344 Rest_Pulse = 65 Upper 95% CL Predict = 123.24 Lower 95% CL Predict = 98.344 Rest_Pulse = 61 Upper 95% CL Predict = 120.36 Lower 95% CL Predict = 95.361 Rest_Pulse = 65 Upper 95% CL Predict = 123.24 Lower 95% CL Predict = 98.344 Rest_Pulse = 61 Upper 95% CL Predict = 120.36 Lower 95% CL Predict = 95.361 Rest_Pulse = 61 Upper 95% CL Predict = 120.36 Lower 95% CL Predict = 95.361 Rest_Pulse = 61 Upper 95% CL Predict = 120.36 Lower 95% CL Predict = 95.361 Rest_Pulse = 61 Upper 95% CL Predict = 120.36 Lower 95% CL Predict = 95.361 Rest_Pulse = 61 Upper 95% CL Predict = 120.36 Lower 95% CL Predict = 95.361 Rest_Pulse = 61 Upper 95% CL Predict = 120.36 Lower 95% CL Predict = 95.361 Rest_Pulse = 60 Upper 95% CL Predict = 119.65 Lower 95% CL Predict = 94.608 Rest_Pulse = 61 Upper 95% CL Predict = 120.36 Lower 95% CL Predict = 95.361 Rest_Pulse = 60 Upper 95% CL Predict = 119.65 Lower 95% CL Predict = 94.608 Rest_Pulse = 60 Upper 95% CL Predict = 119.65 Lower 95% CL Predict = 94.608 Rest_Pulse = 59 Upper 95% CL Predict = 118.94 Lower 95% CL Predict = 93.853 Rest_Pulse = 60 Upper 95% CL Predict = 119.65 Lower 95% CL Predict = 94.608 Rest_Pulse = 59 Upper 95% CL Predict = 118.94 Lower 95% CL Predict = 93.853 Rest_Pulse = 59 Upper 95% CL Predict = 118.94 Lower 95% CL Predict = 93.853 Rest_Pulse = 59 Upper 95% CL Predict = 118.94 Lower 95% CL Predict = 93.853 Rest_Pulse = 59 Upper 95% CL Predict = 118.94 Lower 95% CL Predict = 93.853 Rest_Pulse = 59 Upper 95% CL Predict = 118.94 Lower 95% CL Predict = 93.853 Rest_Pulse = 59 Upper 95% CL Predict = 118.94 Lower 95% CL Predict = 93.853 Rest_Pulse = 59 Upper 95% CL Predict = 118.94 Lower 95% CL Predict = 93.853 Rest_Pulse = 59 Upper 95% CL Predict = 118.94 Lower 95% CL Predict = 93.853 Rest_Pulse = 59 Upper 95% CL Predict = 118.94 Lower 95% CL Predict = 93.853 Rest_Pulse = 59 Upper 95% CL Predict = 118.94 Lower 95% CL Predict = 93.853 Rest_Pulse = 59 Upper 95% CL Predict = 118.94 Lower 95% CL Predict = 93.853 Rest_Pulse = 59 Upper 95% CL Predict = 118.94 Lower 95% CL Predict = 93.853 Rest_Pulse = 59 Upper 95% CL Predict = 118.94 Lower 95% CL Predict = 93.853 Rest_Pulse = 59 Upper 95% CL Predict = 118.94 Lower 95% CL Predict = 93.853 Rest_Pulse = 58 Upper 95% CL Predict = 118.23 Lower 95% CL Predict = 93.096 Rest_Pulse = 59 Upper 95% CL Predict = 118.94 Lower 95% CL Predict = 93.853 Rest_Pulse = 58 Upper 95% CL Predict = 118.23 Lower 95% CL Predict = 93.096 Rest_Pulse = 58 Upper 95% CL Predict = 118.23 Lower 95% CL Predict = 93.096 Rest_Pulse = 55 Upper 95% CL Predict = 116.12 Lower 95% CL Predict = 90.808 Rest_Pulse = 58 Upper 95% CL Predict = 118.23 Lower 95% CL Predict = 93.096 Rest_Pulse = 55 Upper 95% CL Predict = 116.12 Lower 95% CL Predict = 90.808 Rest_Pulse = 55 Upper 95% CL Predict = 116.12 Lower 95% CL Predict = 90.808 Rest_Pulse = 55 Upper 95% CL Predict = 116.12 Lower 95% CL Predict = 90.808 Rest_Pulse = 55 Upper 95% CL Predict = 116.12 Lower 95% CL Predict = 90.808 Rest_Pulse = 55 Upper 95% CL Predict = 116.12 Lower 95% CL Predict = 90.808 Rest_Pulse = 55 Upper 95% CL Predict = 116.12 Lower 95% CL Predict = 90.808 Rest_Pulse = 55 Upper 95% CL Predict = 116.12 Lower 95% CL Predict = 90.808 Rest_Pulse = 55 Upper 95% CL Predict = 116.12 Lower 95% CL Predict = 90.808 Rest_Pulse = 55 Upper 95% CL Predict = 116.12 Lower 95% CL Predict = 90.808 Rest_Pulse = 55 Upper 95% CL Predict = 116.12 Lower 95% CL Predict = 90.808 Rest_Pulse = 55 Upper 95% CL Predict = 116.12 Lower 95% CL Predict = 90.808 Rest_Pulse = 55 Upper 95% CL Predict = 116.12 Lower 95% CL Predict = 90.808 Rest_Pulse = 55 Upper 95% CL Predict = 116.12 Lower 95% CL Predict = 90.808 Rest_Pulse = 55 Upper 95% CL Predict = 116.12 Lower 95% CL Predict = 90.808 Rest_Pulse = 55 Upper 95% CL Predict = 116.12 Lower 95% CL Predict = 90.808 Rest_Pulse = 55 Upper 95% CL Predict = 116.12 Lower 95% CL Predict = 90.808 Rest_Pulse = 55 Upper 95% CL Predict = 116.12 Lower 95% CL Predict = 90.808 Rest_Pulse = 55 Upper 95% CL Predict = 116.12 Lower 95% CL Predict = 90.808 Rest_Pulse = 52 Upper 95% CL Predict = 114.03 Lower 95% CL Predict = 88.498 Rest_Pulse = 55 Upper 95% CL Predict = 116.12 Lower 95% CL Predict = 90.808 Rest_Pulse = 52 Upper 95% CL Predict = 114.03 Lower 95% CL Predict = 88.498 Rest_Pulse = 52 Upper 95% CL Predict = 114.03 Lower 95% CL Predict = 88.498 Rest_Pulse = 51 Upper 95% CL Predict = 113.34 Lower 95% CL Predict = 87.723 Rest_Pulse = 52 Upper 95% CL Predict = 114.03 Lower 95% CL Predict = 88.498 Rest_Pulse = 51 Upper 95% CL Predict = 113.34 Lower 95% CL Predict = 87.723 Rest_Pulse = 51 Upper 95% CL Predict = 113.34 Lower 95% CL Predict = 87.723 Rest_Pulse = 49 Upper 95% CL Predict = 111.97 Lower 95% CL Predict = 86.165 Rest_Pulse = 51 Upper 95% CL Predict = 113.34 Lower 95% CL Predict = 87.723 Rest_Pulse = 49 Upper 95% CL Predict = 111.97 Lower 95% CL Predict = 86.165 Rest_Pulse = 88 Upper 95% CL Mean = 131.69 Lower 95% CL Mean = 123.62 Rest_Pulse = 86 Upper 95% CL Mean = 129.9 Lower 95% CL Mean = 122.47 Rest_Pulse = 86 Upper 95% CL Mean = 129.9 Lower 95% CL Mean = 122.47 Rest_Pulse = 85 Upper 95% CL Mean = 129.01 Lower 95% CL Mean = 121.9 Rest_Pulse = 85 Upper 95% CL Mean = 129.01 Lower 95% CL Mean = 121.9 Rest_Pulse = 84 Upper 95% CL Mean = 128.12 Lower 95% CL Mean = 121.32 Rest_Pulse = 84 Upper 95% CL Mean = 128.12 Lower 95% CL Mean = 121.32 Rest_Pulse = 82 Upper 95% CL Mean = 126.35 Lower 95% CL Mean = 120.16 Rest_Pulse = 82 Upper 95% CL Mean = 126.35 Lower 95% CL Mean = 120.16 Rest_Pulse = 78 Upper 95% CL Mean = 122.85 Lower 95% CL Mean = 117.8 Rest_Pulse = 78 Upper 95% CL Mean = 122.85 Lower 95% CL Mean = 117.8 Rest_Pulse = 77 Upper 95% CL Mean = 121.99 Lower 95% CL Mean = 117.19 Rest_Pulse = 77 Upper 95% CL Mean = 121.99 Lower 95% CL Mean = 117.19 Rest_Pulse = 76 Upper 95% CL Mean = 121.13 Lower 95% CL Mean = 116.58 Rest_Pulse = 76 Upper 95% CL Mean = 121.13 Lower 95% CL Mean = 116.58 Rest_Pulse = 75 Upper 95% CL Mean = 120.29 Lower 95% CL Mean = 115.96 Rest_Pulse = 75 Upper 95% CL Mean = 120.29 Lower 95% CL Mean = 115.96 Rest_Pulse = 74 Upper 95% CL Mean = 119.45 Lower 95% CL Mean = 115.33 Rest_Pulse = 74 Upper 95% CL Mean = 119.45 Lower 95% CL Mean = 115.33 Rest_Pulse = 73 Upper 95% CL Mean = 118.63 Lower 95% CL Mean = 114.69 Rest_Pulse = 73 Upper 95% CL Mean = 118.63 Lower 95% CL Mean = 114.69 Rest_Pulse = 71 Upper 95% CL Mean = 117.02 Lower 95% CL Mean = 113.36 Rest_Pulse = 71 Upper 95% CL Mean = 117.02 Lower 95% CL Mean = 113.36 Rest_Pulse = 70 Upper 95% CL Mean = 116.24 Lower 95% CL Mean = 112.68 Rest_Pulse = 70 Upper 95% CL Mean = 116.24 Lower 95% CL Mean = 112.68 Rest_Pulse = 69 Upper 95% CL Mean = 115.48 Lower 95% CL Mean = 111.97 Rest_Pulse = 69 Upper 95% CL Mean = 115.48 Lower 95% CL Mean = 111.97 Rest_Pulse = 68 Upper 95% CL Mean = 114.74 Lower 95% CL Mean = 111.25 Rest_Pulse = 68 Upper 95% CL Mean = 114.74 Lower 95% CL Mean = 111.25 Rest_Pulse = 67 Upper 95% CL Mean = 114.01 Lower 95% CL Mean = 110.51 Rest_Pulse = 67 Upper 95% CL Mean = 114.01 Lower 95% CL Mean = 110.51 Rest_Pulse = 66 Upper 95% CL Mean = 113.3 Lower 95% CL Mean = 109.75 Rest_Pulse = 66 Upper 95% CL Mean = 113.3 Lower 95% CL Mean = 109.75 Rest_Pulse = 65 Upper 95% CL Mean = 112.61 Lower 95% CL Mean = 108.98 Rest_Pulse = 65 Upper 95% CL Mean = 112.61 Lower 95% CL Mean = 108.98 Rest_Pulse = 61 Upper 95% CL Mean = 110.01 Lower 95% CL Mean = 105.72 Rest_Pulse = 61 Upper 95% CL Mean = 110.01 Lower 95% CL Mean = 105.72 Rest_Pulse = 60 Upper 95% CL Mean = 109.38 Lower 95% CL Mean = 104.88 Rest_Pulse = 60 Upper 95% CL Mean = 109.38 Lower 95% CL Mean = 104.88 Rest_Pulse = 59 Upper 95% CL Mean = 108.77 Lower 95% CL Mean = 104.02 Rest_Pulse = 59 Upper 95% CL Mean = 108.77 Lower 95% CL Mean = 104.02 Rest_Pulse = 58 Upper 95% CL Mean = 108.16 Lower 95% CL Mean = 103.16 Rest_Pulse = 58 Upper 95% CL Mean = 108.16 Lower 95% CL Mean = 103.16 Rest_Pulse = 55 Upper 95% CL Mean = 106.38 Lower 95% CL Mean = 100.55 Rest_Pulse = 55 Upper 95% CL Mean = 106.38 Lower 95% CL Mean = 100.55 Rest_Pulse = 52 Upper 95% CL Mean = 104.63 Lower 95% CL Mean = 97.9 Rest_Pulse = 52 Upper 95% CL Mean = 104.63 Lower 95% CL Mean = 97.9 Rest_Pulse = 51 Upper 95% CL Mean = 104.05 Lower 95% CL Mean = 97.011 Rest_Pulse = 51 Upper 95% CL Mean = 104.05 Lower 95% CL Mean = 97.011 Rest_Pulse = 49 Upper 95% CL Mean = 102.91 Lower 95% CL Mean = 95.226
Scatterplot of Run_Pulse by Rest_Pulse overlaid with the fit line, a 95% confidence band and lower and upper 95% prediction limits.

  • “The mean square due to the model is much larger than the mean square due to error, yielding a very large F-value and a low p-value. The mean of the dependent variable Run_Pulse is 112.92, and the adjusted R-square is .5710. (The addition of independent variables in a model causes the value of R-square to increase even if independent variables are only randomly correlated with the dependent variable; Adj R-Sq adjusts for the number of independent variables in the model and is a way to compare models with different numbers of independent variables.)”

  • The model is: Run_Pulse = 63.15163 + (.73297 * Rest_Pulse).

  • “The Residual by Predicted for Run_Pulse plot shows points that seem mostly random. The spread of the points around 0 does not tend to increase or decrease with different values of Run_Pulse.”

  • “The Cook’s D for Run_Pulse plot shows the Cook’s D value for each observation, where larger values indicates the more influential points.”

  • “The Q-Q Plot of Residuals for Run_Pulse shows the distribution of the residuals, where the points fall very closely around the straight line.”

  • “The shaded portion of the Fit plot for Run_Pulse graph represents the 95% confidence limit for the prediction of Run_Pulse for any given value of Rest_Pulse. The other, wider confidence limits marked with dashed lines are for individual data points. Given a value of Rest_Pulse, you are 95% confident that a random data point will be within these limits.”

Multiple Regression.

SAS Code, click to expand

SAS Code:

#  (&path1 and biostats libname previously defined)
/* Multiple Regression - generated code - start */

ods noproctitle;
ods graphics / imagemap=on;
title1 "Multiple Regression - Correlation Matrix"; 
proc corr data=work.exercise pearson spearman nosimple 
        plots(maxpoints=none)=matrix(histogram nvar=10);
    var Age Pushups Rest_Pulse Max_Pulse Run_Pulse;
run;

/* Strongest correlations are between Max_Pulse and Run_Pulse at 0.93634 with a p-value of <.0001.  The relationships between Age and Max_Pulse or Age and Run_Pulse are not statistically significant at the 0.05 level.   
 Nonparametric Spearman correlation matrix also provided.  
 "There are some strong correlations among the variables, and the condition where the predictor variables are highly correlated is called multi-collinearity.  This causes serious problems when these variables are all used in multiple regression."
*/ 

title1 "Multiple Regression - Linear Regression, part 1"; 
proc reg data=work.exercise  alpha=0.05 
  plots(only label)=(diagnostics residuals observedbypredicted);
    model Run_Pulse=Age Pushups Rest_Pulse Max_Pulse / vif;
    run;
quit;

/* This initial Linear Regression model's R-square .8869 and adjusted R-square .8768 appear highly significant, but once when we look at the parameter estimates we see that only Max_Pulse looks significant.  Also, a negative parameter estimate for Rest_Pulse also looks off.  
"VIF is a popular diagnostic test for multi-collinearity, and large values of VIF indicate multi-collinearity problems."  
Rest_Pulse has the highest value for Variance Inflation (VIF) at 4.30537, so we drop this parameter and rerun the regression.
*/

title1 "Multiple Regression - Linear Regression, part 2"; 
proc reg data=work.exercise  alpha=0.05 
  plots(only label)=(diagnostics residuals observedbypredicted);
    model Run_Pulse=Age Pushups Max_Pulse / vif;
    run;
quit;

/* The revised Linear Regression model's parameter estimates Variance Inflation (VIF) values are lower after Rest_Pulse is removed.
*/

title1; 
/* Multiple Regression - generated code - end */

SAS Output

Results: biostats_by_ex_SAScode.sas

Results: biostats_by_ex_SAScode.sas

Multiple Regression - Correlation Matrix

The Corr Procedure

Variables Information

5 Variables: Age Pushups Rest_Pulse Max_Pulse Run_Pulse

Pearson Correlations

Pearson Correlation Coefficients, N = 50
Prob > |r| under H0: Rho=0
  Age Pushups Rest_Pulse Max_Pulse Run_Pulse
Age
Age
1.00000
 
-0.49191
0.0003
0.48774
0.0003
0.26582
0.0621
0.25097
0.0788
Pushups
Pushups
-0.49191
0.0003
1.00000
 
-0.49639
0.0002
-0.45010
0.0010
-0.34555
0.0140
Rest_Pulse
Rest_Pulse
0.48774
0.0003
-0.49639
0.0002
1.00000
 
0.83112
<.0001
0.76139
<.0001
Max_Pulse
Max_Pulse
0.26582
0.0621
-0.45010
0.0010
0.83112
<.0001
1.00000
 
0.93634
<.0001
Run_Pulse
Run_Pulse
0.25097
0.0788
-0.34555
0.0140
0.76139
<.0001
0.93634
<.0001
1.00000
 

Spearman Correlations

Spearman Correlation Coefficients, N = 50
Prob > |r| under H0: Rho=0
  Age Pushups Rest_Pulse Max_Pulse Run_Pulse
Age
Age
1.00000
 
-0.46625
0.0006
0.48269
0.0004
0.25725
0.0713
0.25123
0.0784
Pushups
Pushups
-0.46625
0.0006
1.00000
 
-0.48882
0.0003
-0.45181
0.0010
-0.33960
0.0158
Rest_Pulse
Rest_Pulse
0.48269
0.0004
-0.48882
0.0003
1.00000
 
0.80310
<.0001
0.70668
<.0001
Max_Pulse
Max_Pulse
0.25725
0.0713
-0.45181
0.0010
0.80310
<.0001
1.00000
 
0.91251
<.0001
Run_Pulse
Run_Pulse
0.25123
0.0784
-0.33960
0.0158
0.70668
<.0001
0.91251
<.0001
1.00000
 

Scatter Plot Matrix

Age = 84 Percent = 6 Age = 84 Percent = 6 Age = 72 Percent = 12 Age = 72 Percent = 12 Age = 60 Percent = 28 Age = 60 Percent = 28 Age = 48 Percent = 28 Age = 48 Percent = 28 Age = 36 Percent = 18 Age = 36 Percent = 18 Age = 24 Percent = 8 Age = 24 Percent = 8 Age = 79 Pushups = 10 Observation = 50 Age = 31 Pushups = 22 Observation = 49 Age = 46 Pushups = 19 Observation = 48 Age = 59 Pushups = 25 Observation = 47 Age = 31 Pushups = 48 Observation = 46 Age = 49 Pushups = 22 Observation = 45 Age = 52 Pushups = 27 Observation = 44 Age = 49 Pushups = 33 Observation = 43 Age = 34 Pushups = 38 Observation = 42 Age = 41 Pushups = 17 Observation = 41 Age = 55 Pushups = 21 Observation = 40 Age = 56 Pushups = 8 Observation = 39 Age = 31 Pushups = 30 Observation = 38 Age = 64 Pushups = 20 Observation = 37 Age = 64 Pushups = 22 Observation = 36 Age = 60 Pushups = 36 Observation = 35 Age = 69 Pushups = 26 Observation = 34 Age = 48 Pushups = 21 Observation = 33 Age = 44 Pushups = 1 Observation = 32 Age = 26 Pushups = 40 Observation = 31 Age = 23 Pushups = 30 Observation = 30 Age = 53 Pushups = 9 Observation = 29 Age = 57 Pushups = 31 Observation = 28 Age = 68 Pushups = 32 Observation = 27 Age = 43 Pushups = 33 Observation = 26 Age = 73 Pushups = 8 Observation = 25 Age = 36 Pushups = 25 Observation = 24 Age = 73 Pushups = 12 Observation = 23 Age = 84 Pushups = 11 Observation = 22 Age = 26 Pushups = 52 Observation = 21 Age = 81 Pushups = 16 Observation = 20 Age = 31 Pushups = 50 Observation = 19 Age = 43 Pushups = 29 Observation = 18 Age = 49 Pushups = 11 Observation = 17 Age = 48 Pushups = 43 Observation = 16 Age = 54 Pushups = 7 Observation = 15 Age = 51 Pushups = 23 Observation = 14 Age = 19 Pushups = 34 Observation = 13 Age = 63 Pushups = 30 Observation = 12 Age = 63 Pushups = 51 Observation = 11 Age = 49 Pushups = 9 Observation = 10 Age = 35 Pushups = 25 Observation = 9 Age = 30 Pushups = 48 Observation = 8 Age = 64 Pushups = 21 Observation = 7 Age = 57 Pushups = 14 Observation = 6 Age = 55 Pushups = 24 Observation = 5 Age = 44 Pushups = 35 Observation = 4 Age = 76 Pushups = 11 Observation = 3 Age = 64 Pushups = 36 Observation = 2 Age = 68 Pushups = 19 Observation = 1 Age = 79 Rest_Pulse = 82 Observation = 50 Age = 31 Rest_Pulse = 74 Observation = 49 Age = 46 Rest_Pulse = 84 Observation = 48 Age = 59 Rest_Pulse = 71 Observation = 47 Age = 31 Rest_Pulse = 55 Observation = 46 Age = 49 Rest_Pulse = 61 Observation = 45 Age = 52 Rest_Pulse = 52 Observation = 44 Age = 49 Rest_Pulse = 51 Observation = 43 Age = 34 Rest_Pulse = 73 Observation = 42 Age = 41 Rest_Pulse = 74 Observation = 41 Age = 55 Rest_Pulse = 71 Observation = 40 Age = 56 Rest_Pulse = 74 Observation = 39 Age = 31 Rest_Pulse = 65 Observation = 38 Age = 64 Rest_Pulse = 85 Observation = 37 Age = 64 Rest_Pulse = 78 Observation = 36 Age = 60 Rest_Pulse = 65 Observation = 35 Age = 69 Rest_Pulse = 69 Observation = 34 Age = 48 Rest_Pulse = 59 Observation = 33 Age = 44 Rest_Pulse = 59 Observation = 32 Age = 26 Rest_Pulse = 55 Observation = 31 Age = 23 Rest_Pulse = 58 Observation = 30 Age = 53 Rest_Pulse = 66 Observation = 29 Age = 57 Rest_Pulse = 67 Observation = 28 Age = 68 Rest_Pulse = 70 Observation = 27 Age = 43 Rest_Pulse = 70 Observation = 26 Age = 73 Rest_Pulse = 67 Observation = 25 Age = 36 Rest_Pulse = 66 Observation = 24 Age = 73 Rest_Pulse = 77 Observation = 23 Age = 84 Rest_Pulse = 75 Observation = 22 Age = 26 Rest_Pulse = 49 Observation = 21 Age = 81 Rest_Pulse = 86 Observation = 20 Age = 31 Rest_Pulse = 55 Observation = 19 Age = 43 Rest_Pulse = 78 Observation = 18 Age = 49 Rest_Pulse = 68 Observation = 17 Age = 48 Rest_Pulse = 77 Observation = 16 Age = 54 Rest_Pulse = 59 Observation = 15 Age = 51 Rest_Pulse = 66 Observation = 14 Age = 19 Rest_Pulse = 65 Observation = 13 Age = 63 Rest_Pulse = 73 Observation = 12 Age = 63 Rest_Pulse = 55 Observation = 11 Age = 49 Rest_Pulse = 88 Observation = 10 Age = 35 Rest_Pulse = 55 Observation = 9 Age = 30 Rest_Pulse = 60 Observation = 8 Age = 64 Rest_Pulse = 69 Observation = 7 Age = 57 Rest_Pulse = 74 Observation = 6 Age = 55 Rest_Pulse = 76 Observation = 5 Age = 44 Rest_Pulse = 59 Observation = 4 Age = 76 Rest_Pulse = 74 Observation = 3 Age = 64 Rest_Pulse = 61 Observation = 2 Age = 68 Rest_Pulse = 75 Observation = 1 Age = 79 Max_Pulse = 124 Observation = 50 Age = 31 Max_Pulse = 118 Observation = 49 Age = 46 Max_Pulse = 130 Observation = 48 Age = 59 Max_Pulse = 110 Observation = 47 Age = 31 Max_Pulse = 109 Observation = 46 Age = 49 Max_Pulse = 118 Observation = 45 Age = 52 Max_Pulse = 104 Observation = 44 Age = 49 Max_Pulse = 94 Observation = 43 Age = 34 Max_Pulse = 120 Observation = 42 Age = 41 Max_Pulse = 127 Observation = 41 Age = 55 Max_Pulse = 112 Observation = 40 Age = 56 Max_Pulse = 122 Observation = 39 Age = 31 Max_Pulse = 111 Observation = 38 Age = 64 Max_Pulse = 137 Observation = 37 Age = 64 Max_Pulse = 126 Observation = 36 Age = 60 Max_Pulse = 111 Observation = 35 Age = 69 Max_Pulse = 112 Observation = 34 Age = 48 Max_Pulse = 109 Observation = 33 Age = 44 Max_Pulse = 107 Observation = 32 Age = 26 Max_Pulse = 114 Observation = 31 Age = 23 Max_Pulse = 105 Observation = 30 Age = 53 Max_Pulse = 127 Observation = 29 Age = 57 Max_Pulse = 111 Observation = 28 Age = 68 Max_Pulse = 125 Observation = 27 Age = 43 Max_Pulse = 111 Observation = 26 Age = 73 Max_Pulse = 112 Observation = 25 Age = 36 Max_Pulse = 117 Observation = 24 Age = 73 Max_Pulse = 119 Observation = 23 Age = 84 Max_Pulse = 114 Observation = 22 Age = 26 Max_Pulse = 100 Observation = 21 Age = 81 Max_Pulse = 127 Observation = 20 Age = 31 Max_Pulse = 100 Observation = 19 Age = 43 Max_Pulse = 122 Observation = 18 Age = 49 Max_Pulse = 118 Observation = 17 Age = 48 Max_Pulse = 119 Observation = 16 Age = 54 Max_Pulse = 113 Observation = 15 Age = 51 Max_Pulse = 114 Observation = 14 Age = 19 Max_Pulse = 118 Observation = 13 Age = 63 Max_Pulse = 126 Observation = 12 Age = 63 Max_Pulse = 102 Observation = 11 Age = 49 Max_Pulse = 137 Observation = 10 Age = 35 Max_Pulse = 107 Observation = 9 Age = 30 Max_Pulse = 114 Observation = 8 Age = 64 Max_Pulse = 106 Observation = 7 Age = 57 Max_Pulse = 121 Observation = 6 Age = 55 Max_Pulse = 115 Observation = 5 Age = 44 Max_Pulse = 111 Observation = 4 Age = 76 Max_Pulse = 115 Observation = 3 Age = 64 Max_Pulse = 107 Observation = 2 Age = 68 Max_Pulse = 124 Observation = 1 Age = 79 Run_Pulse = 124 Observation = 50 Age = 31 Run_Pulse = 108 Observation = 49 Age = 46 Run_Pulse = 127 Observation = 48 Age = 59 Run_Pulse = 108 Observation = 47 Age = 31 Run_Pulse = 104 Observation = 46 Age = 49 Run_Pulse = 115 Observation = 45 Age = 52 Run_Pulse = 103 Observation = 44 Age = 49 Run_Pulse = 92 Observation = 43 Age = 34 Run_Pulse = 125 Observation = 42 Age = 41 Run_Pulse = 122 Observation = 41 Age = 55 Run_Pulse = 108 Observation = 40 Age = 56 Run_Pulse = 118 Observation = 39 Age = 31 Run_Pulse = 111 Observation = 38 Age = 64 Run_Pulse = 141 Observation = 37 Age = 64 Run_Pulse = 127 Observation = 36 Age = 60 Run_Pulse = 109 Observation = 35 Age = 69 Run_Pulse = 112 Observation = 34 Age = 48 Run_Pulse = 108 Observation = 33 Age = 44 Run_Pulse = 104 Observation = 32 Age = 26 Run_Pulse = 116 Observation = 31 Age = 23 Run_Pulse = 104 Observation = 30 Age = 53 Run_Pulse = 119 Observation = 29 Age = 57 Run_Pulse = 114 Observation = 28 Age = 68 Run_Pulse = 120 Observation = 27 Age = 43 Run_Pulse = 105 Observation = 26 Age = 73 Run_Pulse = 111 Observation = 25 Age = 36 Run_Pulse = 117 Observation = 24 Age = 73 Run_Pulse = 116 Observation = 23 Age = 84 Run_Pulse = 108 Observation = 22 Age = 26 Run_Pulse = 95 Observation = 21 Age = 81 Run_Pulse = 119 Observation = 20 Age = 31 Run_Pulse = 101 Observation = 19 Age = 43 Run_Pulse = 120 Observation = 18 Age = 49 Run_Pulse = 113 Observation = 17 Age = 48 Run_Pulse = 117 Observation = 16 Age = 54 Run_Pulse = 111 Observation = 15 Age = 51 Run_Pulse = 110 Observation = 14 Age = 19 Run_Pulse = 110 Observation = 13 Age = 63 Run_Pulse = 125 Observation = 12 Age = 63 Run_Pulse = 103 Observation = 11 Age = 49 Run_Pulse = 134 Observation = 10 Age = 35 Run_Pulse = 107 Observation = 9 Age = 30 Run_Pulse = 110 Observation = 8 Age = 64 Run_Pulse = 103 Observation = 7 Age = 57 Run_Pulse = 118 Observation = 6 Age = 55 Run_Pulse = 110 Observation = 5 Age = 44 Run_Pulse = 108 Observation = 4 Age = 76 Run_Pulse = 105 Observation = 3 Age = 64 Run_Pulse = 110 Observation = 2 Age = 68 Run_Pulse = 121 Observation = 1 Pushups = 10 Age = 79 Observation = 50 Pushups = 22 Age = 31 Observation = 49 Pushups = 19 Age = 46 Observation = 48 Pushups = 25 Age = 59 Observation = 47 Pushups = 48 Age = 31 Observation = 46 Pushups = 22 Age = 49 Observation = 45 Pushups = 27 Age = 52 Observation = 44 Pushups = 33 Age = 49 Observation = 43 Pushups = 38 Age = 34 Observation = 42 Pushups = 17 Age = 41 Observation = 41 Pushups = 21 Age = 55 Observation = 40 Pushups = 8 Age = 56 Observation = 39 Pushups = 30 Age = 31 Observation = 38 Pushups = 20 Age = 64 Observation = 37 Pushups = 22 Age = 64 Observation = 36 Pushups = 36 Age = 60 Observation = 35 Pushups = 26 Age = 69 Observation = 34 Pushups = 21 Age = 48 Observation = 33 Pushups = 1 Age = 44 Observation = 32 Pushups = 40 Age = 26 Observation = 31 Pushups = 30 Age = 23 Observation = 30 Pushups = 9 Age = 53 Observation = 29 Pushups = 31 Age = 57 Observation = 28 Pushups = 32 Age = 68 Observation = 27 Pushups = 33 Age = 43 Observation = 26 Pushups = 8 Age = 73 Observation = 25 Pushups = 25 Age = 36 Observation = 24 Pushups = 12 Age = 73 Observation = 23 Pushups = 11 Age = 84 Observation = 22 Pushups = 52 Age = 26 Observation = 21 Pushups = 16 Age = 81 Observation = 20 Pushups = 50 Age = 31 Observation = 19 Pushups = 29 Age = 43 Observation = 18 Pushups = 11 Age = 49 Observation = 17 Pushups = 43 Age = 48 Observation = 16 Pushups = 7 Age = 54 Observation = 15 Pushups = 23 Age = 51 Observation = 14 Pushups = 34 Age = 19 Observation = 13 Pushups = 30 Age = 63 Observation = 12 Pushups = 51 Age = 63 Observation = 11 Pushups = 9 Age = 49 Observation = 10 Pushups = 25 Age = 35 Observation = 9 Pushups = 48 Age = 30 Observation = 8 Pushups = 21 Age = 64 Observation = 7 Pushups = 14 Age = 57 Observation = 6 Pushups = 24 Age = 55 Observation = 5 Pushups = 35 Age = 44 Observation = 4 Pushups = 11 Age = 76 Observation = 3 Pushups = 36 Age = 64 Observation = 2 Pushups = 19 Age = 68 Observation = 1 Pushups = 50 Percent = 10 Pushups = 50 Percent = 10 Pushups = 40 Percent = 12 Pushups = 40 Percent = 12 Pushups = 30 Percent = 28 Pushups = 30 Percent = 28 Pushups = 20 Percent = 26 Pushups = 20 Percent = 26 Pushups = 10 Percent = 22 Pushups = 10 Percent = 22 Pushups = 0 Percent = 2 Pushups = 0 Percent = 2 Pushups = 10 Rest_Pulse = 82 Observation = 50 Pushups = 22 Rest_Pulse = 74 Observation = 49 Pushups = 19 Rest_Pulse = 84 Observation = 48 Pushups = 25 Rest_Pulse = 71 Observation = 47 Pushups = 48 Rest_Pulse = 55 Observation = 46 Pushups = 22 Rest_Pulse = 61 Observation = 45 Pushups = 27 Rest_Pulse = 52 Observation = 44 Pushups = 33 Rest_Pulse = 51 Observation = 43 Pushups = 38 Rest_Pulse = 73 Observation = 42 Pushups = 17 Rest_Pulse = 74 Observation = 41 Pushups = 21 Rest_Pulse = 71 Observation = 40 Pushups = 8 Rest_Pulse = 74 Observation = 39 Pushups = 30 Rest_Pulse = 65 Observation = 38 Pushups = 20 Rest_Pulse = 85 Observation = 37 Pushups = 22 Rest_Pulse = 78 Observation = 36 Pushups = 36 Rest_Pulse = 65 Observation = 35 Pushups = 26 Rest_Pulse = 69 Observation = 34 Pushups = 21 Rest_Pulse = 59 Observation = 33 Pushups = 1 Rest_Pulse = 59 Observation = 32 Pushups = 40 Rest_Pulse = 55 Observation = 31 Pushups = 30 Rest_Pulse = 58 Observation = 30 Pushups = 9 Rest_Pulse = 66 Observation = 29 Pushups = 31 Rest_Pulse = 67 Observation = 28 Pushups = 32 Rest_Pulse = 70 Observation = 27 Pushups = 33 Rest_Pulse = 70 Observation = 26 Pushups = 8 Rest_Pulse = 67 Observation = 25 Pushups = 25 Rest_Pulse = 66 Observation = 24 Pushups = 12 Rest_Pulse = 77 Observation = 23 Pushups = 11 Rest_Pulse = 75 Observation = 22 Pushups = 52 Rest_Pulse = 49 Observation = 21 Pushups = 16 Rest_Pulse = 86 Observation = 20 Pushups = 50 Rest_Pulse = 55 Observation = 19 Pushups = 29 Rest_Pulse = 78 Observation = 18 Pushups = 11 Rest_Pulse = 68 Observation = 17 Pushups = 43 Rest_Pulse = 77 Observation = 16 Pushups = 7 Rest_Pulse = 59 Observation = 15 Pushups = 23 Rest_Pulse = 66 Observation = 14 Pushups = 34 Rest_Pulse = 65 Observation = 13 Pushups = 30 Rest_Pulse = 73 Observation = 12 Pushups = 51 Rest_Pulse = 55 Observation = 11 Pushups = 9 Rest_Pulse = 88 Observation = 10 Pushups = 25 Rest_Pulse = 55 Observation = 9 Pushups = 48 Rest_Pulse = 60 Observation = 8 Pushups = 21 Rest_Pulse = 69 Observation = 7 Pushups = 14 Rest_Pulse = 74 Observation = 6 Pushups = 24 Rest_Pulse = 76 Observation = 5 Pushups = 35 Rest_Pulse = 59 Observation = 4 Pushups = 11 Rest_Pulse = 74 Observation = 3 Pushups = 36 Rest_Pulse = 61 Observation = 2 Pushups = 19 Rest_Pulse = 75 Observation = 1 Pushups = 10 Max_Pulse = 124 Observation = 50 Pushups = 22 Max_Pulse = 118 Observation = 49 Pushups = 19 Max_Pulse = 130 Observation = 48 Pushups = 25 Max_Pulse = 110 Observation = 47 Pushups = 48 Max_Pulse = 109 Observation = 46 Pushups = 22 Max_Pulse = 118 Observation = 45 Pushups = 27 Max_Pulse = 104 Observation = 44 Pushups = 33 Max_Pulse = 94 Observation = 43 Pushups = 38 Max_Pulse = 120 Observation = 42 Pushups = 17 Max_Pulse = 127 Observation = 41 Pushups = 21 Max_Pulse = 112 Observation = 40 Pushups = 8 Max_Pulse = 122 Observation = 39 Pushups = 30 Max_Pulse = 111 Observation = 38 Pushups = 20 Max_Pulse = 137 Observation = 37 Pushups = 22 Max_Pulse = 126 Observation = 36 Pushups = 36 Max_Pulse = 111 Observation = 35 Pushups = 26 Max_Pulse = 112 Observation = 34 Pushups = 21 Max_Pulse = 109 Observation = 33 Pushups = 1 Max_Pulse = 107 Observation = 32 Pushups = 40 Max_Pulse = 114 Observation = 31 Pushups = 30 Max_Pulse = 105 Observation = 30 Pushups = 9 Max_Pulse = 127 Observation = 29 Pushups = 31 Max_Pulse = 111 Observation = 28 Pushups = 32 Max_Pulse = 125 Observation = 27 Pushups = 33 Max_Pulse = 111 Observation = 26 Pushups = 8 Max_Pulse = 112 Observation = 25 Pushups = 25 Max_Pulse = 117 Observation = 24 Pushups = 12 Max_Pulse = 119 Observation = 23 Pushups = 11 Max_Pulse = 114 Observation = 22 Pushups = 52 Max_Pulse = 100 Observation = 21 Pushups = 16 Max_Pulse = 127 Observation = 20 Pushups = 50 Max_Pulse = 100 Observation = 19 Pushups = 29 Max_Pulse = 122 Observation = 18 Pushups = 11 Max_Pulse = 118 Observation = 17 Pushups = 43 Max_Pulse = 119 Observation = 16 Pushups = 7 Max_Pulse = 113 Observation = 15 Pushups = 23 Max_Pulse = 114 Observation = 14 Pushups = 34 Max_Pulse = 118 Observation = 13 Pushups = 30 Max_Pulse = 126 Observation = 12 Pushups = 51 Max_Pulse = 102 Observation = 11 Pushups = 9 Max_Pulse = 137 Observation = 10 Pushups = 25 Max_Pulse = 107 Observation = 9 Pushups = 48 Max_Pulse = 114 Observation = 8 Pushups = 21 Max_Pulse = 106 Observation = 7 Pushups = 14 Max_Pulse = 121 Observation = 6 Pushups = 24 Max_Pulse = 115 Observation = 5 Pushups = 35 Max_Pulse = 111 Observation = 4 Pushups = 11 Max_Pulse = 115 Observation = 3 Pushups = 36 Max_Pulse = 107 Observation = 2 Pushups = 19 Max_Pulse = 124 Observation = 1 Pushups = 10 Run_Pulse = 124 Observation = 50 Pushups = 22 Run_Pulse = 108 Observation = 49 Pushups = 19 Run_Pulse = 127 Observation = 48 Pushups = 25 Run_Pulse = 108 Observation = 47 Pushups = 48 Run_Pulse = 104 Observation = 46 Pushups = 22 Run_Pulse = 115 Observation = 45 Pushups = 27 Run_Pulse = 103 Observation = 44 Pushups = 33 Run_Pulse = 92 Observation = 43 Pushups = 38 Run_Pulse = 125 Observation = 42 Pushups = 17 Run_Pulse = 122 Observation = 41 Pushups = 21 Run_Pulse = 108 Observation = 40 Pushups = 8 Run_Pulse = 118 Observation = 39 Pushups = 30 Run_Pulse = 111 Observation = 38 Pushups = 20 Run_Pulse = 141 Observation = 37 Pushups = 22 Run_Pulse = 127 Observation = 36 Pushups = 36 Run_Pulse = 109 Observation = 35 Pushups = 26 Run_Pulse = 112 Observation = 34 Pushups = 21 Run_Pulse = 108 Observation = 33 Pushups = 1 Run_Pulse = 104 Observation = 32 Pushups = 40 Run_Pulse = 116 Observation = 31 Pushups = 30 Run_Pulse = 104 Observation = 30 Pushups = 9 Run_Pulse = 119 Observation = 29 Pushups = 31 Run_Pulse = 114 Observation = 28 Pushups = 32 Run_Pulse = 120 Observation = 27 Pushups = 33 Run_Pulse = 105 Observation = 26 Pushups = 8 Run_Pulse = 111 Observation = 25 Pushups = 25 Run_Pulse = 117 Observation = 24 Pushups = 12 Run_Pulse = 116 Observation = 23 Pushups = 11 Run_Pulse = 108 Observation = 22 Pushups = 52 Run_Pulse = 95 Observation = 21 Pushups = 16 Run_Pulse = 119 Observation = 20 Pushups = 50 Run_Pulse = 101 Observation = 19 Pushups = 29 Run_Pulse = 120 Observation = 18 Pushups = 11 Run_Pulse = 113 Observation = 17 Pushups = 43 Run_Pulse = 117 Observation = 16 Pushups = 7 Run_Pulse = 111 Observation = 15 Pushups = 23 Run_Pulse = 110 Observation = 14 Pushups = 34 Run_Pulse = 110 Observation = 13 Pushups = 30 Run_Pulse = 125 Observation = 12 Pushups = 51 Run_Pulse = 103 Observation = 11 Pushups = 9 Run_Pulse = 134 Observation = 10 Pushups = 25 Run_Pulse = 107 Observation = 9 Pushups = 48 Run_Pulse = 110 Observation = 8 Pushups = 21 Run_Pulse = 103 Observation = 7 Pushups = 14 Run_Pulse = 118 Observation = 6 Pushups = 24 Run_Pulse = 110 Observation = 5 Pushups = 35 Run_Pulse = 108 Observation = 4 Pushups = 11 Run_Pulse = 105 Observation = 3 Pushups = 36 Run_Pulse = 110 Observation = 2 Pushups = 19 Run_Pulse = 121 Observation = 1 Rest_Pulse = 82 Age = 79 Observation = 50 Rest_Pulse = 74 Age = 31 Observation = 49 Rest_Pulse = 84 Age = 46 Observation = 48 Rest_Pulse = 71 Age = 59 Observation = 47 Rest_Pulse = 55 Age = 31 Observation = 46 Rest_Pulse = 61 Age = 49 Observation = 45 Rest_Pulse = 52 Age = 52 Observation = 44 Rest_Pulse = 51 Age = 49 Observation = 43 Rest_Pulse = 73 Age = 34 Observation = 42 Rest_Pulse = 74 Age = 41 Observation = 41 Rest_Pulse = 71 Age = 55 Observation = 40 Rest_Pulse = 74 Age = 56 Observation = 39 Rest_Pulse = 65 Age = 31 Observation = 38 Rest_Pulse = 85 Age = 64 Observation = 37 Rest_Pulse = 78 Age = 64 Observation = 36 Rest_Pulse = 65 Age = 60 Observation = 35 Rest_Pulse = 69 Age = 69 Observation = 34 Rest_Pulse = 59 Age = 48 Observation = 33 Rest_Pulse = 59 Age = 44 Observation = 32 Rest_Pulse = 55 Age = 26 Observation = 31 Rest_Pulse = 58 Age = 23 Observation = 30 Rest_Pulse = 66 Age = 53 Observation = 29 Rest_Pulse = 67 Age = 57 Observation = 28 Rest_Pulse = 70 Age = 68 Observation = 27 Rest_Pulse = 70 Age = 43 Observation = 26 Rest_Pulse = 67 Age = 73 Observation = 25 Rest_Pulse = 66 Age = 36 Observation = 24 Rest_Pulse = 77 Age = 73 Observation = 23 Rest_Pulse = 75 Age = 84 Observation = 22 Rest_Pulse = 49 Age = 26 Observation = 21 Rest_Pulse = 86 Age = 81 Observation = 20 Rest_Pulse = 55 Age = 31 Observation = 19 Rest_Pulse = 78 Age = 43 Observation = 18 Rest_Pulse = 68 Age = 49 Observation = 17 Rest_Pulse = 77 Age = 48 Observation = 16 Rest_Pulse = 59 Age = 54 Observation = 15 Rest_Pulse = 66 Age = 51 Observation = 14 Rest_Pulse = 65 Age = 19 Observation = 13 Rest_Pulse = 73 Age = 63 Observation = 12 Rest_Pulse = 55 Age = 63 Observation = 11 Rest_Pulse = 88 Age = 49 Observation = 10 Rest_Pulse = 55 Age = 35 Observation = 9 Rest_Pulse = 60 Age = 30 Observation = 8 Rest_Pulse = 69 Age = 64 Observation = 7 Rest_Pulse = 74 Age = 57 Observation = 6 Rest_Pulse = 76 Age = 55 Observation = 5 Rest_Pulse = 59 Age = 44 Observation = 4 Rest_Pulse = 74 Age = 76 Observation = 3 Rest_Pulse = 61 Age = 64 Observation = 2 Rest_Pulse = 75 Age = 68 Observation = 1 Rest_Pulse = 82 Pushups = 10 Observation = 50 Rest_Pulse = 74 Pushups = 22 Observation = 49 Rest_Pulse = 84 Pushups = 19 Observation = 48 Rest_Pulse = 71 Pushups = 25 Observation = 47 Rest_Pulse = 55 Pushups = 48 Observation = 46 Rest_Pulse = 61 Pushups = 22 Observation = 45 Rest_Pulse = 52 Pushups = 27 Observation = 44 Rest_Pulse = 51 Pushups = 33 Observation = 43 Rest_Pulse = 73 Pushups = 38 Observation = 42 Rest_Pulse = 74 Pushups = 17 Observation = 41 Rest_Pulse = 71 Pushups = 21 Observation = 40 Rest_Pulse = 74 Pushups = 8 Observation = 39 Rest_Pulse = 65 Pushups = 30 Observation = 38 Rest_Pulse = 85 Pushups = 20 Observation = 37 Rest_Pulse = 78 Pushups = 22 Observation = 36 Rest_Pulse = 65 Pushups = 36 Observation = 35 Rest_Pulse = 69 Pushups = 26 Observation = 34 Rest_Pulse = 59 Pushups = 21 Observation = 33 Rest_Pulse = 59 Pushups = 1 Observation = 32 Rest_Pulse = 55 Pushups = 40 Observation = 31 Rest_Pulse = 58 Pushups = 30 Observation = 30 Rest_Pulse = 66 Pushups = 9 Observation = 29 Rest_Pulse = 67 Pushups = 31 Observation = 28 Rest_Pulse = 70 Pushups = 32 Observation = 27 Rest_Pulse = 70 Pushups = 33 Observation = 26 Rest_Pulse = 67 Pushups = 8 Observation = 25 Rest_Pulse = 66 Pushups = 25 Observation = 24 Rest_Pulse = 77 Pushups = 12 Observation = 23 Rest_Pulse = 75 Pushups = 11 Observation = 22 Rest_Pulse = 49 Pushups = 52 Observation = 21 Rest_Pulse = 86 Pushups = 16 Observation = 20 Rest_Pulse = 55 Pushups = 50 Observation = 19 Rest_Pulse = 78 Pushups = 29 Observation = 18 Rest_Pulse = 68 Pushups = 11 Observation = 17 Rest_Pulse = 77 Pushups = 43 Observation = 16 Rest_Pulse = 59 Pushups = 7 Observation = 15 Rest_Pulse = 66 Pushups = 23 Observation = 14 Rest_Pulse = 65 Pushups = 34 Observation = 13 Rest_Pulse = 73 Pushups = 30 Observation = 12 Rest_Pulse = 55 Pushups = 51 Observation = 11 Rest_Pulse = 88 Pushups = 9 Observation = 10 Rest_Pulse = 55 Pushups = 25 Observation = 9 Rest_Pulse = 60 Pushups = 48 Observation = 8 Rest_Pulse = 69 Pushups = 21 Observation = 7 Rest_Pulse = 74 Pushups = 14 Observation = 6 Rest_Pulse = 76 Pushups = 24 Observation = 5 Rest_Pulse = 59 Pushups = 35 Observation = 4 Rest_Pulse = 74 Pushups = 11 Observation = 3 Rest_Pulse = 61 Pushups = 36 Observation = 2 Rest_Pulse = 75 Pushups = 19 Observation = 1 Rest_Pulse = 87 Percent = 8 Rest_Pulse = 87 Percent = 8 Rest_Pulse = 81 Percent = 6 Rest_Pulse = 81 Percent = 6 Rest_Pulse = 75 Percent = 24 Rest_Pulse = 75 Percent = 24 Rest_Pulse = 69 Percent = 24 Rest_Pulse = 69 Percent = 24 Rest_Pulse = 63 Percent = 12 Rest_Pulse = 63 Percent = 12 Rest_Pulse = 57 Percent = 20 Rest_Pulse = 57 Percent = 20 Rest_Pulse = 51 Percent = 6 Rest_Pulse = 51 Percent = 6 Rest_Pulse = 82 Max_Pulse = 124 Observation = 50 Rest_Pulse = 74 Max_Pulse = 118 Observation = 49 Rest_Pulse = 84 Max_Pulse = 130 Observation = 48 Rest_Pulse = 71 Max_Pulse = 110 Observation = 47 Rest_Pulse = 55 Max_Pulse = 109 Observation = 46 Rest_Pulse = 61 Max_Pulse = 118 Observation = 45 Rest_Pulse = 52 Max_Pulse = 104 Observation = 44 Rest_Pulse = 51 Max_Pulse = 94 Observation = 43 Rest_Pulse = 73 Max_Pulse = 120 Observation = 42 Rest_Pulse = 74 Max_Pulse = 127 Observation = 41 Rest_Pulse = 71 Max_Pulse = 112 Observation = 40 Rest_Pulse = 74 Max_Pulse = 122 Observation = 39 Rest_Pulse = 65 Max_Pulse = 111 Observation = 38 Rest_Pulse = 85 Max_Pulse = 137 Observation = 37 Rest_Pulse = 78 Max_Pulse = 126 Observation = 36 Rest_Pulse = 65 Max_Pulse = 111 Observation = 35 Rest_Pulse = 69 Max_Pulse = 112 Observation = 34 Rest_Pulse = 59 Max_Pulse = 109 Observation = 33 Rest_Pulse = 59 Max_Pulse = 107 Observation = 32 Rest_Pulse = 55 Max_Pulse = 114 Observation = 31 Rest_Pulse = 58 Max_Pulse = 105 Observation = 30 Rest_Pulse = 66 Max_Pulse = 127 Observation = 29 Rest_Pulse = 67 Max_Pulse = 111 Observation = 28 Rest_Pulse = 70 Max_Pulse = 125 Observation = 27 Rest_Pulse = 70 Max_Pulse = 111 Observation = 26 Rest_Pulse = 67 Max_Pulse = 112 Observation = 25 Rest_Pulse = 66 Max_Pulse = 117 Observation = 24 Rest_Pulse = 77 Max_Pulse = 119 Observation = 23 Rest_Pulse = 75 Max_Pulse = 114 Observation = 22 Rest_Pulse = 49 Max_Pulse = 100 Observation = 21 Rest_Pulse = 86 Max_Pulse = 127 Observation = 20 Rest_Pulse = 55 Max_Pulse = 100 Observation = 19 Rest_Pulse = 78 Max_Pulse = 122 Observation = 18 Rest_Pulse = 68 Max_Pulse = 118 Observation = 17 Rest_Pulse = 77 Max_Pulse = 119 Observation = 16 Rest_Pulse = 59 Max_Pulse = 113 Observation = 15 Rest_Pulse = 66 Max_Pulse = 114 Observation = 14 Rest_Pulse = 65 Max_Pulse = 118 Observation = 13 Rest_Pulse = 73 Max_Pulse = 126 Observation = 12 Rest_Pulse = 55 Max_Pulse = 102 Observation = 11 Rest_Pulse = 88 Max_Pulse = 137 Observation = 10 Rest_Pulse = 55 Max_Pulse = 107 Observation = 9 Rest_Pulse = 60 Max_Pulse = 114 Observation = 8 Rest_Pulse = 69 Max_Pulse = 106 Observation = 7 Rest_Pulse = 74 Max_Pulse = 121 Observation = 6 Rest_Pulse = 76 Max_Pulse = 115 Observation = 5 Rest_Pulse = 59 Max_Pulse = 111 Observation = 4 Rest_Pulse = 74 Max_Pulse = 115 Observation = 3 Rest_Pulse = 61 Max_Pulse = 107 Observation = 2 Rest_Pulse = 75 Max_Pulse = 124 Observation = 1 Rest_Pulse = 82 Run_Pulse = 124 Observation = 50 Rest_Pulse = 74 Run_Pulse = 108 Observation = 49 Rest_Pulse = 84 Run_Pulse = 127 Observation = 48 Rest_Pulse = 71 Run_Pulse = 108 Observation = 47 Rest_Pulse = 55 Run_Pulse = 104 Observation = 46 Rest_Pulse = 61 Run_Pulse = 115 Observation = 45 Rest_Pulse = 52 Run_Pulse = 103 Observation = 44 Rest_Pulse = 51 Run_Pulse = 92 Observation = 43 Rest_Pulse = 73 Run_Pulse = 125 Observation = 42 Rest_Pulse = 74 Run_Pulse = 122 Observation = 41 Rest_Pulse = 71 Run_Pulse = 108 Observation = 40 Rest_Pulse = 74 Run_Pulse = 118 Observation = 39 Rest_Pulse = 65 Run_Pulse = 111 Observation = 38 Rest_Pulse = 85 Run_Pulse = 141 Observation = 37 Rest_Pulse = 78 Run_Pulse = 127 Observation = 36 Rest_Pulse = 65 Run_Pulse = 109 Observation = 35 Rest_Pulse = 69 Run_Pulse = 112 Observation = 34 Rest_Pulse = 59 Run_Pulse = 108 Observation = 33 Rest_Pulse = 59 Run_Pulse = 104 Observation = 32 Rest_Pulse = 55 Run_Pulse = 116 Observation = 31 Rest_Pulse = 58 Run_Pulse = 104 Observation = 30 Rest_Pulse = 66 Run_Pulse = 119 Observation = 29 Rest_Pulse = 67 Run_Pulse = 114 Observation = 28 Rest_Pulse = 70 Run_Pulse = 120 Observation = 27 Rest_Pulse = 70 Run_Pulse = 105 Observation = 26 Rest_Pulse = 67 Run_Pulse = 111 Observation = 25 Rest_Pulse = 66 Run_Pulse = 117 Observation = 24 Rest_Pulse = 77 Run_Pulse = 116 Observation = 23 Rest_Pulse = 75 Run_Pulse = 108 Observation = 22 Rest_Pulse = 49 Run_Pulse = 95 Observation = 21 Rest_Pulse = 86 Run_Pulse = 119 Observation = 20 Rest_Pulse = 55 Run_Pulse = 101 Observation = 19 Rest_Pulse = 78 Run_Pulse = 120 Observation = 18 Rest_Pulse = 68 Run_Pulse = 113 Observation = 17 Rest_Pulse = 77 Run_Pulse = 117 Observation = 16 Rest_Pulse = 59 Run_Pulse = 111 Observation = 15 Rest_Pulse = 66 Run_Pulse = 110 Observation = 14 Rest_Pulse = 65 Run_Pulse = 110 Observation = 13 Rest_Pulse = 73 Run_Pulse = 125 Observation = 12 Rest_Pulse = 55 Run_Pulse = 103 Observation = 11 Rest_Pulse = 88 Run_Pulse = 134 Observation = 10 Rest_Pulse = 55 Run_Pulse = 107 Observation = 9 Rest_Pulse = 60 Run_Pulse = 110 Observation = 8 Rest_Pulse = 69 Run_Pulse = 103 Observation = 7 Rest_Pulse = 74 Run_Pulse = 118 Observation = 6 Rest_Pulse = 76 Run_Pulse = 110 Observation = 5 Rest_Pulse = 59 Run_Pulse = 108 Observation = 4 Rest_Pulse = 74 Run_Pulse = 105 Observation = 3 Rest_Pulse = 61 Run_Pulse = 110 Observation = 2 Rest_Pulse = 75 Run_Pulse = 121 Observation = 1 Max_Pulse = 124 Age = 79 Observation = 50 Max_Pulse = 118 Age = 31 Observation = 49 Max_Pulse = 130 Age = 46 Observation = 48 Max_Pulse = 110 Age = 59 Observation = 47 Max_Pulse = 109 Age = 31 Observation = 46 Max_Pulse = 118 Age = 49 Observation = 45 Max_Pulse = 104 Age = 52 Observation = 44 Max_Pulse = 94 Age = 49 Observation = 43 Max_Pulse = 120 Age = 34 Observation = 42 Max_Pulse = 127 Age = 41 Observation = 41 Max_Pulse = 112 Age = 55 Observation = 40 Max_Pulse = 122 Age = 56 Observation = 39 Max_Pulse = 111 Age = 31 Observation = 38 Max_Pulse = 137 Age = 64 Observation = 37 Max_Pulse = 126 Age = 64 Observation = 36 Max_Pulse = 111 Age = 60 Observation = 35 Max_Pulse = 112 Age = 69 Observation = 34 Max_Pulse = 109 Age = 48 Observation = 33 Max_Pulse = 107 Age = 44 Observation = 32 Max_Pulse = 114 Age = 26 Observation = 31 Max_Pulse = 105 Age = 23 Observation = 30 Max_Pulse = 127 Age = 53 Observation = 29 Max_Pulse = 111 Age = 57 Observation = 28 Max_Pulse = 125 Age = 68 Observation = 27 Max_Pulse = 111 Age = 43 Observation = 26 Max_Pulse = 112 Age = 73 Observation = 25 Max_Pulse = 117 Age = 36 Observation = 24 Max_Pulse = 119 Age = 73 Observation = 23 Max_Pulse = 114 Age = 84 Observation = 22 Max_Pulse = 100 Age = 26 Observation = 21 Max_Pulse = 127 Age = 81 Observation = 20 Max_Pulse = 100 Age = 31 Observation = 19 Max_Pulse = 122 Age = 43 Observation = 18 Max_Pulse = 118 Age = 49 Observation = 17 Max_Pulse = 119 Age = 48 Observation = 16 Max_Pulse = 113 Age = 54 Observation = 15 Max_Pulse = 114 Age = 51 Observation = 14 Max_Pulse = 118 Age = 19 Observation = 13 Max_Pulse = 126 Age = 63 Observation = 12 Max_Pulse = 102 Age = 63 Observation = 11 Max_Pulse = 137 Age = 49 Observation = 10 Max_Pulse = 107 Age = 35 Observation = 9 Max_Pulse = 114 Age = 30 Observation = 8 Max_Pulse = 106 Age = 64 Observation = 7 Max_Pulse = 121 Age = 57 Observation = 6 Max_Pulse = 115 Age = 55 Observation = 5 Max_Pulse = 111 Age = 44 Observation = 4 Max_Pulse = 115 Age = 76 Observation = 3 Max_Pulse = 107 Age = 64 Observation = 2 Max_Pulse = 124 Age = 68 Observation = 1 Max_Pulse = 124 Pushups = 10 Observation = 50 Max_Pulse = 118 Pushups = 22 Observation = 49 Max_Pulse = 130 Pushups = 19 Observation = 48 Max_Pulse = 110 Pushups = 25 Observation = 47 Max_Pulse = 109 Pushups = 48 Observation = 46 Max_Pulse = 118 Pushups = 22 Observation = 45 Max_Pulse = 104 Pushups = 27 Observation = 44 Max_Pulse = 94 Pushups = 33 Observation = 43 Max_Pulse = 120 Pushups = 38 Observation = 42 Max_Pulse = 127 Pushups = 17 Observation = 41 Max_Pulse = 112 Pushups = 21 Observation = 40 Max_Pulse = 122 Pushups = 8 Observation = 39 Max_Pulse = 111 Pushups = 30 Observation = 38 Max_Pulse = 137 Pushups = 20 Observation = 37 Max_Pulse = 126 Pushups = 22 Observation = 36 Max_Pulse = 111 Pushups = 36 Observation = 35 Max_Pulse = 112 Pushups = 26 Observation = 34 Max_Pulse = 109 Pushups = 21 Observation = 33 Max_Pulse = 107 Pushups = 1 Observation = 32 Max_Pulse = 114 Pushups = 40 Observation = 31 Max_Pulse = 105 Pushups = 30 Observation = 30 Max_Pulse = 127 Pushups = 9 Observation = 29 Max_Pulse = 111 Pushups = 31 Observation = 28 Max_Pulse = 125 Pushups = 32 Observation = 27 Max_Pulse = 111 Pushups = 33 Observation = 26 Max_Pulse = 112 Pushups = 8 Observation = 25 Max_Pulse = 117 Pushups = 25 Observation = 24 Max_Pulse = 119 Pushups = 12 Observation = 23 Max_Pulse = 114 Pushups = 11 Observation = 22 Max_Pulse = 100 Pushups = 52 Observation = 21 Max_Pulse = 127 Pushups = 16 Observation = 20 Max_Pulse = 100 Pushups = 50 Observation = 19 Max_Pulse = 122 Pushups = 29 Observation = 18 Max_Pulse = 118 Pushups = 11 Observation = 17 Max_Pulse = 119 Pushups = 43 Observation = 16 Max_Pulse = 113 Pushups = 7 Observation = 15 Max_Pulse = 114 Pushups = 23 Observation = 14 Max_Pulse = 118 Pushups = 34 Observation = 13 Max_Pulse = 126 Pushups = 30 Observation = 12 Max_Pulse = 102 Pushups = 51 Observation = 11 Max_Pulse = 137 Pushups = 9 Observation = 10 Max_Pulse = 107 Pushups = 25 Observation = 9 Max_Pulse = 114 Pushups = 48 Observation = 8 Max_Pulse = 106 Pushups = 21 Observation = 7 Max_Pulse = 121 Pushups = 14 Observation = 6 Max_Pulse = 115 Pushups = 24 Observation = 5 Max_Pulse = 111 Pushups = 35 Observation = 4 Max_Pulse = 115 Pushups = 11 Observation = 3 Max_Pulse = 107 Pushups = 36 Observation = 2 Max_Pulse = 124 Pushups = 19 Observation = 1 Max_Pulse = 124 Rest_Pulse = 82 Observation = 50 Max_Pulse = 118 Rest_Pulse = 74 Observation = 49 Max_Pulse = 130 Rest_Pulse = 84 Observation = 48 Max_Pulse = 110 Rest_Pulse = 71 Observation = 47 Max_Pulse = 109 Rest_Pulse = 55 Observation = 46 Max_Pulse = 118 Rest_Pulse = 61 Observation = 45 Max_Pulse = 104 Rest_Pulse = 52 Observation = 44 Max_Pulse = 94 Rest_Pulse = 51 Observation = 43 Max_Pulse = 120 Rest_Pulse = 73 Observation = 42 Max_Pulse = 127 Rest_Pulse = 74 Observation = 41 Max_Pulse = 112 Rest_Pulse = 71 Observation = 40 Max_Pulse = 122 Rest_Pulse = 74 Observation = 39 Max_Pulse = 111 Rest_Pulse = 65 Observation = 38 Max_Pulse = 137 Rest_Pulse = 85 Observation = 37 Max_Pulse = 126 Rest_Pulse = 78 Observation = 36 Max_Pulse = 111 Rest_Pulse = 65 Observation = 35 Max_Pulse = 112 Rest_Pulse = 69 Observation = 34 Max_Pulse = 109 Rest_Pulse = 59 Observation = 33 Max_Pulse = 107 Rest_Pulse = 59 Observation = 32 Max_Pulse = 114 Rest_Pulse = 55 Observation = 31 Max_Pulse = 105 Rest_Pulse = 58 Observation = 30 Max_Pulse = 127 Rest_Pulse = 66 Observation = 29 Max_Pulse = 111 Rest_Pulse = 67 Observation = 28 Max_Pulse = 125 Rest_Pulse = 70 Observation = 27 Max_Pulse = 111 Rest_Pulse = 70 Observation = 26 Max_Pulse = 112 Rest_Pulse = 67 Observation = 25 Max_Pulse = 117 Rest_Pulse = 66 Observation = 24 Max_Pulse = 119 Rest_Pulse = 77 Observation = 23 Max_Pulse = 114 Rest_Pulse = 75 Observation = 22 Max_Pulse = 100 Rest_Pulse = 49 Observation = 21 Max_Pulse = 127 Rest_Pulse = 86 Observation = 20 Max_Pulse = 100 Rest_Pulse = 55 Observation = 19 Max_Pulse = 122 Rest_Pulse = 78 Observation = 18 Max_Pulse = 118 Rest_Pulse = 68 Observation = 17 Max_Pulse = 119 Rest_Pulse = 77 Observation = 16 Max_Pulse = 113 Rest_Pulse = 59 Observation = 15 Max_Pulse = 114 Rest_Pulse = 66 Observation = 14 Max_Pulse = 118 Rest_Pulse = 65 Observation = 13 Max_Pulse = 126 Rest_Pulse = 73 Observation = 12 Max_Pulse = 102 Rest_Pulse = 55 Observation = 11 Max_Pulse = 137 Rest_Pulse = 88 Observation = 10 Max_Pulse = 107 Rest_Pulse = 55 Observation = 9 Max_Pulse = 114 Rest_Pulse = 60 Observation = 8 Max_Pulse = 106 Rest_Pulse = 69 Observation = 7 Max_Pulse = 121 Rest_Pulse = 74 Observation = 6 Max_Pulse = 115 Rest_Pulse = 76 Observation = 5 Max_Pulse = 111 Rest_Pulse = 59 Observation = 4 Max_Pulse = 115 Rest_Pulse = 74 Observation = 3 Max_Pulse = 107 Rest_Pulse = 61 Observation = 2 Max_Pulse = 124 Rest_Pulse = 75 Observation = 1 Max_Pulse = 136 Percent = 4 Max_Pulse = 136 Percent = 4 Max_Pulse = 128 Percent = 18 Max_Pulse = 128 Percent = 18 Max_Pulse = 120 Percent = 22 Max_Pulse = 120 Percent = 22 Max_Pulse = 112 Percent = 36 Max_Pulse = 112 Percent = 36 Max_Pulse = 104 Percent = 18 Max_Pulse = 104 Percent = 18 Max_Pulse = 96 Percent = 2 Max_Pulse = 96 Percent = 2 Max_Pulse = 124 Run_Pulse = 124 Observation = 50 Max_Pulse = 118 Run_Pulse = 108 Observation = 49 Max_Pulse = 130 Run_Pulse = 127 Observation = 48 Max_Pulse = 110 Run_Pulse = 108 Observation = 47 Max_Pulse = 109 Run_Pulse = 104 Observation = 46 Max_Pulse = 118 Run_Pulse = 115 Observation = 45 Max_Pulse = 104 Run_Pulse = 103 Observation = 44 Max_Pulse = 94 Run_Pulse = 92 Observation = 43 Max_Pulse = 120 Run_Pulse = 125 Observation = 42 Max_Pulse = 127 Run_Pulse = 122 Observation = 41 Max_Pulse = 112 Run_Pulse = 108 Observation = 40 Max_Pulse = 122 Run_Pulse = 118 Observation = 39 Max_Pulse = 111 Run_Pulse = 111 Observation = 38 Max_Pulse = 137 Run_Pulse = 141 Observation = 37 Max_Pulse = 126 Run_Pulse = 127 Observation = 36 Max_Pulse = 111 Run_Pulse = 109 Observation = 35 Max_Pulse = 112 Run_Pulse = 112 Observation = 34 Max_Pulse = 109 Run_Pulse = 108 Observation = 33 Max_Pulse = 107 Run_Pulse = 104 Observation = 32 Max_Pulse = 114 Run_Pulse = 116 Observation = 31 Max_Pulse = 105 Run_Pulse = 104 Observation = 30 Max_Pulse = 127 Run_Pulse = 119 Observation = 29 Max_Pulse = 111 Run_Pulse = 114 Observation = 28 Max_Pulse = 125 Run_Pulse = 120 Observation = 27 Max_Pulse = 111 Run_Pulse = 105 Observation = 26 Max_Pulse = 112 Run_Pulse = 111 Observation = 25 Max_Pulse = 117 Run_Pulse = 117 Observation = 24 Max_Pulse = 119 Run_Pulse = 116 Observation = 23 Max_Pulse = 114 Run_Pulse = 108 Observation = 22 Max_Pulse = 100 Run_Pulse = 95 Observation = 21 Max_Pulse = 127 Run_Pulse = 119 Observation = 20 Max_Pulse = 100 Run_Pulse = 101 Observation = 19 Max_Pulse = 122 Run_Pulse = 120 Observation = 18 Max_Pulse = 118 Run_Pulse = 113 Observation = 17 Max_Pulse = 119 Run_Pulse = 117 Observation = 16 Max_Pulse = 113 Run_Pulse = 111 Observation = 15 Max_Pulse = 114 Run_Pulse = 110 Observation = 14 Max_Pulse = 118 Run_Pulse = 110 Observation = 13 Max_Pulse = 126 Run_Pulse = 125 Observation = 12 Max_Pulse = 102 Run_Pulse = 103 Observation = 11 Max_Pulse = 137 Run_Pulse = 134 Observation = 10 Max_Pulse = 107 Run_Pulse = 107 Observation = 9 Max_Pulse = 114 Run_Pulse = 110 Observation = 8 Max_Pulse = 106 Run_Pulse = 103 Observation = 7 Max_Pulse = 121 Run_Pulse = 118 Observation = 6 Max_Pulse = 115 Run_Pulse = 110 Observation = 5 Max_Pulse = 111 Run_Pulse = 108 Observation = 4 Max_Pulse = 115 Run_Pulse = 105 Observation = 3 Max_Pulse = 107 Run_Pulse = 110 Observation = 2 Max_Pulse = 124 Run_Pulse = 121 Observation = 1 Run_Pulse = 124 Age = 79 Observation = 50 Run_Pulse = 108 Age = 31 Observation = 49 Run_Pulse = 127 Age = 46 Observation = 48 Run_Pulse = 108 Age = 59 Observation = 47 Run_Pulse = 104 Age = 31 Observation = 46 Run_Pulse = 115 Age = 49 Observation = 45 Run_Pulse = 103 Age = 52 Observation = 44 Run_Pulse = 92 Age = 49 Observation = 43 Run_Pulse = 125 Age = 34 Observation = 42 Run_Pulse = 122 Age = 41 Observation = 41 Run_Pulse = 108 Age = 55 Observation = 40 Run_Pulse = 118 Age = 56 Observation = 39 Run_Pulse = 111 Age = 31 Observation = 38 Run_Pulse = 141 Age = 64 Observation = 37 Run_Pulse = 127 Age = 64 Observation = 36 Run_Pulse = 109 Age = 60 Observation = 35 Run_Pulse = 112 Age = 69 Observation = 34 Run_Pulse = 108 Age = 48 Observation = 33 Run_Pulse = 104 Age = 44 Observation = 32 Run_Pulse = 116 Age = 26 Observation = 31 Run_Pulse = 104 Age = 23 Observation = 30 Run_Pulse = 119 Age = 53 Observation = 29 Run_Pulse = 114 Age = 57 Observation = 28 Run_Pulse = 120 Age = 68 Observation = 27 Run_Pulse = 105 Age = 43 Observation = 26 Run_Pulse = 111 Age = 73 Observation = 25 Run_Pulse = 117 Age = 36 Observation = 24 Run_Pulse = 116 Age = 73 Observation = 23 Run_Pulse = 108 Age = 84 Observation = 22 Run_Pulse = 95 Age = 26 Observation = 21 Run_Pulse = 119 Age = 81 Observation = 20 Run_Pulse = 101 Age = 31 Observation = 19 Run_Pulse = 120 Age = 43 Observation = 18 Run_Pulse = 113 Age = 49 Observation = 17 Run_Pulse = 117 Age = 48 Observation = 16 Run_Pulse = 111 Age = 54 Observation = 15 Run_Pulse = 110 Age = 51 Observation = 14 Run_Pulse = 110 Age = 19 Observation = 13 Run_Pulse = 125 Age = 63 Observation = 12 Run_Pulse = 103 Age = 63 Observation = 11 Run_Pulse = 134 Age = 49 Observation = 10 Run_Pulse = 107 Age = 35 Observation = 9 Run_Pulse = 110 Age = 30 Observation = 8 Run_Pulse = 103 Age = 64 Observation = 7 Run_Pulse = 118 Age = 57 Observation = 6 Run_Pulse = 110 Age = 55 Observation = 5 Run_Pulse = 108 Age = 44 Observation = 4 Run_Pulse = 105 Age = 76 Observation = 3 Run_Pulse = 110 Age = 64 Observation = 2 Run_Pulse = 121 Age = 68 Observation = 1 Run_Pulse = 124 Pushups = 10 Observation = 50 Run_Pulse = 108 Pushups = 22 Observation = 49 Run_Pulse = 127 Pushups = 19 Observation = 48 Run_Pulse = 108 Pushups = 25 Observation = 47 Run_Pulse = 104 Pushups = 48 Observation = 46 Run_Pulse = 115 Pushups = 22 Observation = 45 Run_Pulse = 103 Pushups = 27 Observation = 44 Run_Pulse = 92 Pushups = 33 Observation = 43 Run_Pulse = 125 Pushups = 38 Observation = 42 Run_Pulse = 122 Pushups = 17 Observation = 41 Run_Pulse = 108 Pushups = 21 Observation = 40 Run_Pulse = 118 Pushups = 8 Observation = 39 Run_Pulse = 111 Pushups = 30 Observation = 38 Run_Pulse = 141 Pushups = 20 Observation = 37 Run_Pulse = 127 Pushups = 22 Observation = 36 Run_Pulse = 109 Pushups = 36 Observation = 35 Run_Pulse = 112 Pushups = 26 Observation = 34 Run_Pulse = 108 Pushups = 21 Observation = 33 Run_Pulse = 104 Pushups = 1 Observation = 32 Run_Pulse = 116 Pushups = 40 Observation = 31 Run_Pulse = 104 Pushups = 30 Observation = 30 Run_Pulse = 119 Pushups = 9 Observation = 29 Run_Pulse = 114 Pushups = 31 Observation = 28 Run_Pulse = 120 Pushups = 32 Observation = 27 Run_Pulse = 105 Pushups = 33 Observation = 26 Run_Pulse = 111 Pushups = 8 Observation = 25 Run_Pulse = 117 Pushups = 25 Observation = 24 Run_Pulse = 116 Pushups = 12 Observation = 23 Run_Pulse = 108 Pushups = 11 Observation = 22 Run_Pulse = 95 Pushups = 52 Observation = 21 Run_Pulse = 119 Pushups = 16 Observation = 20 Run_Pulse = 101 Pushups = 50 Observation = 19 Run_Pulse = 120 Pushups = 29 Observation = 18 Run_Pulse = 113 Pushups = 11 Observation = 17 Run_Pulse = 117 Pushups = 43 Observation = 16 Run_Pulse = 111 Pushups = 7 Observation = 15 Run_Pulse = 110 Pushups = 23 Observation = 14 Run_Pulse = 110 Pushups = 34 Observation = 13 Run_Pulse = 125 Pushups = 30 Observation = 12 Run_Pulse = 103 Pushups = 51 Observation = 11 Run_Pulse = 134 Pushups = 9 Observation = 10 Run_Pulse = 107 Pushups = 25 Observation = 9 Run_Pulse = 110 Pushups = 48 Observation = 8 Run_Pulse = 103 Pushups = 21 Observation = 7 Run_Pulse = 118 Pushups = 14 Observation = 6 Run_Pulse = 110 Pushups = 24 Observation = 5 Run_Pulse = 108 Pushups = 35 Observation = 4 Run_Pulse = 105 Pushups = 11 Observation = 3 Run_Pulse = 110 Pushups = 36 Observation = 2 Run_Pulse = 121 Pushups = 19 Observation = 1 Run_Pulse = 124 Rest_Pulse = 82 Observation = 50 Run_Pulse = 108 Rest_Pulse = 74 Observation = 49 Run_Pulse = 127 Rest_Pulse = 84 Observation = 48 Run_Pulse = 108 Rest_Pulse = 71 Observation = 47 Run_Pulse = 104 Rest_Pulse = 55 Observation = 46 Run_Pulse = 115 Rest_Pulse = 61 Observation = 45 Run_Pulse = 103 Rest_Pulse = 52 Observation = 44 Run_Pulse = 92 Rest_Pulse = 51 Observation = 43 Run_Pulse = 125 Rest_Pulse = 73 Observation = 42 Run_Pulse = 122 Rest_Pulse = 74 Observation = 41 Run_Pulse = 108 Rest_Pulse = 71 Observation = 40 Run_Pulse = 118 Rest_Pulse = 74 Observation = 39 Run_Pulse = 111 Rest_Pulse = 65 Observation = 38 Run_Pulse = 141 Rest_Pulse = 85 Observation = 37 Run_Pulse = 127 Rest_Pulse = 78 Observation = 36 Run_Pulse = 109 Rest_Pulse = 65 Observation = 35 Run_Pulse = 112 Rest_Pulse = 69 Observation = 34 Run_Pulse = 108 Rest_Pulse = 59 Observation = 33 Run_Pulse = 104 Rest_Pulse = 59 Observation = 32 Run_Pulse = 116 Rest_Pulse = 55 Observation = 31 Run_Pulse = 104 Rest_Pulse = 58 Observation = 30 Run_Pulse = 119 Rest_Pulse = 66 Observation = 29 Run_Pulse = 114 Rest_Pulse = 67 Observation = 28 Run_Pulse = 120 Rest_Pulse = 70 Observation = 27 Run_Pulse = 105 Rest_Pulse = 70 Observation = 26 Run_Pulse = 111 Rest_Pulse = 67 Observation = 25 Run_Pulse = 117 Rest_Pulse = 66 Observation = 24 Run_Pulse = 116 Rest_Pulse = 77 Observation = 23 Run_Pulse = 108 Rest_Pulse = 75 Observation = 22 Run_Pulse = 95 Rest_Pulse = 49 Observation = 21 Run_Pulse = 119 Rest_Pulse = 86 Observation = 20 Run_Pulse = 101 Rest_Pulse = 55 Observation = 19 Run_Pulse = 120 Rest_Pulse = 78 Observation = 18 Run_Pulse = 113 Rest_Pulse = 68 Observation = 17 Run_Pulse = 117 Rest_Pulse = 77 Observation = 16 Run_Pulse = 111 Rest_Pulse = 59 Observation = 15 Run_Pulse = 110 Rest_Pulse = 66 Observation = 14 Run_Pulse = 110 Rest_Pulse = 65 Observation = 13 Run_Pulse = 125 Rest_Pulse = 73 Observation = 12 Run_Pulse = 103 Rest_Pulse = 55 Observation = 11 Run_Pulse = 134 Rest_Pulse = 88 Observation = 10 Run_Pulse = 107 Rest_Pulse = 55 Observation = 9 Run_Pulse = 110 Rest_Pulse = 60 Observation = 8 Run_Pulse = 103 Rest_Pulse = 69 Observation = 7 Run_Pulse = 118 Rest_Pulse = 74 Observation = 6 Run_Pulse = 110 Rest_Pulse = 76 Observation = 5 Run_Pulse = 108 Rest_Pulse = 59 Observation = 4 Run_Pulse = 105 Rest_Pulse = 74 Observation = 3 Run_Pulse = 110 Rest_Pulse = 61 Observation = 2 Run_Pulse = 121 Rest_Pulse = 75 Observation = 1 Run_Pulse = 124 Max_Pulse = 124 Observation = 50 Run_Pulse = 108 Max_Pulse = 118 Observation = 49 Run_Pulse = 127 Max_Pulse = 130 Observation = 48 Run_Pulse = 108 Max_Pulse = 110 Observation = 47 Run_Pulse = 104 Max_Pulse = 109 Observation = 46 Run_Pulse = 115 Max_Pulse = 118 Observation = 45 Run_Pulse = 103 Max_Pulse = 104 Observation = 44 Run_Pulse = 92 Max_Pulse = 94 Observation = 43 Run_Pulse = 125 Max_Pulse = 120 Observation = 42 Run_Pulse = 122 Max_Pulse = 127 Observation = 41 Run_Pulse = 108 Max_Pulse = 112 Observation = 40 Run_Pulse = 118 Max_Pulse = 122 Observation = 39 Run_Pulse = 111 Max_Pulse = 111 Observation = 38 Run_Pulse = 141 Max_Pulse = 137 Observation = 37 Run_Pulse = 127 Max_Pulse = 126 Observation = 36 Run_Pulse = 109 Max_Pulse = 111 Observation = 35 Run_Pulse = 112 Max_Pulse = 112 Observation = 34 Run_Pulse = 108 Max_Pulse = 109 Observation = 33 Run_Pulse = 104 Max_Pulse = 107 Observation = 32 Run_Pulse = 116 Max_Pulse = 114 Observation = 31 Run_Pulse = 104 Max_Pulse = 105 Observation = 30 Run_Pulse = 119 Max_Pulse = 127 Observation = 29 Run_Pulse = 114 Max_Pulse = 111 Observation = 28 Run_Pulse = 120 Max_Pulse = 125 Observation = 27 Run_Pulse = 105 Max_Pulse = 111 Observation = 26 Run_Pulse = 111 Max_Pulse = 112 Observation = 25 Run_Pulse = 117 Max_Pulse = 117 Observation = 24 Run_Pulse = 116 Max_Pulse = 119 Observation = 23 Run_Pulse = 108 Max_Pulse = 114 Observation = 22 Run_Pulse = 95 Max_Pulse = 100 Observation = 21 Run_Pulse = 119 Max_Pulse = 127 Observation = 20 Run_Pulse = 101 Max_Pulse = 100 Observation = 19 Run_Pulse = 120 Max_Pulse = 122 Observation = 18 Run_Pulse = 113 Max_Pulse = 118 Observation = 17 Run_Pulse = 117 Max_Pulse = 119 Observation = 16 Run_Pulse = 111 Max_Pulse = 113 Observation = 15 Run_Pulse = 110 Max_Pulse = 114 Observation = 14 Run_Pulse = 110 Max_Pulse = 118 Observation = 13 Run_Pulse = 125 Max_Pulse = 126 Observation = 12 Run_Pulse = 103 Max_Pulse = 102 Observation = 11 Run_Pulse = 134 Max_Pulse = 137 Observation = 10 Run_Pulse = 107 Max_Pulse = 107 Observation = 9 Run_Pulse = 110 Max_Pulse = 114 Observation = 8 Run_Pulse = 103 Max_Pulse = 106 Observation = 7 Run_Pulse = 118 Max_Pulse = 121 Observation = 6 Run_Pulse = 110 Max_Pulse = 115 Observation = 5 Run_Pulse = 108 Max_Pulse = 111 Observation = 4 Run_Pulse = 105 Max_Pulse = 115 Observation = 3 Run_Pulse = 110 Max_Pulse = 107 Observation = 2 Run_Pulse = 121 Max_Pulse = 124 Observation = 1 Run_Pulse = 140 Percent = 2 Run_Pulse = 140 Percent = 2 Run_Pulse = 132 Percent = 2 Run_Pulse = 132 Percent = 2 Run_Pulse = 124 Percent = 18 Run_Pulse = 124 Percent = 18 Run_Pulse = 116 Percent = 24 Run_Pulse = 116 Percent = 24 Run_Pulse = 108 Percent = 42 Run_Pulse = 108 Percent = 42 Run_Pulse = 100 Percent = 8 Run_Pulse = 100 Percent = 8 Run_Pulse = 92 Percent = 4 Run_Pulse = 92 Percent = 4
Scatter Plot Matrix

Multiple Regression - Linear Regression, part 1

Model: MODEL1

Dependent Variable: Run_Pulse Run_Pulse

The Reg Procedure

MODEL1

Fit

Run_Pulse

Number of Observations

Number of Observations Read 50
Number of Observations Used 50

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 4 3800.80979 950.20245 88.19 <.0001
Error 45 484.87021 10.77489    
Corrected Total 49 4285.68000      

Fit Statistics

Root MSE 3.28251 R-Square 0.8869
Dependent Mean 112.92000 Adj R-Sq 0.8768
Coeff Var 2.90694    

Parameter Estimates

Parameter Estimates
Variable Label DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t| Variance
Inflation
Intercept Intercept 1 -7.80929 8.04006 -0.97 0.3366 0
Age Age 1 0.03955 0.03738 1.06 0.2956 1.65524
Pushups Pushups 1 0.08573 0.04576 1.87 0.0675 1.54495
Rest_Pulse Rest_Pulse 1 -0.06462 0.10016 -0.65 0.5221 4.30537
Max_Pulse Max_Pulse 1 1.04744 0.09786 10.70 <.0001 3.65824

Multiple Regression - Linear Regression, part 1

Model: MODEL1

Dependent Variable: Run_Pulse Run_Pulse

Observation-wise Statistics

Run_Pulse

Diagnostic Plots

Observed by Predicted

Run_Pulse = 124 Predicted Value = 120.76 Observation Number = 50 Run_Pulse = 108 Predicted Value = 114.12 Observation Number = 49 Run_Pulse = 127 Predicted Value = 126.38 Observation Number = 48 Run_Pulse = 108 Predicted Value = 107.3 Observation Number = 47 Run_Pulse = 104 Predicted Value = 108.15 Observation Number = 46 Run_Pulse = 115 Predicted Value = 115.67 Observation Number = 45 Run_Pulse = 103 Predicted Value = 102.14 Observation Number = 44 Run_Pulse = 92 Predicted Value = 92.122 Observation Number = 43 Run_Pulse = 125 Predicted Value = 117.77 Observation Number = 42 Run_Pulse = 122 Predicted Value = 123.51 Observation Number = 41 Run_Pulse = 108 Predicted Value = 108.89 Observation Number = 40 Run_Pulse = 118 Predicted Value = 118.1 Observation Number = 39 Run_Pulse = 111 Predicted Value = 108.05 Observation Number = 38 Run_Pulse = 141 Predicted Value = 134.44 Observation Number = 37 Run_Pulse = 127 Predicted Value = 123.55 Observation Number = 36 Run_Pulse = 109 Predicted Value = 109.72 Observation Number = 35 Run_Pulse = 112 Predicted Value = 110 Observation Number = 34 Run_Pulse = 108 Predicted Value = 106.25 Observation Number = 33 Run_Pulse = 104 Predicted Value = 102.28 Observation Number = 32 Run_Pulse = 116 Predicted Value = 112.5 Observation Number = 31 Run_Pulse = 104 Predicted Value = 101.91 Observation Number = 30 Run_Pulse = 119 Predicted Value = 123.82 Observation Number = 29 Run_Pulse = 114 Predicted Value = 109.04 Observation Number = 28 Run_Pulse = 120 Predicted Value = 124.03 Observation Number = 27 Run_Pulse = 105 Predicted Value = 108.46 Observation Number = 26 Run_Pulse = 111 Predicted Value = 108.75 Observation Number = 25 Run_Pulse = 117 Predicted Value = 114.04 Observation Number = 24 Run_Pulse = 116 Predicted Value = 115.78 Observation Number = 23 Run_Pulse = 108 Predicted Value = 111.02 Observation Number = 22 Run_Pulse = 95 Predicted Value = 99.255 Observation Number = 21 Run_Pulse = 119 Predicted Value = 124.23 Observation Number = 20 Run_Pulse = 101 Predicted Value = 98.893 Observation Number = 19 Run_Pulse = 120 Predicted Value = 119.13 Observation Number = 18 Run_Pulse = 113 Predicted Value = 114.28 Observation Number = 17 Run_Pulse = 117 Predicted Value = 117.45 Observation Number = 16 Run_Pulse = 111 Predicted Value = 109.47 Observation Number = 15 Run_Pulse = 110 Predicted Value = 111.32 Observation Number = 14 Run_Pulse = 110 Predicted Value = 115.25 Observation Number = 13 Run_Pulse = 125 Predicted Value = 124.51 Observation Number = 12 Run_Pulse = 103 Predicted Value = 102.34 Observation Number = 11 Run_Pulse = 134 Predicted Value = 132.71 Observation Number = 10 Run_Pulse = 107 Predicted Value = 104.24 Observation Number = 9 Run_Pulse = 110 Predicted Value = 113.02 Observation Number = 8 Run_Pulse = 103 Predicted Value = 103.09 Observation Number = 7 Run_Pulse = 118 Predicted Value = 117.6 Observation Number = 6 Run_Pulse = 110 Predicted Value = 111.97 Observation Number = 5 Run_Pulse = 108 Predicted Value = 109.39 Observation Number = 4 Run_Pulse = 105 Predicted Value = 111.81 Observation Number = 3 Run_Pulse = 110 Predicted Value = 105.94 Observation Number = 2 Run_Pulse = 121 Predicted Value = 121.55 Observation Number = 1 Slope = 1 Y = 0
Scatter plot of observed by predicted values for Run_Pulse.

Fit Diagnostics

Residual = 3.2436 Predicted Value = 120.76 Observation Number = 50 Residual = -6.119 Predicted Value = 114.12 Observation Number = 49 Residual = 0.6218 Predicted Value = 126.38 Observation Number = 48 Residual = 0.702 Predicted Value = 107.3 Observation Number = 47 Residual = -4.149 Predicted Value = 108.15 Observation Number = 46 Residual = -0.671 Predicted Value = 115.67 Observation Number = 45 Residual = 0.8642 Predicted Value = 102.14 Observation Number = 44 Residual = -0.122 Predicted Value = 92.122 Observation Number = 43 Residual = 7.231 Predicted Value = 117.77 Observation Number = 42 Residual = -1.513 Predicted Value = 123.51 Observation Number = 41 Residual = -0.892 Predicted Value = 108.89 Observation Number = 40 Residual = -0.097 Predicted Value = 118.1 Observation Number = 39 Residual = 2.9456 Predicted Value = 108.05 Observation Number = 38 Residual = 6.5567 Predicted Value = 134.44 Observation Number = 37 Residual = 3.4547 Predicted Value = 123.55 Observation Number = 36 Residual = -0.716 Predicted Value = 109.72 Observation Number = 35 Residual = 1.9966 Predicted Value = 110 Observation Number = 34 Residual = 1.7519 Predicted Value = 106.25 Observation Number = 33 Residual = 1.7197 Predicted Value = 102.28 Observation Number = 32 Residual = 3.4974 Predicted Value = 112.5 Observation Number = 31 Residual = 2.0943 Predicted Value = 101.91 Observation Number = 30 Residual = -4.819 Predicted Value = 123.82 Observation Number = 29 Residual = 4.9607 Predicted Value = 109.04 Observation Number = 28 Residual = -4.03 Predicted Value = 124.03 Observation Number = 27 Residual = -3.463 Predicted Value = 108.46 Observation Number = 26 Residual = 2.2523 Predicted Value = 108.75 Observation Number = 25 Residual = 2.9564 Predicted Value = 114.04 Observation Number = 24 Residual = 0.2235 Predicted Value = 115.78 Observation Number = 23 Residual = -3.018 Predicted Value = 111.02 Observation Number = 22 Residual = -4.255 Predicted Value = 99.255 Observation Number = 21 Residual = -5.234 Predicted Value = 124.23 Observation Number = 20 Residual = 2.1065 Predicted Value = 98.893 Observation Number = 19 Residual = 0.8749 Predicted Value = 119.13 Observation Number = 18 Residual = -1.276 Predicted Value = 114.28 Observation Number = 17 Residual = -0.445 Predicted Value = 117.45 Observation Number = 16 Residual = 1.5251 Predicted Value = 109.47 Observation Number = 15 Residual = -1.323 Predicted Value = 111.32 Observation Number = 14 Residual = -5.255 Predicted Value = 115.25 Observation Number = 13 Residual = 0.4853 Predicted Value = 124.51 Observation Number = 12 Residual = 0.6602 Predicted Value = 102.34 Observation Number = 11 Residual = 1.2869 Predicted Value = 132.71 Observation Number = 10 Residual = 2.7596 Predicted Value = 104.24 Observation Number = 9 Residual = -3.024 Predicted Value = 113.02 Observation Number = 8 Residual = -0.092 Predicted Value = 103.09 Observation Number = 7 Residual = 0.3961 Predicted Value = 117.6 Observation Number = 6 Residual = -1.968 Predicted Value = 111.97 Observation Number = 5 Residual = -1.385 Predicted Value = 109.39 Observation Number = 4 Residual = -6.813 Predicted Value = 111.81 Observation Number = 3 Residual = 4.0572 Predicted Value = 105.94 Observation Number = 2 Residual = -0.545 Predicted Value = 121.55 Observation Number = 1 Y = 0 RStudent = 1.0376 Predicted Value = 120.76 Observation Number = 50 RStudent = -2.065 Predicted Value = 114.12 Observation Number = 49 RStudent = 0.1987 Predicted Value = 126.38 Observation Number = 48 RStudent = 0.2195 Predicted Value = 107.3 Observation Number = 47 RStudent = -1.347 Predicted Value = 108.15 Observation Number = 46 RStudent = -0.212 Predicted Value = 115.67 Observation Number = 45 RStudent = 0.2749 Predicted Value = 102.14 Observation Number = 44 RStudent = -0.04 Predicted Value = 92.122 Observation Number = 43 RStudent = 2.4383 Predicted Value = 117.77 Observation Number = 42 RStudent = -0.477 Predicted Value = 123.51 Observation Number = 41 RStudent = -0.276 Predicted Value = 108.89 Observation Number = 40 RStudent = -0.03 Predicted Value = 118.1 Observation Number = 39 RStudent = 0.9299 Predicted Value = 108.05 Observation Number = 38 RStudent = 2.2689 Predicted Value = 134.44 Observation Number = 37 RStudent = 1.0869 Predicted Value = 123.55 Observation Number = 36 RStudent = -0.223 Predicted Value = 109.72 Observation Number = 35 RStudent = 0.6227 Predicted Value = 110 Observation Number = 34 RStudent = 0.5445 Predicted Value = 106.25 Observation Number = 33 RStudent = 0.5899 Predicted Value = 102.28 Observation Number = 32 RStudent = 1.1448 Predicted Value = 112.5 Observation Number = 31 RStudent = 0.6756 Predicted Value = 101.91 Observation Number = 30 RStudent = -1.674 Predicted Value = 123.82 Observation Number = 29 RStudent = 1.5657 Predicted Value = 109.04 Observation Number = 28 RStudent = -1.36 Predicted Value = 124.03 Observation Number = 27 RStudent = -1.101 Predicted Value = 108.46 Observation Number = 26 RStudent = 0.7198 Predicted Value = 108.75 Observation Number = 25 RStudent = 0.9208 Predicted Value = 114.04 Observation Number = 24 RStudent = 0.0697 Predicted Value = 115.78 Observation Number = 23 RStudent = -0.982 Predicted Value = 111.02 Observation Number = 22 RStudent = -1.408 Predicted Value = 99.255 Observation Number = 21 RStudent = -1.739 Predicted Value = 124.23 Observation Number = 20 RStudent = 0.6819 Predicted Value = 98.893 Observation Number = 19 RStudent = 0.2754 Predicted Value = 119.13 Observation Number = 18 RStudent = -0.398 Predicted Value = 114.28 Observation Number = 17 RStudent = -0.145 Predicted Value = 117.45 Observation Number = 16 RStudent = 0.4985 Predicted Value = 109.47 Observation Number = 15 RStudent = -0.404 Predicted Value = 111.32 Observation Number = 14 RStudent = -1.742 Predicted Value = 115.25 Observation Number = 13 RStudent = 0.155 Predicted Value = 124.51 Observation Number = 12 RStudent = 0.2234 Predicted Value = 102.34 Observation Number = 11 RStudent = 0.4248 Predicted Value = 132.71 Observation Number = 10 RStudent = 0.8738 Predicted Value = 104.24 Observation Number = 9 RStudent = -0.975 Predicted Value = 113.02 Observation Number = 8 RStudent = -0.029 Predicted Value = 103.09 Observation Number = 7 RStudent = 0.1217 Predicted Value = 117.6 Observation Number = 6 RStudent = -0.62 Predicted Value = 111.97 Observation Number = 5 RStudent = -0.428 Predicted Value = 109.39 Observation Number = 4 RStudent = -2.267 Predicted Value = 111.81 Observation Number = 3 RStudent = 1.3035 Predicted Value = 105.94 Observation Number = 2 RStudent = -0.169 Predicted Value = 121.55 Observation Number = 1 Y = 2 Y = -2 RStudent = 1.0376 Hat Diagonal = 0.0916 Observation Number = 50 RStudent = -2.065 Hat Diagonal = 0.126 Observation Number = 49 RStudent = 0.1987 Hat Diagonal = 0.1109 Observation Number = 48 RStudent = 0.2195 Hat Diagonal = 0.0709 Observation Number = 47 RStudent = -1.347 Hat Diagonal = 0.104 Observation Number = 46 RStudent = -0.212 Hat Diagonal = 0.0929 Observation Number = 45 RStudent = 0.2749 Hat Diagonal = 0.1019 Observation Number = 44 RStudent = -0.04 Hat Diagonal = 0.1391 Observation Number = 43 RStudent = 2.4383 Hat Diagonal = 0.0941 Observation Number = 42 RStudent = -0.477 Hat Diagonal = 0.0825 Observation Number = 41 RStudent = -0.276 Hat Diagonal = 0.0542 Observation Number = 40 RStudent = -0.03 Hat Diagonal = 0.062 Observation Number = 39 RStudent = 0.9299 Hat Diagonal = 0.0715 Observation Number = 38 RStudent = 2.2689 Hat Diagonal = 0.1535 Observation Number = 37 RStudent = 1.0869 Hat Diagonal = 0.0586 Observation Number = 36 RStudent = -0.223 Hat Diagonal = 0.0597 Observation Number = 35 RStudent = 0.6227 Hat Diagonal = 0.059 Observation Number = 34 RStudent = 0.5445 Hat Diagonal = 0.0542 Observation Number = 33 RStudent = 0.5899 Hat Diagonal = 0.2226 Observation Number = 32 RStudent = 1.1448 Hat Diagonal = 0.1279 Observation Number = 31 RStudent = 0.6756 Hat Diagonal = 0.119 Observation Number = 30 RStudent = -1.674 Hat Diagonal = 0.1998 Observation Number = 29 RStudent = 1.5657 Hat Diagonal = 0.0383 Observation Number = 28 RStudent = -1.36 Hat Diagonal = 0.1691 Observation Number = 27 RStudent = -1.101 Hat Diagonal = 0.0774 Observation Number = 26 RStudent = 0.7198 Hat Diagonal = 0.101 Observation Number = 25 RStudent = 0.9208 Hat Diagonal = 0.0465 Observation Number = 24 RStudent = 0.0697 Hat Diagonal = 0.0666 Observation Number = 23 RStudent = -0.982 Hat Diagonal = 0.1242 Observation Number = 22 RStudent = -1.408 Hat Diagonal = 0.134 Observation Number = 21 RStudent = -1.739 Hat Diagonal = 0.1217 Observation Number = 20 RStudent = 0.6819 Hat Diagonal = 0.1248 Observation Number = 19 RStudent = 0.2754 Hat Diagonal = 0.0827 Observation Number = 18 RStudent = -0.398 Hat Diagonal = 0.0627 Observation Number = 17 RStudent = -0.145 Hat Diagonal = 0.1383 Observation Number = 16 RStudent = 0.4985 Hat Diagonal = 0.1458 Observation Number = 15 RStudent = -0.404 Hat Diagonal = 0.0229 Observation Number = 14 RStudent = -1.742 Hat Diagonal = 0.1169 Observation Number = 13 RStudent = 0.155 Hat Diagonal = 0.1102 Observation Number = 12 RStudent = 0.2234 Hat Diagonal = 0.2063 Observation Number = 11 RStudent = 0.4248 Hat Diagonal = 0.164 Observation Number = 10 RStudent = 0.8738 Hat Diagonal = 0.0792 Observation Number = 9 RStudent = -0.975 Hat Diagonal = 0.109 Observation Number = 8 RStudent = -0.029 Hat Diagonal = 0.1086 Observation Number = 7 RStudent = 0.1217 Hat Diagonal = 0.0377 Observation Number = 6 RStudent = -0.62 Hat Diagonal = 0.0782 Observation Number = 5 RStudent = -0.428 Hat Diagonal = 0.0472 Observation Number = 4 RStudent = -2.267 Hat Diagonal = 0.0848 Observation Number = 3 RStudent = 1.3035 Hat Diagonal = 0.0868 Observation Number = 2 RStudent = -0.169 Hat Diagonal = 0.0592 Observation Number = 1 X = 0.2 Y = -2 Y = 2 Quantile = 2.2433 Residual = 7.231 Quantile = 1.8475 Residual = 6.5567 Quantile = 1.6235 Residual = 4.9607 Quantile = 1.46 Residual = 4.0572 Quantile = 1.3283 Residual = 3.4974 Quantile = 1.2163 Residual = 3.4547 Quantile = 1.1177 Residual = 3.2436 Quantile = 1.029 Residual = 2.9564 Quantile = 0.9477 Residual = 2.9456 Quantile = 0.8722 Residual = 2.7596 Quantile = 0.8014 Residual = 2.2523 Quantile = 0.7344 Residual = 2.1065 Quantile = 0.6706 Residual = 2.0943 Quantile = 0.6094 Residual = 1.9966 Quantile = 0.5503 Residual = 1.7519 Quantile = 0.4932 Residual = 1.7197 Quantile = 0.4376 Residual = 1.5251 Quantile = 0.3833 Residual = 1.2869 Quantile = 0.3301 Residual = 0.8749 Quantile = 0.2779 Residual = 0.8642 Quantile = 0.2264 Residual = 0.702 Quantile = 0.1755 Residual = 0.6602 Quantile = 0.125 Residual = 0.6218 Quantile = 0.0749 Residual = 0.4853 Quantile = 0.0249 Residual = 0.3961 Quantile = -0.025 Residual = 0.2235 Quantile = -0.075 Residual = -0.092 Quantile = -0.125 Residual = -0.097 Quantile = -0.175 Residual = -0.122 Quantile = -0.226 Residual = -0.445 Quantile = -0.278 Residual = -0.545 Quantile = -0.33 Residual = -0.671 Quantile = -0.383 Residual = -0.716 Quantile = -0.438 Residual = -0.892 Quantile = -0.493 Residual = -1.276 Quantile = -0.55 Residual = -1.323 Quantile = -0.609 Residual = -1.385 Quantile = -0.671 Residual = -1.513 Quantile = -0.734 Residual = -1.968 Quantile = -0.801 Residual = -3.018 Quantile = -0.872 Residual = -3.024 Quantile = -0.948 Residual = -3.463 Quantile = -1.029 Residual = -4.03 Quantile = -1.118 Residual = -4.149 Quantile = -1.216 Residual = -4.255 Quantile = -1.328 Residual = -4.819 Quantile = -1.46 Residual = -5.234 Quantile = -1.624 Residual = -5.255 Quantile = -1.847 Residual = -6.119 Quantile = -2.243 Residual = -6.813 Slope = 3.1457 Y = -9E-15 Run_Pulse = 124 Predicted Value = 120.76 Observation Number = 50 Run_Pulse = 108 Predicted Value = 114.12 Observation Number = 49 Run_Pulse = 127 Predicted Value = 126.38 Observation Number = 48 Run_Pulse = 108 Predicted Value = 107.3 Observation Number = 47 Run_Pulse = 104 Predicted Value = 108.15 Observation Number = 46 Run_Pulse = 115 Predicted Value = 115.67 Observation Number = 45 Run_Pulse = 103 Predicted Value = 102.14 Observation Number = 44 Run_Pulse = 92 Predicted Value = 92.122 Observation Number = 43 Run_Pulse = 125 Predicted Value = 117.77 Observation Number = 42 Run_Pulse = 122 Predicted Value = 123.51 Observation Number = 41 Run_Pulse = 108 Predicted Value = 108.89 Observation Number = 40 Run_Pulse = 118 Predicted Value = 118.1 Observation Number = 39 Run_Pulse = 111 Predicted Value = 108.05 Observation Number = 38 Run_Pulse = 141 Predicted Value = 134.44 Observation Number = 37 Run_Pulse = 127 Predicted Value = 123.55 Observation Number = 36 Run_Pulse = 109 Predicted Value = 109.72 Observation Number = 35 Run_Pulse = 112 Predicted Value = 110 Observation Number = 34 Run_Pulse = 108 Predicted Value = 106.25 Observation Number = 33 Run_Pulse = 104 Predicted Value = 102.28 Observation Number = 32 Run_Pulse = 116 Predicted Value = 112.5 Observation Number = 31 Run_Pulse = 104 Predicted Value = 101.91 Observation Number = 30 Run_Pulse = 119 Predicted Value = 123.82 Observation Number = 29 Run_Pulse = 114 Predicted Value = 109.04 Observation Number = 28 Run_Pulse = 120 Predicted Value = 124.03 Observation Number = 27 Run_Pulse = 105 Predicted Value = 108.46 Observation Number = 26 Run_Pulse = 111 Predicted Value = 108.75 Observation Number = 25 Run_Pulse = 117 Predicted Value = 114.04 Observation Number = 24 Run_Pulse = 116 Predicted Value = 115.78 Observation Number = 23 Run_Pulse = 108 Predicted Value = 111.02 Observation Number = 22 Run_Pulse = 95 Predicted Value = 99.255 Observation Number = 21 Run_Pulse = 119 Predicted Value = 124.23 Observation Number = 20 Run_Pulse = 101 Predicted Value = 98.893 Observation Number = 19 Run_Pulse = 120 Predicted Value = 119.13 Observation Number = 18 Run_Pulse = 113 Predicted Value = 114.28 Observation Number = 17 Run_Pulse = 117 Predicted Value = 117.45 Observation Number = 16 Run_Pulse = 111 Predicted Value = 109.47 Observation Number = 15 Run_Pulse = 110 Predicted Value = 111.32 Observation Number = 14 Run_Pulse = 110 Predicted Value = 115.25 Observation Number = 13 Run_Pulse = 125 Predicted Value = 124.51 Observation Number = 12 Run_Pulse = 103 Predicted Value = 102.34 Observation Number = 11 Run_Pulse = 134 Predicted Value = 132.71 Observation Number = 10 Run_Pulse = 107 Predicted Value = 104.24 Observation Number = 9 Run_Pulse = 110 Predicted Value = 113.02 Observation Number = 8 Run_Pulse = 103 Predicted Value = 103.09 Observation Number = 7 Run_Pulse = 118 Predicted Value = 117.6 Observation Number = 6 Run_Pulse = 110 Predicted Value = 111.97 Observation Number = 5 Run_Pulse = 108 Predicted Value = 109.39 Observation Number = 4 Run_Pulse = 105 Predicted Value = 111.81 Observation Number = 3 Run_Pulse = 110 Predicted Value = 105.94 Observation Number = 2 Run_Pulse = 121 Predicted Value = 121.55 Observation Number = 1 Slope = 1 Y = 0 Cook's D = 0.0217 Observation Number = 50 Cook's D = 0.1147 Observation Number = 49 Cook's D = 0.001 Observation Number = 48 Cook's D = .00075 Observation Number = 47 Cook's D = 0.0414 Observation Number = 46 Cook's D = .00094 Observation Number = 45 Cook's D = 0.0018 Observation Number = 44 Cook's D = 5.2E-5 Observation Number = 43 Cook's D = 0.1113 Observation Number = 42 Cook's D = 0.0042 Observation Number = 41 Cook's D = .00089 Observation Number = 40 Cook's D = 1.2E-5 Observation Number = 39 Cook's D = 0.0134 Observation Number = 38 Cook's D = 0.171 Observation Number = 37 Cook's D = 0.0147 Observation Number = 36 Cook's D = .00064 Observation Number = 35 Cook's D = 0.0049 Observation Number = 34 Cook's D = 0.0034 Observation Number = 33 Cook's D = 0.0202 Observation Number = 32 Cook's D = 0.0382 Observation Number = 31 Cook's D = 0.0125 Observation Number = 30 Cook's D = 0.1344 Observation Number = 29 Cook's D = 0.0189 Observation Number = 28 Cook's D = 0.0739 Observation Number = 27 Cook's D = 0.0202 Observation Number = 26 Cook's D = 0.0118 Observation Number = 25 Cook's D = 0.0083 Observation Number = 24 Cook's D = 7.1E-5 Observation Number = 23 Cook's D = 0.0274 Observation Number = 22 Cook's D = 0.0601 Observation Number = 21 Cook's D = 0.0802 Observation Number = 20 Cook's D = 0.0134 Observation Number = 19 Cook's D = 0.0014 Observation Number = 18 Cook's D = 0.0022 Observation Number = 17 Cook's D = .00069 Observation Number = 16 Cook's D = 0.0086 Observation Number = 15 Cook's D = .00078 Observation Number = 14 Cook's D = 0.0768 Observation Number = 13 Cook's D = .00061 Observation Number = 12 Cook's D = 0.0027 Observation Number = 11 Cook's D = 0.0072 Observation Number = 10 Cook's D = 0.0132 Observation Number = 9 Cook's D = 0.0233 Observation Number = 8 Cook's D = 2.2E-5 Observation Number = 7 Cook's D = .00012 Observation Number = 6 Cook's D = 0.0066 Observation Number = 5 Cook's D = 0.0019 Observation Number = 4 Cook's D = 0.0873 Observation Number = 3 Cook's D = 0.0318 Observation Number = 2 Cook's D = .00037 Observation Number = 1 Cook's D = 0.0217 Observation Number = 50 Cook's D = 0.1147 Observation Number = 49 Cook's D = 0.001 Observation Number = 48 Cook's D = .00075 Observation Number = 47 Cook's D = 0.0414 Observation Number = 46 Cook's D = .00094 Observation Number = 45 Cook's D = 0.0018 Observation Number = 44 Cook's D = 5.2E-5 Observation Number = 43 Cook's D = 0.1113 Observation Number = 42 Cook's D = 0.0042 Observation Number = 41 Cook's D = .00089 Observation Number = 40 Cook's D = 1.2E-5 Observation Number = 39 Cook's D = 0.0134 Observation Number = 38 Cook's D = 0.171 Observation Number = 37 Cook's D = 0.0147 Observation Number = 36 Cook's D = .00064 Observation Number = 35 Cook's D = 0.0049 Observation Number = 34 Cook's D = 0.0034 Observation Number = 33 Cook's D = 0.0202 Observation Number = 32 Cook's D = 0.0382 Observation Number = 31 Cook's D = 0.0125 Observation Number = 30 Cook's D = 0.1344 Observation Number = 29 Cook's D = 0.0189 Observation Number = 28 Cook's D = 0.0739 Observation Number = 27 Cook's D = 0.0202 Observation Number = 26 Cook's D = 0.0118 Observation Number = 25 Cook's D = 0.0083 Observation Number = 24 Cook's D = 7.1E-5 Observation Number = 23 Cook's D = 0.0274 Observation Number = 22 Cook's D = 0.0601 Observation Number = 21 Cook's D = 0.0802 Observation Number = 20 Cook's D = 0.0134 Observation Number = 19 Cook's D = 0.0014 Observation Number = 18 Cook's D = 0.0022 Observation Number = 17 Cook's D = .00069 Observation Number = 16 Cook's D = 0.0086 Observation Number = 15 Cook's D = .00078 Observation Number = 14 Cook's D = 0.0768 Observation Number = 13 Cook's D = .00061 Observation Number = 12 Cook's D = 0.0027 Observation Number = 11 Cook's D = 0.0072 Observation Number = 10 Cook's D = 0.0132 Observation Number = 9 Cook's D = 0.0233 Observation Number = 8 Cook's D = 2.2E-5 Observation Number = 7 Cook's D = .00012 Observation Number = 6 Cook's D = 0.0066 Observation Number = 5 Cook's D = 0.0019 Observation Number = 4 Cook's D = 0.0873 Observation Number = 3 Cook's D = 0.0318 Observation Number = 2 Cook's D = .00037 Observation Number = 1 Y = 0.08 Residual = 9.437 Percent = 0.3522 Residual = 9.3417 Percent = 0.3856 Residual = 9.3417 Percent = 0.3856 Residual = 9.2464 Percent = 0.4217 Residual = 9.2464 Percent = 0.4217 Residual = 9.1511 Percent = 0.4607 Residual = 9.1511 Percent = 0.4607 Residual = 9.0557 Percent = 0.503 Residual = 9.0557 Percent = 0.503 Residual = 8.9604 Percent = 0.5486 Residual = 8.9604 Percent = 0.5486 Residual = 8.8651 Percent = 0.5978 Residual = 8.8651 Percent = 0.5978 Residual = 8.7698 Percent = 0.6507 Residual = 8.7698 Percent = 0.6507 Residual = 8.6745 Percent = 0.7078 Residual = 8.6745 Percent = 0.7078 Residual = 8.5791 Percent = 0.7691 Residual = 8.5791 Percent = 0.7691 Residual = 8.4838 Percent = 0.835 Residual = 8.4838 Percent = 0.835 Residual = 8.3885 Percent = 0.9057 Residual = 8.3885 Percent = 0.9057 Residual = 8.2932 Percent = 0.9815 Residual = 8.2932 Percent = 0.9815 Residual = 8.1978 Percent = 1.0626 Residual = 8.1978 Percent = 1.0626 Residual = 8.1025 Percent = 1.1494 Residual = 8.1025 Percent = 1.1494 Residual = 8.0072 Percent = 1.2421 Residual = 8.0072 Percent = 1.2421 Residual = 7.9119 Percent = 1.3411 Residual = 7.9119 Percent = 1.3411 Residual = 7.8165 Percent = 1.4467 Residual = 7.8165 Percent = 1.4467 Residual = 7.7212 Percent = 1.5591 Residual = 7.7212 Percent = 1.5591 Residual = 7.6259 Percent = 1.6787 Residual = 7.6259 Percent = 1.6787 Residual = 7.5306 Percent = 1.8058 Residual = 7.5306 Percent = 1.8058 Residual = 7.4352 Percent = 1.9408 Residual = 7.4352 Percent = 1.9408 Residual = 7.3399 Percent = 2.084 Residual = 7.3399 Percent = 2.084 Residual = 7.2446 Percent = 2.2356 Residual = 7.2446 Percent = 2.2356 Residual = 7.1493 Percent = 2.3961 Residual = 7.1493 Percent = 2.3961 Residual = 7.054 Percent = 2.5658 Residual = 7.054 Percent = 2.5658 Residual = 6.9586 Percent = 2.7449 Residual = 6.9586 Percent = 2.7449 Residual = 6.8633 Percent = 2.9339 Residual = 6.8633 Percent = 2.9339 Residual = 6.768 Percent = 3.133 Residual = 6.768 Percent = 3.133 Residual = 6.6727 Percent = 3.3425 Residual = 6.6727 Percent = 3.3425 Residual = 6.5773 Percent = 3.5628 Residual = 6.5773 Percent = 3.5628 Residual = 6.482 Percent = 3.7941 Residual = 6.482 Percent = 3.7941 Residual = 6.3867 Percent = 4.0367 Residual = 6.3867 Percent = 4.0367 Residual = 6.2914 Percent = 4.2909 Residual = 6.2914 Percent = 4.2909 Residual = 6.196 Percent = 4.5569 Residual = 6.196 Percent = 4.5569 Residual = 6.1007 Percent = 4.8349 Residual = 6.1007 Percent = 4.8349 Residual = 6.0054 Percent = 5.1252 Residual = 6.0054 Percent = 5.1252 Residual = 5.9101 Percent = 5.428 Residual = 5.9101 Percent = 5.428 Residual = 5.8147 Percent = 5.7434 Residual = 5.8147 Percent = 5.7434 Residual = 5.7194 Percent = 6.0715 Residual = 5.7194 Percent = 6.0715 Residual = 5.6241 Percent = 6.4124 Residual = 5.6241 Percent = 6.4124 Residual = 5.5288 Percent = 6.7663 Residual = 5.5288 Percent = 6.7663 Residual = 5.4334 Percent = 7.1332 Residual = 5.4334 Percent = 7.1332 Residual = 5.3381 Percent = 7.513 Residual = 5.3381 Percent = 7.513 Residual = 5.2428 Percent = 7.9059 Residual = 5.2428 Percent = 7.9059 Residual = 5.1475 Percent = 8.3116 Residual = 5.1475 Percent = 8.3116 Residual = 4.9568 Percent = 9.1613 Residual = 4.9568 Percent = 9.1613 Residual = 4.7662 Percent = 10.061 Residual = 4.7662 Percent = 10.061 Residual = 4.5755 Percent = 11.008 Residual = 4.5755 Percent = 11.008 Residual = 4.3849 Percent = 12.001 Residual = 4.3849 Percent = 12.001 Residual = 4.1942 Percent = 13.035 Residual = 4.1942 Percent = 13.035 Residual = 2.7644 Percent = 21.55 Residual = 2.7644 Percent = 21.55 Residual = 2.4784 Percent = 23.246 Residual = 2.4784 Percent = 23.246 Residual = 2.2878 Percent = 24.338 Residual = 2.2878 Percent = 24.338 Residual = 2.0971 Percent = 25.388 Residual = 2.0971 Percent = 25.388 Residual = 1.9065 Percent = 26.386 Residual = 1.9065 Percent = 26.386 Residual = 1.8111 Percent = 26.863 Residual = 1.8111 Percent = 26.863 Residual = 1.7158 Percent = 27.323 Residual = 1.7158 Percent = 27.323 Residual = 1.6205 Percent = 27.766 Residual = 1.6205 Percent = 27.766 Residual = 1.5252 Percent = 28.19 Residual = 1.5252 Percent = 28.19 Residual = 1.4299 Percent = 28.594 Residual = 1.4299 Percent = 28.594 Residual = 1.3345 Percent = 28.977 Residual = 1.3345 Percent = 28.977 Residual = 1.2392 Percent = 29.338 Residual = 1.2392 Percent = 29.338 Residual = 1.1439 Percent = 29.677 Residual = 1.1439 Percent = 29.677 Residual = 1.0486 Percent = 29.992 Residual = 1.0486 Percent = 29.992 Residual = 0.9532 Percent = 30.283 Residual = 0.9532 Percent = 30.283 Residual = 0.8579 Percent = 30.548 Residual = 0.8579 Percent = 30.548 Residual = 0.7626 Percent = 30.787 Residual = 0.7626 Percent = 30.787 Residual = 0.6673 Percent = 31 Residual = 0.6673 Percent = 31 Residual = 0.5719 Percent = 31.186 Residual = 0.5719 Percent = 31.186 Residual = 0.4766 Percent = 31.344 Residual = 0.4766 Percent = 31.344 Residual = 0.3813 Percent = 31.473 Residual = 0.3813 Percent = 31.473 Residual = 0.286 Percent = 31.575 Residual = 0.286 Percent = 31.575 Residual = 0.1906 Percent = 31.647 Residual = 0.1906 Percent = 31.647 Residual = 0.0953 Percent = 31.691 Residual = 0.0953 Percent = 31.691 Residual = -5E-15 Percent = 31.706 Residual = -5E-15 Percent = 31.706 Residual = -0.095 Percent = 31.691 Residual = -0.095 Percent = 31.691 Residual = -0.191 Percent = 31.647 Residual = -0.191 Percent = 31.647 Residual = -0.286 Percent = 31.575 Residual = -0.286 Percent = 31.575 Residual = -0.381 Percent = 31.473 Residual = -0.381 Percent = 31.473 Residual = -0.477 Percent = 31.344 Residual = -0.477 Percent = 31.344 Residual = -0.572 Percent = 31.186 Residual = -0.572 Percent = 31.186 Residual = -0.667 Percent = 31 Residual = -0.667 Percent = 31 Residual = -0.763 Percent = 30.787 Residual = -0.763 Percent = 30.787 Residual = -0.858 Percent = 30.548 Residual = -0.858 Percent = 30.548 Residual = -0.953 Percent = 30.283 Residual = -0.953 Percent = 30.283 Residual = -1.049 Percent = 29.992 Residual = -1.049 Percent = 29.992 Residual = -1.144 Percent = 29.677 Residual = -1.144 Percent = 29.677 Residual = -1.239 Percent = 29.338 Residual = -1.239 Percent = 29.338 Residual = -1.335 Percent = 28.977 Residual = -1.335 Percent = 28.977 Residual = -1.43 Percent = 28.594 Residual = -1.43 Percent = 28.594 Residual = -1.525 Percent = 28.19 Residual = -1.525 Percent = 28.19 Residual = -1.621 Percent = 27.766 Residual = -1.621 Percent = 27.766 Residual = -1.716 Percent = 27.323 Residual = -1.716 Percent = 27.323 Residual = -1.811 Percent = 26.863 Residual = -1.811 Percent = 26.863 Residual = -1.906 Percent = 26.386 Residual = -1.906 Percent = 26.386 Residual = -2.097 Percent = 25.388 Residual = -2.097 Percent = 25.388 Residual = -2.288 Percent = 24.338 Residual = -2.288 Percent = 24.338 Residual = -3.432 Percent = 17.487 Residual = -3.432 Percent = 17.487 Residual = -3.813 Percent = 15.209 Residual = -3.813 Percent = 15.209 Residual = -4.099 Percent = 13.566 Residual = -4.099 Percent = 13.566 Residual = -4.29 Percent = 12.513 Residual = -4.29 Percent = 12.513 Residual = -4.48 Percent = 11.499 Residual = -4.48 Percent = 11.499 Residual = -4.671 Percent = 10.529 Residual = -4.671 Percent = 10.529 Residual = -4.862 Percent = 9.6049 Residual = -4.862 Percent = 9.6049 Residual = -5.052 Percent = 8.7301 Residual = -5.052 Percent = 8.7301 Residual = -5.147 Percent = 8.3116 Residual = -5.147 Percent = 8.3116 Residual = -5.243 Percent = 7.9059 Residual = -5.243 Percent = 7.9059 Residual = -5.338 Percent = 7.513 Residual = -5.338 Percent = 7.513 Residual = -5.433 Percent = 7.1332 Residual = -5.433 Percent = 7.1332 Residual = -5.529 Percent = 6.7663 Residual = -5.529 Percent = 6.7663 Residual = -5.624 Percent = 6.4124 Residual = -5.624 Percent = 6.4124 Residual = -5.719 Percent = 6.0715 Residual = -5.719 Percent = 6.0715 Residual = -5.815 Percent = 5.7434 Residual = -5.815 Percent = 5.7434 Residual = -5.91 Percent = 5.428 Residual = -5.91 Percent = 5.428 Residual = -6.005 Percent = 5.1252 Residual = -6.005 Percent = 5.1252 Residual = -6.101 Percent = 4.8349 Residual = -6.101 Percent = 4.8349 Residual = -6.196 Percent = 4.5569 Residual = -6.196 Percent = 4.5569 Residual = -6.291 Percent = 4.2909 Residual = -6.291 Percent = 4.2909 Residual = -6.387 Percent = 4.0367 Residual = -6.387 Percent = 4.0367 Residual = -6.482 Percent = 3.7941 Residual = -6.482 Percent = 3.7941 Residual = -6.577 Percent = 3.5628 Residual = -6.577 Percent = 3.5628 Residual = -6.673 Percent = 3.3425 Residual = -6.673 Percent = 3.3425 Residual = -6.768 Percent = 3.133 Residual = -6.768 Percent = 3.133 Residual = -6.863 Percent = 2.9339 Residual = -6.863 Percent = 2.9339 Residual = -6.959 Percent = 2.7449 Residual = -6.959 Percent = 2.7449 Residual = -7.054 Percent = 2.5658 Residual = -7.054 Percent = 2.5658 Residual = -7.149 Percent = 2.3961 Residual = -7.149 Percent = 2.3961 Residual = -7.245 Percent = 2.2356 Residual = -7.245 Percent = 2.2356 Residual = -7.34 Percent = 2.084 Residual = -7.34 Percent = 2.084 Residual = -7.435 Percent = 1.9408 Residual = -7.435 Percent = 1.9408 Residual = -7.531 Percent = 1.8058 Residual = -7.531 Percent = 1.8058 Residual = -7.626 Percent = 1.6787 Residual = -7.626 Percent = 1.6787 Residual = -7.721 Percent = 1.5591 Residual = -7.721 Percent = 1.5591 Residual = -7.817 Percent = 1.4467 Residual = -7.817 Percent = 1.4467 Residual = -7.912 Percent = 1.3411 Residual = -7.912 Percent = 1.3411 Residual = -8.007 Percent = 1.2421 Residual = -8.007 Percent = 1.2421 Residual = -8.103 Percent = 1.1494 Residual = -8.103 Percent = 1.1494 Residual = -8.198 Percent = 1.0626 Residual = -8.198 Percent = 1.0626 Residual = -8.293 Percent = 0.9815 Residual = -8.293 Percent = 0.9815 Residual = -8.388 Percent = 0.9057 Residual = -8.388 Percent = 0.9057 Residual = -8.484 Percent = 0.835 Residual = -8.484 Percent = 0.835 Residual = -8.579 Percent = 0.7691 Residual = -8.579 Percent = 0.7691 Residual = -8.674 Percent = 0.7078 Residual = -8.674 Percent = 0.7078 Residual = -8.77 Percent = 0.6507 Residual = -8.77 Percent = 0.6507 Residual = -8.865 Percent = 0.5978 Residual = -8.865 Percent = 0.5978 Residual = -8.96 Percent = 0.5486 Residual = -8.96 Percent = 0.5486 Residual = -9.056 Percent = 0.503 Residual = -9.056 Percent = 0.503 Residual = -9.151 Percent = 0.4607 Residual = -9.151 Percent = 0.4607 Residual = -9.246 Percent = 0.4217 Residual = -9.246 Percent = 0.4217 Residual = -9.342 Percent = 0.3856 Residual = -9.342 Percent = 0.3856 Residual = -9.437 Percent = 0.3522 Residual = 6.25 Percent = 4 Residual = 6.25 Percent = 4 Residual = 3.75 Percent = 16 Residual = 3.75 Percent = 16 Residual = 1.25 Percent = 32 Residual = 1.25 Percent = 32 Residual = -1.25 Percent = 26 Residual = -1.25 Percent = 26 Residual = -3.75 Percent = 14 Residual = -3.75 Percent = 14 Residual = -6.25 Percent = 8 Residual = -6.25 Percent = 8 Proportion Less = 0.9876 Fit-Mean = 21.523 Proportion Less = 0.9677 Fit-Mean = 19.793 Proportion Less = 0.9478 Fit-Mean = 13.458 Proportion Less = 0.9279 Fit-Mean = 11.595 Proportion Less = 0.908 Fit-Mean = 11.314 Proportion Less = 0.8881 Fit-Mean = 11.11 Proportion Less = 0.8682 Fit-Mean = 10.899 Proportion Less = 0.8483 Fit-Mean = 10.625 Proportion Less = 0.8284 Fit-Mean = 10.593 Proportion Less = 0.8085 Fit-Mean = 8.6253 Proportion Less = 0.7886 Fit-Mean = 7.8364 Proportion Less = 0.7687 Fit-Mean = 6.2051 Proportion Less = 0.7488 Fit-Mean = 5.1773 Proportion Less = 0.7289 Fit-Mean = 4.849 Proportion Less = 0.709 Fit-Mean = 4.6839 Proportion Less = 0.6891 Fit-Mean = 4.5254 Proportion Less = 0.6692 Fit-Mean = 2.8565 Proportion Less = 0.6493 Fit-Mean = 2.7511 Proportion Less = 0.6294 Fit-Mean = 2.3349 Proportion Less = 0.6095 Fit-Mean = 1.3557 Proportion Less = 0.5896 Fit-Mean = 1.1991 Proportion Less = 0.5697 Fit-Mean = 1.1236 Proportion Less = 0.5498 Fit-Mean = 0.1035 Proportion Less = 0.5299 Fit-Mean = -0.417 Proportion Less = 0.51 Fit-Mean = -0.952 Proportion Less = 0.49 Fit-Mean = -1.107 Proportion Less = 0.4701 Fit-Mean = -1.597 Proportion Less = 0.4502 Fit-Mean = -1.902 Proportion Less = 0.4303 Fit-Mean = -2.917 Proportion Less = 0.4104 Fit-Mean = -3.204 Proportion Less = 0.3905 Fit-Mean = -3.445 Proportion Less = 0.3706 Fit-Mean = -3.535 Proportion Less = 0.3507 Fit-Mean = -3.881 Proportion Less = 0.3308 Fit-Mean = -4.028 Proportion Less = 0.3109 Fit-Mean = -4.172 Proportion Less = 0.291 Fit-Mean = -4.457 Proportion Less = 0.2711 Fit-Mean = -4.771 Proportion Less = 0.2512 Fit-Mean = -4.866 Proportion Less = 0.2313 Fit-Mean = -5.622 Proportion Less = 0.2114 Fit-Mean = -6.672 Proportion Less = 0.1915 Fit-Mean = -6.977 Proportion Less = 0.1716 Fit-Mean = -8.68 Proportion Less = 0.1517 Fit-Mean = -9.828 Proportion Less = 0.1318 Fit-Mean = -10.58 Proportion Less = 0.1119 Fit-Mean = -10.64 Proportion Less = 0.092 Fit-Mean = -10.78 Proportion Less = 0.0721 Fit-Mean = -11.01 Proportion Less = 0.0522 Fit-Mean = -13.67 Proportion Less = 0.0323 Fit-Mean = -14.03 Proportion Less = 0.0124 Fit-Mean = -20.8 Proportion Less = 0.9876 Residual = 7.231 Proportion Less = 0.9677 Residual = 6.5567 Proportion Less = 0.9478 Residual = 4.9607 Proportion Less = 0.9279 Residual = 4.0572 Proportion Less = 0.908 Residual = 3.4974 Proportion Less = 0.8881 Residual = 3.4547 Proportion Less = 0.8682 Residual = 3.2436 Proportion Less = 0.8483 Residual = 2.9564 Proportion Less = 0.8284 Residual = 2.9456 Proportion Less = 0.8085 Residual = 2.7596 Proportion Less = 0.7886 Residual = 2.2523 Proportion Less = 0.7687 Residual = 2.1065 Proportion Less = 0.7488 Residual = 2.0943 Proportion Less = 0.7289 Residual = 1.9966 Proportion Less = 0.709 Residual = 1.7519 Proportion Less = 0.6891 Residual = 1.7197 Proportion Less = 0.6692 Residual = 1.5251 Proportion Less = 0.6493 Residual = 1.2869 Proportion Less = 0.6294 Residual = 0.8749 Proportion Less = 0.6095 Residual = 0.8642 Proportion Less = 0.5896 Residual = 0.702 Proportion Less = 0.5697 Residual = 0.6602 Proportion Less = 0.5498 Residual = 0.6218 Proportion Less = 0.5299 Residual = 0.4853 Proportion Less = 0.51 Residual = 0.3961 Proportion Less = 0.49 Residual = 0.2235 Proportion Less = 0.4701 Residual = -0.092 Proportion Less = 0.4502 Residual = -0.097 Proportion Less = 0.4303 Residual = -0.122 Proportion Less = 0.4104 Residual = -0.445 Proportion Less = 0.3905 Residual = -0.545 Proportion Less = 0.3706 Residual = -0.671 Proportion Less = 0.3507 Residual = -0.716 Proportion Less = 0.3308 Residual = -0.892 Proportion Less = 0.3109 Residual = -1.276 Proportion Less = 0.291 Residual = -1.323 Proportion Less = 0.2711 Residual = -1.385 Proportion Less = 0.2512 Residual = -1.513 Proportion Less = 0.2313 Residual = -1.968 Proportion Less = 0.2114 Residual = -3.018 Proportion Less = 0.1915 Residual = -3.024 Proportion Less = 0.1716 Residual = -3.463 Proportion Less = 0.1517 Residual = -4.03 Proportion Less = 0.1318 Residual = -4.149 Proportion Less = 0.1119 Residual = -4.255 Proportion Less = 0.092 Residual = -4.819 Proportion Less = 0.0721 Residual = -5.234 Proportion Less = 0.0522 Residual = -5.255 Proportion Less = 0.0323 Residual = -6.119 Proportion Less = 0.0124 Residual = -6.813
Panel of fit diagnostics for Run_Pulse.

Residual Plots

Panel 1

Residual = 3.2436 Age = 79 Observation Number = 50 Residual = -6.119 Age = 31 Observation Number = 49 Residual = 0.6218 Age = 46 Observation Number = 48 Residual = 0.702 Age = 59 Observation Number = 47 Residual = -4.149 Age = 31 Observation Number = 46 Residual = -0.671 Age = 49 Observation Number = 45 Residual = 0.8642 Age = 52 Observation Number = 44 Residual = -0.122 Age = 49 Observation Number = 43 Residual = 7.231 Age = 34 Observation Number = 42 Residual = -1.513 Age = 41 Observation Number = 41 Residual = -0.892 Age = 55 Observation Number = 40 Residual = -0.097 Age = 56 Observation Number = 39 Residual = 2.9456 Age = 31 Observation Number = 38 Residual = 6.5567 Age = 64 Observation Number = 37 Residual = 3.4547 Age = 64 Observation Number = 36 Residual = -0.716 Age = 60 Observation Number = 35 Residual = 1.9966 Age = 69 Observation Number = 34 Residual = 1.7519 Age = 48 Observation Number = 33 Residual = 1.7197 Age = 44 Observation Number = 32 Residual = 3.4974 Age = 26 Observation Number = 31 Residual = 2.0943 Age = 23 Observation Number = 30 Residual = -4.819 Age = 53 Observation Number = 29 Residual = 4.9607 Age = 57 Observation Number = 28 Residual = -4.03 Age = 68 Observation Number = 27 Residual = -3.463 Age = 43 Observation Number = 26 Residual = 2.2523 Age = 73 Observation Number = 25 Residual = 2.9564 Age = 36 Observation Number = 24 Residual = 0.2235 Age = 73 Observation Number = 23 Residual = -3.018 Age = 84 Observation Number = 22 Residual = -4.255 Age = 26 Observation Number = 21 Residual = -5.234 Age = 81 Observation Number = 20 Residual = 2.1065 Age = 31 Observation Number = 19 Residual = 0.8749 Age = 43 Observation Number = 18 Residual = -1.276 Age = 49 Observation Number = 17 Residual = -0.445 Age = 48 Observation Number = 16 Residual = 1.5251 Age = 54 Observation Number = 15 Residual = -1.323 Age = 51 Observation Number = 14 Residual = -5.255 Age = 19 Observation Number = 13 Residual = 0.4853 Age = 63 Observation Number = 12 Residual = 0.6602 Age = 63 Observation Number = 11 Residual = 1.2869 Age = 49 Observation Number = 10 Residual = 2.7596 Age = 35 Observation Number = 9 Residual = -3.024 Age = 30 Observation Number = 8 Residual = -0.092 Age = 64 Observation Number = 7 Residual = 0.3961 Age = 57 Observation Number = 6 Residual = -1.968 Age = 55 Observation Number = 5 Residual = -1.385 Age = 44 Observation Number = 4 Residual = -6.813 Age = 76 Observation Number = 3 Residual = 4.0572 Age = 64 Observation Number = 2 Residual = -0.545 Age = 68 Observation Number = 1 Y = 0 Residual = 3.2436 Pushups = 10 Observation Number = 50 Residual = -6.119 Pushups = 22 Observation Number = 49 Residual = 0.6218 Pushups = 19 Observation Number = 48 Residual = 0.702 Pushups = 25 Observation Number = 47 Residual = -4.149 Pushups = 48 Observation Number = 46 Residual = -0.671 Pushups = 22 Observation Number = 45 Residual = 0.8642 Pushups = 27 Observation Number = 44 Residual = -0.122 Pushups = 33 Observation Number = 43 Residual = 7.231 Pushups = 38 Observation Number = 42 Residual = -1.513 Pushups = 17 Observation Number = 41 Residual = -0.892 Pushups = 21 Observation Number = 40 Residual = -0.097 Pushups = 8 Observation Number = 39 Residual = 2.9456 Pushups = 30 Observation Number = 38 Residual = 6.5567 Pushups = 20 Observation Number = 37 Residual = 3.4547 Pushups = 22 Observation Number = 36 Residual = -0.716 Pushups = 36 Observation Number = 35 Residual = 1.9966 Pushups = 26 Observation Number = 34 Residual = 1.7519 Pushups = 21 Observation Number = 33 Residual = 1.7197 Pushups = 1 Observation Number = 32 Residual = 3.4974 Pushups = 40 Observation Number = 31 Residual = 2.0943 Pushups = 30 Observation Number = 30 Residual = -4.819 Pushups = 9 Observation Number = 29 Residual = 4.9607 Pushups = 31 Observation Number = 28 Residual = -4.03 Pushups = 32 Observation Number = 27 Residual = -3.463 Pushups = 33 Observation Number = 26 Residual = 2.2523 Pushups = 8 Observation Number = 25 Residual = 2.9564 Pushups = 25 Observation Number = 24 Residual = 0.2235 Pushups = 12 Observation Number = 23 Residual = -3.018 Pushups = 11 Observation Number = 22 Residual = -4.255 Pushups = 52 Observation Number = 21 Residual = -5.234 Pushups = 16 Observation Number = 20 Residual = 2.1065 Pushups = 50 Observation Number = 19 Residual = 0.8749 Pushups = 29 Observation Number = 18 Residual = -1.276 Pushups = 11 Observation Number = 17 Residual = -0.445 Pushups = 43 Observation Number = 16 Residual = 1.5251 Pushups = 7 Observation Number = 15 Residual = -1.323 Pushups = 23 Observation Number = 14 Residual = -5.255 Pushups = 34 Observation Number = 13 Residual = 0.4853 Pushups = 30 Observation Number = 12 Residual = 0.6602 Pushups = 51 Observation Number = 11 Residual = 1.2869 Pushups = 9 Observation Number = 10 Residual = 2.7596 Pushups = 25 Observation Number = 9 Residual = -3.024 Pushups = 48 Observation Number = 8 Residual = -0.092 Pushups = 21 Observation Number = 7 Residual = 0.3961 Pushups = 14 Observation Number = 6 Residual = -1.968 Pushups = 24 Observation Number = 5 Residual = -1.385 Pushups = 35 Observation Number = 4 Residual = -6.813 Pushups = 11 Observation Number = 3 Residual = 4.0572 Pushups = 36 Observation Number = 2 Residual = -0.545 Pushups = 19 Observation Number = 1 Y = 0 Residual = 3.2436 Rest_Pulse = 82 Observation Number = 50 Residual = -6.119 Rest_Pulse = 74 Observation Number = 49 Residual = 0.6218 Rest_Pulse = 84 Observation Number = 48 Residual = 0.702 Rest_Pulse = 71 Observation Number = 47 Residual = -4.149 Rest_Pulse = 55 Observation Number = 46 Residual = -0.671 Rest_Pulse = 61 Observation Number = 45 Residual = 0.8642 Rest_Pulse = 52 Observation Number = 44 Residual = -0.122 Rest_Pulse = 51 Observation Number = 43 Residual = 7.231 Rest_Pulse = 73 Observation Number = 42 Residual = -1.513 Rest_Pulse = 74 Observation Number = 41 Residual = -0.892 Rest_Pulse = 71 Observation Number = 40 Residual = -0.097 Rest_Pulse = 74 Observation Number = 39 Residual = 2.9456 Rest_Pulse = 65 Observation Number = 38 Residual = 6.5567 Rest_Pulse = 85 Observation Number = 37 Residual = 3.4547 Rest_Pulse = 78 Observation Number = 36 Residual = -0.716 Rest_Pulse = 65 Observation Number = 35 Residual = 1.9966 Rest_Pulse = 69 Observation Number = 34 Residual = 1.7519 Rest_Pulse = 59 Observation Number = 33 Residual = 1.7197 Rest_Pulse = 59 Observation Number = 32 Residual = 3.4974 Rest_Pulse = 55 Observation Number = 31 Residual = 2.0943 Rest_Pulse = 58 Observation Number = 30 Residual = -4.819 Rest_Pulse = 66 Observation Number = 29 Residual = 4.9607 Rest_Pulse = 67 Observation Number = 28 Residual = -4.03 Rest_Pulse = 70 Observation Number = 27 Residual = -3.463 Rest_Pulse = 70 Observation Number = 26 Residual = 2.2523 Rest_Pulse = 67 Observation Number = 25 Residual = 2.9564 Rest_Pulse = 66 Observation Number = 24 Residual = 0.2235 Rest_Pulse = 77 Observation Number = 23 Residual = -3.018 Rest_Pulse = 75 Observation Number = 22 Residual = -4.255 Rest_Pulse = 49 Observation Number = 21 Residual = -5.234 Rest_Pulse = 86 Observation Number = 20 Residual = 2.1065 Rest_Pulse = 55 Observation Number = 19 Residual = 0.8749 Rest_Pulse = 78 Observation Number = 18 Residual = -1.276 Rest_Pulse = 68 Observation Number = 17 Residual = -0.445 Rest_Pulse = 77 Observation Number = 16 Residual = 1.5251 Rest_Pulse = 59 Observation Number = 15 Residual = -1.323 Rest_Pulse = 66 Observation Number = 14 Residual = -5.255 Rest_Pulse = 65 Observation Number = 13 Residual = 0.4853 Rest_Pulse = 73 Observation Number = 12 Residual = 0.6602 Rest_Pulse = 55 Observation Number = 11 Residual = 1.2869 Rest_Pulse = 88 Observation Number = 10 Residual = 2.7596 Rest_Pulse = 55 Observation Number = 9 Residual = -3.024 Rest_Pulse = 60 Observation Number = 8 Residual = -0.092 Rest_Pulse = 69 Observation Number = 7 Residual = 0.3961 Rest_Pulse = 74 Observation Number = 6 Residual = -1.968 Rest_Pulse = 76 Observation Number = 5 Residual = -1.385 Rest_Pulse = 59 Observation Number = 4 Residual = -6.813 Rest_Pulse = 74 Observation Number = 3 Residual = 4.0572 Rest_Pulse = 61 Observation Number = 2 Residual = -0.545 Rest_Pulse = 75 Observation Number = 1 Y = 0 Residual = 3.2436 Max_Pulse = 124 Observation Number = 50 Residual = -6.119 Max_Pulse = 118 Observation Number = 49 Residual = 0.6218 Max_Pulse = 130 Observation Number = 48 Residual = 0.702 Max_Pulse = 110 Observation Number = 47 Residual = -4.149 Max_Pulse = 109 Observation Number = 46 Residual = -0.671 Max_Pulse = 118 Observation Number = 45 Residual = 0.8642 Max_Pulse = 104 Observation Number = 44 Residual = -0.122 Max_Pulse = 94 Observation Number = 43 Residual = 7.231 Max_Pulse = 120 Observation Number = 42 Residual = -1.513 Max_Pulse = 127 Observation Number = 41 Residual = -0.892 Max_Pulse = 112 Observation Number = 40 Residual = -0.097 Max_Pulse = 122 Observation Number = 39 Residual = 2.9456 Max_Pulse = 111 Observation Number = 38 Residual = 6.5567 Max_Pulse = 137 Observation Number = 37 Residual = 3.4547 Max_Pulse = 126 Observation Number = 36 Residual = -0.716 Max_Pulse = 111 Observation Number = 35 Residual = 1.9966 Max_Pulse = 112 Observation Number = 34 Residual = 1.7519 Max_Pulse = 109 Observation Number = 33 Residual = 1.7197 Max_Pulse = 107 Observation Number = 32 Residual = 3.4974 Max_Pulse = 114 Observation Number = 31 Residual = 2.0943 Max_Pulse = 105 Observation Number = 30 Residual = -4.819 Max_Pulse = 127 Observation Number = 29 Residual = 4.9607 Max_Pulse = 111 Observation Number = 28 Residual = -4.03 Max_Pulse = 125 Observation Number = 27 Residual = -3.463 Max_Pulse = 111 Observation Number = 26 Residual = 2.2523 Max_Pulse = 112 Observation Number = 25 Residual = 2.9564 Max_Pulse = 117 Observation Number = 24 Residual = 0.2235 Max_Pulse = 119 Observation Number = 23 Residual = -3.018 Max_Pulse = 114 Observation Number = 22 Residual = -4.255 Max_Pulse = 100 Observation Number = 21 Residual = -5.234 Max_Pulse = 127 Observation Number = 20 Residual = 2.1065 Max_Pulse = 100 Observation Number = 19 Residual = 0.8749 Max_Pulse = 122 Observation Number = 18 Residual = -1.276 Max_Pulse = 118 Observation Number = 17 Residual = -0.445 Max_Pulse = 119 Observation Number = 16 Residual = 1.5251 Max_Pulse = 113 Observation Number = 15 Residual = -1.323 Max_Pulse = 114 Observation Number = 14 Residual = -5.255 Max_Pulse = 118 Observation Number = 13 Residual = 0.4853 Max_Pulse = 126 Observation Number = 12 Residual = 0.6602 Max_Pulse = 102 Observation Number = 11 Residual = 1.2869 Max_Pulse = 137 Observation Number = 10 Residual = 2.7596 Max_Pulse = 107 Observation Number = 9 Residual = -3.024 Max_Pulse = 114 Observation Number = 8 Residual = -0.092 Max_Pulse = 106 Observation Number = 7 Residual = 0.3961 Max_Pulse = 121 Observation Number = 6 Residual = -1.968 Max_Pulse = 115 Observation Number = 5 Residual = -1.385 Max_Pulse = 111 Observation Number = 4 Residual = -6.813 Max_Pulse = 115 Observation Number = 3 Residual = 4.0572 Max_Pulse = 107 Observation Number = 2 Residual = -0.545 Max_Pulse = 124 Observation Number = 1 Y = 0
Panel of scatterplots of residuals by regressors for Run_Pulse.

Multiple Regression - Linear Regression, part 2

Model: MODEL1

Dependent Variable: Run_Pulse Run_Pulse

The Reg Procedure

MODEL1

Fit

Run_Pulse

Number of Observations

Number of Observations Read 50
Number of Observations Used 50

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 3 3796.32397 1265.44132 118.95 <.0001
Error 46 489.35603 10.63817    
Corrected Total 49 4285.68000      

Fit Statistics

Root MSE 3.26162 R-Square 0.8858
Dependent Mean 112.92000 Adj R-Sq 0.8784
Coeff Var 2.88844    

Parameter Estimates

Parameter Estimates
Variable Label DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t| Variance
Inflation
Intercept Intercept 1 -5.76862 7.34483 -0.79 0.4362 0
Age Age 1 0.02876 0.03321 0.87 0.3910 1.32353
Pushups Pushups 1 0.08691 0.04544 1.91 0.0620 1.54251
Max_Pulse Max_Pulse 1 0.99630 0.05702 17.47 <.0001 1.25817

Multiple Regression - Linear Regression, part 2

Model: MODEL1

Dependent Variable: Run_Pulse Run_Pulse

Observation-wise Statistics

Run_Pulse

Diagnostic Plots

Observed by Predicted

Run_Pulse = 124 Predicted Value = 120.91 Observation Number = 50 Run_Pulse = 108 Predicted Value = 114.6 Observation Number = 49 Run_Pulse = 127 Predicted Value = 126.72 Observation Number = 48 Run_Pulse = 108 Predicted Value = 107.69 Observation Number = 47 Run_Pulse = 104 Predicted Value = 107.89 Observation Number = 46 Run_Pulse = 115 Predicted Value = 115.12 Observation Number = 45 Run_Pulse = 103 Predicted Value = 101.69 Observation Number = 44 Run_Pulse = 92 Predicted Value = 92.161 Observation Number = 43 Run_Pulse = 125 Predicted Value = 118.07 Observation Number = 42 Run_Pulse = 122 Predicted Value = 123.42 Observation Number = 41 Run_Pulse = 108 Predicted Value = 109.22 Observation Number = 40 Run_Pulse = 118 Predicted Value = 118.09 Observation Number = 39 Run_Pulse = 111 Predicted Value = 108.32 Observation Number = 38 Run_Pulse = 141 Predicted Value = 134.3 Observation Number = 37 Run_Pulse = 127 Predicted Value = 123.52 Observation Number = 36 Run_Pulse = 109 Predicted Value = 109.67 Observation Number = 35 Run_Pulse = 112 Predicted Value = 110.06 Observation Number = 34 Run_Pulse = 108 Predicted Value = 106.03 Observation Number = 33 Run_Pulse = 104 Predicted Value = 102.19 Observation Number = 32 Run_Pulse = 116 Predicted Value = 112.03 Observation Number = 31 Run_Pulse = 104 Predicted Value = 102.11 Observation Number = 30 Run_Pulse = 119 Predicted Value = 123.07 Observation Number = 29 Run_Pulse = 114 Predicted Value = 109.15 Observation Number = 28 Run_Pulse = 120 Predicted Value = 123.51 Observation Number = 27 Run_Pulse = 105 Predicted Value = 108.93 Observation Number = 26 Run_Pulse = 111 Predicted Value = 108.61 Observation Number = 25 Run_Pulse = 117 Predicted Value = 114.01 Observation Number = 24 Run_Pulse = 116 Predicted Value = 115.93 Observation Number = 23 Run_Pulse = 108 Predicted Value = 111.18 Observation Number = 22 Run_Pulse = 95 Predicted Value = 99.128 Observation Number = 21 Run_Pulse = 119 Predicted Value = 124.48 Observation Number = 20 Run_Pulse = 101 Predicted Value = 99.098 Observation Number = 19 Run_Pulse = 120 Predicted Value = 119.54 Observation Number = 18 Run_Pulse = 113 Predicted Value = 114.16 Observation Number = 17 Run_Pulse = 117 Predicted Value = 117.91 Observation Number = 16 Run_Pulse = 111 Predicted Value = 108.97 Observation Number = 15 Run_Pulse = 110 Predicted Value = 111.28 Observation Number = 14 Run_Pulse = 110 Predicted Value = 115.3 Observation Number = 13 Run_Pulse = 125 Predicted Value = 124.18 Observation Number = 12 Run_Pulse = 103 Predicted Value = 102.1 Observation Number = 11 Run_Pulse = 134 Predicted Value = 132.92 Observation Number = 10 Run_Pulse = 107 Predicted Value = 104.01 Observation Number = 9 Run_Pulse = 110 Predicted Value = 112.84 Observation Number = 8 Run_Pulse = 103 Predicted Value = 103.5 Observation Number = 7 Run_Pulse = 118 Predicted Value = 117.64 Observation Number = 6 Run_Pulse = 110 Predicted Value = 112.47 Observation Number = 5 Run_Pulse = 108 Predicted Value = 109.13 Observation Number = 4 Run_Pulse = 105 Predicted Value = 111.95 Observation Number = 3 Run_Pulse = 110 Predicted Value = 105.8 Observation Number = 2 Run_Pulse = 121 Predicted Value = 121.38 Observation Number = 1 Slope = 1 Y = 0
Scatter plot of observed by predicted values for Run_Pulse.

Fit Diagnostics

Residual = 3.0865 Predicted Value = 120.91 Observation Number = 50 Residual = -6.598 Predicted Value = 114.6 Observation Number = 49 Residual = 0.2755 Predicted Value = 126.72 Observation Number = 48 Residual = 0.3063 Predicted Value = 107.69 Observation Number = 47 Residual = -3.891 Predicted Value = 107.89 Observation Number = 46 Residual = -0.116 Predicted Value = 115.12 Observation Number = 45 Residual = 1.3115 Predicted Value = 101.69 Observation Number = 44 Residual = -0.161 Predicted Value = 92.161 Observation Number = 43 Residual = 6.9324 Predicted Value = 118.07 Observation Number = 42 Residual = -1.418 Predicted Value = 123.42 Observation Number = 41 Residual = -1.224 Predicted Value = 109.22 Observation Number = 40 Residual = -0.086 Predicted Value = 118.09 Observation Number = 39 Residual = 2.6806 Predicted Value = 108.32 Observation Number = 38 Residual = 6.6969 Predicted Value = 134.3 Observation Number = 37 Residual = 3.4824 Predicted Value = 123.52 Observation Number = 36 Residual = -0.675 Predicted Value = 109.67 Observation Number = 35 Residual = 1.9392 Predicted Value = 110.06 Observation Number = 34 Residual = 1.9665 Predicted Value = 106.03 Observation Number = 33 Residual = 1.8122 Predicted Value = 102.19 Observation Number = 32 Residual = 3.9664 Predicted Value = 112.03 Observation Number = 31 Residual = 1.8884 Predicted Value = 102.11 Observation Number = 30 Residual = -4.068 Predicted Value = 123.07 Observation Number = 29 Residual = 4.846 Predicted Value = 109.15 Observation Number = 28 Residual = -3.505 Predicted Value = 123.51 Observation Number = 27 Residual = -3.925 Predicted Value = 108.93 Observation Number = 26 Residual = 2.3885 Predicted Value = 108.61 Observation Number = 25 Residual = 2.9935 Predicted Value = 114.01 Observation Number = 24 Residual = 0.0667 Predicted Value = 115.93 Observation Number = 23 Residual = -3.181 Predicted Value = 111.18 Observation Number = 22 Residual = -4.128 Predicted Value = 99.128 Observation Number = 21 Residual = -5.481 Predicted Value = 124.48 Observation Number = 20 Residual = 1.9018 Predicted Value = 99.098 Observation Number = 19 Residual = 0.4631 Predicted Value = 119.54 Observation Number = 18 Residual = -1.16 Predicted Value = 114.16 Observation Number = 17 Residual = -0.908 Predicted Value = 117.91 Observation Number = 16 Residual = 2.0254 Predicted Value = 108.97 Observation Number = 15 Residual = -1.275 Predicted Value = 111.28 Observation Number = 14 Residual = -5.296 Predicted Value = 115.3 Observation Number = 13 Residual = 0.8159 Predicted Value = 124.18 Observation Number = 12 Residual = 0.9021 Predicted Value = 102.1 Observation Number = 11 Residual = 1.0842 Predicted Value = 132.92 Observation Number = 10 Residual = 2.9853 Predicted Value = 104.01 Observation Number = 9 Residual = -2.844 Predicted Value = 112.84 Observation Number = 8 Residual = -0.505 Predicted Value = 103.5 Observation Number = 7 Residual = 0.3604 Predicted Value = 117.64 Observation Number = 6 Residual = -2.473 Predicted Value = 112.47 Observation Number = 5 Residual = -1.128 Predicted Value = 109.13 Observation Number = 4 Residual = -6.947 Predicted Value = 111.95 Observation Number = 3 Residual = 4.1954 Predicted Value = 105.8 Observation Number = 2 Residual = -0.379 Predicted Value = 121.38 Observation Number = 1 Y = 0 RStudent = 0.9896 Predicted Value = 120.91 Observation Number = 50 RStudent = -2.188 Predicted Value = 114.6 Observation Number = 49 RStudent = 0.0873 Predicted Value = 126.72 Observation Number = 48 RStudent = 0.0946 Predicted Value = 107.69 Observation Number = 47 RStudent = -1.258 Predicted Value = 107.89 Observation Number = 46 RStudent = -0.036 Predicted Value = 115.12 Observation Number = 45 RStudent = 0.4104 Predicted Value = 101.69 Observation Number = 44 RStudent = -0.052 Predicted Value = 92.161 Observation Number = 43 RStudent = 2.3108 Predicted Value = 118.07 Observation Number = 42 RStudent = -0.449 Predicted Value = 123.42 Observation Number = 41 RStudent = -0.377 Predicted Value = 109.22 Observation Number = 40 RStudent = -0.027 Predicted Value = 118.09 Observation Number = 39 RStudent = 0.8432 Predicted Value = 108.32 Observation Number = 38 RStudent = 2.3307 Predicted Value = 134.3 Observation Number = 37 RStudent = 1.1029 Predicted Value = 123.52 Observation Number = 36 RStudent = -0.211 Predicted Value = 109.67 Observation Number = 35 RStudent = 0.6085 Predicted Value = 110.06 Observation Number = 34 RStudent = 0.6124 Predicted Value = 106.03 Observation Number = 33 RStudent = 0.6252 Predicted Value = 102.19 Observation Number = 32 RStudent = 1.2757 Predicted Value = 112.03 Observation Number = 31 RStudent = 0.6094 Predicted Value = 102.11 Observation Number = 30 RStudent = -1.306 Predicted Value = 123.07 Observation Number = 29 RStudent = 1.5349 Predicted Value = 109.15 Observation Number = 28 RStudent = -1.141 Predicted Value = 123.51 Observation Number = 27 RStudent = -1.229 Predicted Value = 108.93 Observation Number = 26 RStudent = 0.7671 Predicted Value = 108.61 Observation Number = 25 RStudent = 0.9385 Predicted Value = 114.01 Observation Number = 24 RStudent = 0.0209 Predicted Value = 115.93 Observation Number = 23 RStudent = -1.04 Predicted Value = 111.18 Observation Number = 22 RStudent = -1.37 Predicted Value = 99.128 Observation Number = 21 RStudent = -1.824 Predicted Value = 124.48 Observation Number = 20 RStudent = 0.6158 Predicted Value = 99.098 Observation Number = 19 RStudent = 0.1437 Predicted Value = 119.54 Observation Number = 18 RStudent = -0.363 Predicted Value = 114.16 Observation Number = 17 RStudent = -0.289 Predicted Value = 117.91 Observation Number = 16 RStudent = 0.6469 Predicted Value = 108.97 Observation Number = 15 RStudent = -0.392 Predicted Value = 111.28 Observation Number = 14 RStudent = -1.767 Predicted Value = 115.3 Observation Number = 13 RStudent = 0.259 Predicted Value = 124.18 Observation Number = 12 RStudent = 0.3049 Predicted Value = 102.1 Observation Number = 11 RStudent = 0.3581 Predicted Value = 132.92 Observation Number = 10 RStudent = 0.9469 Predicted Value = 104.01 Observation Number = 9 RStudent = -0.918 Predicted Value = 112.84 Observation Number = 8 RStudent = -0.159 Predicted Value = 103.5 Observation Number = 7 RStudent = 0.1114 Predicted Value = 117.64 Observation Number = 6 RStudent = -0.763 Predicted Value = 112.47 Observation Number = 5 RStudent = -0.348 Predicted Value = 109.13 Observation Number = 4 RStudent = -2.326 Predicted Value = 111.95 Observation Number = 3 RStudent = 1.3551 Predicted Value = 105.8 Observation Number = 2 RStudent = -0.118 Predicted Value = 121.38 Observation Number = 1 Y = 2 Y = -2 RStudent = 0.9896 Hat Diagonal = 0.0861 Observation Number = 50 RStudent = -2.188 Hat Diagonal = 0.0748 Observation Number = 49 RStudent = 0.0873 Hat Diagonal = 0.0842 Observation Number = 48 RStudent = 0.0946 Hat Diagonal = 0.036 Observation Number = 47 RStudent = -1.258 Hat Diagonal = 0.0892 Observation Number = 46 RStudent = -0.036 Hat Diagonal = 0.0242 Observation Number = 45 RStudent = 0.4104 Hat Diagonal = 0.0573 Observation Number = 44 RStudent = -0.052 Hat Diagonal = 0.1387 Observation Number = 43 RStudent = 2.3108 Hat Diagonal = 0.0742 Observation Number = 42 RStudent = -0.449 Hat Diagonal = 0.0805 Observation Number = 41 RStudent = -0.377 Hat Diagonal = 0.0297 Observation Number = 40 RStudent = -0.027 Hat Diagonal = 0.062 Observation Number = 39 RStudent = 0.8432 Hat Diagonal = 0.0558 Observation Number = 38 RStudent = 2.3307 Hat Diagonal = 0.1492 Observation Number = 37 RStudent = 1.1029 Hat Diagonal = 0.0585 Observation Number = 36 RStudent = -0.211 Hat Diagonal = 0.0593 Observation Number = 35 RStudent = 0.6085 Hat Diagonal = 0.0583 Observation Number = 34 RStudent = 0.6124 Hat Diagonal = 0.0439 Observation Number = 33 RStudent = 0.6252 Hat Diagonal = 0.2207 Observation Number = 32 RStudent = 1.2757 Hat Diagonal = 0.0788 Observation Number = 31 RStudent = 0.6094 Hat Diagonal = 0.1095 Observation Number = 30 RStudent = -1.306 Hat Diagonal = 0.0741 Observation Number = 29 RStudent = 1.5349 Hat Diagonal = 0.0354 Observation Number = 28 RStudent = -1.141 Hat Diagonal = 0.1077 Observation Number = 27 RStudent = -1.229 Hat Diagonal = 0.0298 Observation Number = 26 RStudent = 0.7671 Hat Diagonal = 0.0969 Observation Number = 25 RStudent = 0.9385 Hat Diagonal = 0.0462 Observation Number = 24 RStudent = 0.0209 Hat Diagonal = 0.0611 Observation Number = 23 RStudent = -1.04 Hat Diagonal = 0.1183 Observation Number = 22 RStudent = -1.37 Hat Diagonal = 0.1305 Observation Number = 21 RStudent = -1.824 Hat Diagonal = 0.108 Observation Number = 20 RStudent = 0.6158 Hat Diagonal = 0.1155 Observation Number = 19 RStudent = 0.1437 Hat Diagonal = 0.0449 Observation Number = 18 RStudent = -0.363 Hat Diagonal = 0.0597 Observation Number = 17 RStudent = -0.289 Hat Diagonal = 0.0905 Observation Number = 16 RStudent = 0.6469 Hat Diagonal = 0.09 Observation Number = 15 RStudent = -0.392 Hat Diagonal = 0.0224 Observation Number = 14 RStudent = -1.767 Hat Diagonal = 0.1165 Observation Number = 13 RStudent = 0.259 Hat Diagonal = 0.0858 Observation Number = 12 RStudent = 0.3049 Hat Diagonal = 0.1933 Observation Number = 11 RStudent = 0.3581 Hat Diagonal = 0.1548 Observation Number = 10 RStudent = 0.9469 Hat Diagonal = 0.0678 Observation Number = 9 RStudent = -0.918 Hat Diagonal = 0.1018 Observation Number = 8 RStudent = -0.159 Hat Diagonal = 0.0707 Observation Number = 7 RStudent = 0.1114 Hat Diagonal = 0.0374 Observation Number = 6 RStudent = -0.763 Hat Diagonal = 0.0213 Observation Number = 5 RStudent = -0.348 Hat Diagonal = 0.0325 Observation Number = 4 RStudent = -2.326 Hat Diagonal = 0.0808 Observation Number = 3 RStudent = 1.3551 Hat Diagonal = 0.0826 Observation Number = 2 RStudent = -0.118 Hat Diagonal = 0.0531 Observation Number = 1 X = 0.16 Y = -2 Y = 2 Quantile = 2.2433 Residual = 6.9324 Quantile = 1.8475 Residual = 6.6969 Quantile = 1.6235 Residual = 4.846 Quantile = 1.46 Residual = 4.1954 Quantile = 1.3283 Residual = 3.9664 Quantile = 1.2163 Residual = 3.4824 Quantile = 1.1177 Residual = 3.0865 Quantile = 1.029 Residual = 2.9935 Quantile = 0.9477 Residual = 2.9853 Quantile = 0.8722 Residual = 2.6806 Quantile = 0.8014 Residual = 2.3885 Quantile = 0.7344 Residual = 2.0254 Quantile = 0.6706 Residual = 1.9665 Quantile = 0.6094 Residual = 1.9392 Quantile = 0.5503 Residual = 1.9018 Quantile = 0.4932 Residual = 1.8884 Quantile = 0.4376 Residual = 1.8122 Quantile = 0.3833 Residual = 1.3115 Quantile = 0.3301 Residual = 1.0842 Quantile = 0.2779 Residual = 0.9021 Quantile = 0.2264 Residual = 0.8159 Quantile = 0.1755 Residual = 0.4631 Quantile = 0.125 Residual = 0.3604 Quantile = 0.0749 Residual = 0.3063 Quantile = 0.0249 Residual = 0.2755 Quantile = -0.025 Residual = 0.0667 Quantile = -0.075 Residual = -0.086 Quantile = -0.125 Residual = -0.116 Quantile = -0.175 Residual = -0.161 Quantile = -0.226 Residual = -0.379 Quantile = -0.278 Residual = -0.505 Quantile = -0.33 Residual = -0.675 Quantile = -0.383 Residual = -0.908 Quantile = -0.438 Residual = -1.128 Quantile = -0.493 Residual = -1.16 Quantile = -0.55 Residual = -1.224 Quantile = -0.609 Residual = -1.275 Quantile = -0.671 Residual = -1.418 Quantile = -0.734 Residual = -2.473 Quantile = -0.801 Residual = -2.844 Quantile = -0.872 Residual = -3.181 Quantile = -0.948 Residual = -3.505 Quantile = -1.029 Residual = -3.891 Quantile = -1.118 Residual = -3.925 Quantile = -1.216 Residual = -4.068 Quantile = -1.328 Residual = -4.128 Quantile = -1.46 Residual = -5.296 Quantile = -1.624 Residual = -5.481 Quantile = -1.847 Residual = -6.598 Quantile = -2.243 Residual = -6.947 Slope = 3.1602 Y = -1E-14 Run_Pulse = 124 Predicted Value = 120.91 Observation Number = 50 Run_Pulse = 108 Predicted Value = 114.6 Observation Number = 49 Run_Pulse = 127 Predicted Value = 126.72 Observation Number = 48 Run_Pulse = 108 Predicted Value = 107.69 Observation Number = 47 Run_Pulse = 104 Predicted Value = 107.89 Observation Number = 46 Run_Pulse = 115 Predicted Value = 115.12 Observation Number = 45 Run_Pulse = 103 Predicted Value = 101.69 Observation Number = 44 Run_Pulse = 92 Predicted Value = 92.161 Observation Number = 43 Run_Pulse = 125 Predicted Value = 118.07 Observation Number = 42 Run_Pulse = 122 Predicted Value = 123.42 Observation Number = 41 Run_Pulse = 108 Predicted Value = 109.22 Observation Number = 40 Run_Pulse = 118 Predicted Value = 118.09 Observation Number = 39 Run_Pulse = 111 Predicted Value = 108.32 Observation Number = 38 Run_Pulse = 141 Predicted Value = 134.3 Observation Number = 37 Run_Pulse = 127 Predicted Value = 123.52 Observation Number = 36 Run_Pulse = 109 Predicted Value = 109.67 Observation Number = 35 Run_Pulse = 112 Predicted Value = 110.06 Observation Number = 34 Run_Pulse = 108 Predicted Value = 106.03 Observation Number = 33 Run_Pulse = 104 Predicted Value = 102.19 Observation Number = 32 Run_Pulse = 116 Predicted Value = 112.03 Observation Number = 31 Run_Pulse = 104 Predicted Value = 102.11 Observation Number = 30 Run_Pulse = 119 Predicted Value = 123.07 Observation Number = 29 Run_Pulse = 114 Predicted Value = 109.15 Observation Number = 28 Run_Pulse = 120 Predicted Value = 123.51 Observation Number = 27 Run_Pulse = 105 Predicted Value = 108.93 Observation Number = 26 Run_Pulse = 111 Predicted Value = 108.61 Observation Number = 25 Run_Pulse = 117 Predicted Value = 114.01 Observation Number = 24 Run_Pulse = 116 Predicted Value = 115.93 Observation Number = 23 Run_Pulse = 108 Predicted Value = 111.18 Observation Number = 22 Run_Pulse = 95 Predicted Value = 99.128 Observation Number = 21 Run_Pulse = 119 Predicted Value = 124.48 Observation Number = 20 Run_Pulse = 101 Predicted Value = 99.098 Observation Number = 19 Run_Pulse = 120 Predicted Value = 119.54 Observation Number = 18 Run_Pulse = 113 Predicted Value = 114.16 Observation Number = 17 Run_Pulse = 117 Predicted Value = 117.91 Observation Number = 16 Run_Pulse = 111 Predicted Value = 108.97 Observation Number = 15 Run_Pulse = 110 Predicted Value = 111.28 Observation Number = 14 Run_Pulse = 110 Predicted Value = 115.3 Observation Number = 13 Run_Pulse = 125 Predicted Value = 124.18 Observation Number = 12 Run_Pulse = 103 Predicted Value = 102.1 Observation Number = 11 Run_Pulse = 134 Predicted Value = 132.92 Observation Number = 10 Run_Pulse = 107 Predicted Value = 104.01 Observation Number = 9 Run_Pulse = 110 Predicted Value = 112.84 Observation Number = 8 Run_Pulse = 103 Predicted Value = 103.5 Observation Number = 7 Run_Pulse = 118 Predicted Value = 117.64 Observation Number = 6 Run_Pulse = 110 Predicted Value = 112.47 Observation Number = 5 Run_Pulse = 108 Predicted Value = 109.13 Observation Number = 4 Run_Pulse = 105 Predicted Value = 111.95 Observation Number = 3 Run_Pulse = 110 Predicted Value = 105.8 Observation Number = 2 Run_Pulse = 121 Predicted Value = 121.38 Observation Number = 1 Slope = 1 Y = 0 Cook's D = 0.0231 Observation Number = 50 Cook's D = 0.0894 Observation Number = 49 Cook's D = .00018 Observation Number = 48 Cook's D = 8.5E-5 Observation Number = 47 Cook's D = 0.0383 Observation Number = 46 Cook's D = 8E-6 Observation Number = 45 Cook's D = 0.0026 Observation Number = 44 Cook's D = .00011 Observation Number = 43 Cook's D = 0.0978 Observation Number = 42 Cook's D = 0.0045 Observation Number = 41 Cook's D = 0.0011 Observation Number = 40 Cook's D = 1.2E-5 Observation Number = 39 Cook's D = 0.0106 Observation Number = 38 Cook's D = 0.2171 Observation Number = 37 Cook's D = 0.0188 Observation Number = 36 Cook's D = .00072 Observation Number = 35 Cook's D = 0.0058 Observation Number = 34 Cook's D = 0.0044 Observation Number = 33 Cook's D = 0.028 Observation Number = 32 Cook's D = 0.0344 Observation Number = 31 Cook's D = 0.0116 Observation Number = 30 Cook's D = 0.0336 Observation Number = 29 Cook's D = 0.021 Observation Number = 28 Cook's D = 0.039 Observation Number = 27 Cook's D = 0.0115 Observation Number = 26 Cook's D = 0.0159 Observation Number = 25 Cook's D = 0.0107 Observation Number = 24 Cook's D = 7.3E-6 Observation Number = 23 Cook's D = 0.0362 Observation Number = 22 Cook's D = 0.0691 Observation Number = 21 Cook's D = 0.0958 Observation Number = 20 Cook's D = 0.0125 Observation Number = 19 Cook's D = .00025 Observation Number = 18 Cook's D = 0.0021 Observation Number = 17 Cook's D = 0.0021 Observation Number = 16 Cook's D = 0.0105 Observation Number = 15 Cook's D = .00089 Observation Number = 14 Cook's D = 0.0984 Observation Number = 13 Cook's D = 0.0016 Observation Number = 12 Cook's D = 0.0057 Observation Number = 11 Cook's D = 0.006 Observation Number = 10 Cook's D = 0.0163 Observation Number = 9 Cook's D = 0.024 Observation Number = 8 Cook's D = .00049 Observation Number = 7 Cook's D = .00012 Observation Number = 6 Cook's D = 0.0032 Observation Number = 5 Cook's D = 0.001 Observation Number = 4 Cook's D = 0.1085 Observation Number = 3 Cook's D = 0.0406 Observation Number = 2 Cook's D = 0.0002 Observation Number = 1 Cook's D = 0.0231 Observation Number = 50 Cook's D = 0.0894 Observation Number = 49 Cook's D = .00018 Observation Number = 48 Cook's D = 8.5E-5 Observation Number = 47 Cook's D = 0.0383 Observation Number = 46 Cook's D = 8E-6 Observation Number = 45 Cook's D = 0.0026 Observation Number = 44 Cook's D = .00011 Observation Number = 43 Cook's D = 0.0978 Observation Number = 42 Cook's D = 0.0045 Observation Number = 41 Cook's D = 0.0011 Observation Number = 40 Cook's D = 1.2E-5 Observation Number = 39 Cook's D = 0.0106 Observation Number = 38 Cook's D = 0.2171 Observation Number = 37 Cook's D = 0.0188 Observation Number = 36 Cook's D = .00072 Observation Number = 35 Cook's D = 0.0058 Observation Number = 34 Cook's D = 0.0044 Observation Number = 33 Cook's D = 0.028 Observation Number = 32 Cook's D = 0.0344 Observation Number = 31 Cook's D = 0.0116 Observation Number = 30 Cook's D = 0.0336 Observation Number = 29 Cook's D = 0.021 Observation Number = 28 Cook's D = 0.039 Observation Number = 27 Cook's D = 0.0115 Observation Number = 26 Cook's D = 0.0159 Observation Number = 25 Cook's D = 0.0107 Observation Number = 24 Cook's D = 7.3E-6 Observation Number = 23 Cook's D = 0.0362 Observation Number = 22 Cook's D = 0.0691 Observation Number = 21 Cook's D = 0.0958 Observation Number = 20 Cook's D = 0.0125 Observation Number = 19 Cook's D = .00025 Observation Number = 18 Cook's D = 0.0021 Observation Number = 17 Cook's D = 0.0021 Observation Number = 16 Cook's D = 0.0105 Observation Number = 15 Cook's D = .00089 Observation Number = 14 Cook's D = 0.0984 Observation Number = 13 Cook's D = 0.0016 Observation Number = 12 Cook's D = 0.0057 Observation Number = 11 Cook's D = 0.006 Observation Number = 10 Cook's D = 0.0163 Observation Number = 9 Cook's D = 0.024 Observation Number = 8 Cook's D = .00049 Observation Number = 7 Cook's D = .00012 Observation Number = 6 Cook's D = 0.0032 Observation Number = 5 Cook's D = 0.001 Observation Number = 4 Cook's D = 0.1085 Observation Number = 3 Cook's D = 0.0406 Observation Number = 2 Cook's D = 0.0002 Observation Number = 1 Y = 0.08 Residual = 9.4806 Percent = 0.3506 Residual = 9.3848 Percent = 0.3838 Residual = 9.3848 Percent = 0.3838 Residual = 9.2891 Percent = 0.4197 Residual = 9.2891 Percent = 0.4197 Residual = 9.1933 Percent = 0.4586 Residual = 9.1933 Percent = 0.4586 Residual = 9.0975 Percent = 0.5007 Residual = 9.0975 Percent = 0.5007 Residual = 9.0018 Percent = 0.546 Residual = 9.0018 Percent = 0.546 Residual = 8.906 Percent = 0.595 Residual = 8.906 Percent = 0.595 Residual = 8.8103 Percent = 0.6478 Residual = 8.8103 Percent = 0.6478 Residual = 8.7145 Percent = 0.7045 Residual = 8.7145 Percent = 0.7045 Residual = 8.6187 Percent = 0.7656 Residual = 8.6187 Percent = 0.7656 Residual = 8.523 Percent = 0.8312 Residual = 8.523 Percent = 0.8312 Residual = 8.4272 Percent = 0.9015 Residual = 8.4272 Percent = 0.9015 Residual = 8.3314 Percent = 0.977 Residual = 8.3314 Percent = 0.977 Residual = 8.2357 Percent = 1.0577 Residual = 8.2357 Percent = 1.0577 Residual = 8.1399 Percent = 1.1441 Residual = 8.1399 Percent = 1.1441 Residual = 8.0441 Percent = 1.2364 Residual = 8.0441 Percent = 1.2364 Residual = 7.9484 Percent = 1.3349 Residual = 7.9484 Percent = 1.3349 Residual = 7.8526 Percent = 1.44 Residual = 7.8526 Percent = 1.44 Residual = 7.7569 Percent = 1.5519 Residual = 7.7569 Percent = 1.5519 Residual = 7.6611 Percent = 1.671 Residual = 7.6611 Percent = 1.671 Residual = 7.5653 Percent = 1.7975 Residual = 7.5653 Percent = 1.7975 Residual = 7.4696 Percent = 1.9319 Residual = 7.4696 Percent = 1.9319 Residual = 7.3738 Percent = 2.0744 Residual = 7.3738 Percent = 2.0744 Residual = 7.278 Percent = 2.2253 Residual = 7.278 Percent = 2.2253 Residual = 7.1823 Percent = 2.3851 Residual = 7.1823 Percent = 2.3851 Residual = 7.0865 Percent = 2.554 Residual = 7.0865 Percent = 2.554 Residual = 6.9907 Percent = 2.7323 Residual = 6.9907 Percent = 2.7323 Residual = 6.895 Percent = 2.9204 Residual = 6.895 Percent = 2.9204 Residual = 6.7992 Percent = 3.1186 Residual = 6.7992 Percent = 3.1186 Residual = 6.7035 Percent = 3.3272 Residual = 6.7035 Percent = 3.3272 Residual = 6.6077 Percent = 3.5464 Residual = 6.6077 Percent = 3.5464 Residual = 6.5119 Percent = 3.7767 Residual = 6.5119 Percent = 3.7767 Residual = 6.4162 Percent = 4.0182 Residual = 6.4162 Percent = 4.0182 Residual = 6.3204 Percent = 4.2712 Residual = 6.3204 Percent = 4.2712 Residual = 6.2246 Percent = 4.5359 Residual = 6.2246 Percent = 4.5359 Residual = 6.1289 Percent = 4.8127 Residual = 6.1289 Percent = 4.8127 Residual = 6.0331 Percent = 5.1017 Residual = 6.0331 Percent = 5.1017 Residual = 5.9373 Percent = 5.4031 Residual = 5.9373 Percent = 5.4031 Residual = 5.8416 Percent = 5.717 Residual = 5.8416 Percent = 5.717 Residual = 5.7458 Percent = 6.0436 Residual = 5.7458 Percent = 6.0436 Residual = 5.6501 Percent = 6.383 Residual = 5.6501 Percent = 6.383 Residual = 5.5543 Percent = 6.7352 Residual = 5.5543 Percent = 6.7352 Residual = 5.4585 Percent = 7.1004 Residual = 5.4585 Percent = 7.1004 Residual = 5.3628 Percent = 7.4785 Residual = 5.3628 Percent = 7.4785 Residual = 5.267 Percent = 7.8695 Residual = 5.267 Percent = 7.8695 Residual = 5.1712 Percent = 8.2734 Residual = 5.1712 Percent = 8.2734 Residual = 4.9797 Percent = 9.1192 Residual = 4.9797 Percent = 9.1192 Residual = 4.7882 Percent = 10.015 Residual = 4.7882 Percent = 10.015 Residual = 4.5967 Percent = 10.958 Residual = 4.5967 Percent = 10.958 Residual = 4.4051 Percent = 11.945 Residual = 4.4051 Percent = 11.945 Residual = 4.2136 Percent = 12.975 Residual = 4.2136 Percent = 12.975 Residual = 2.7771 Percent = 21.451 Residual = 2.7771 Percent = 21.451 Residual = 2.4899 Percent = 23.139 Residual = 2.4899 Percent = 23.139 Residual = 2.2983 Percent = 24.226 Residual = 2.2983 Percent = 24.226 Residual = 2.1068 Percent = 25.271 Residual = 2.1068 Percent = 25.271 Residual = 1.9153 Percent = 26.265 Residual = 1.9153 Percent = 26.265 Residual = 1.8195 Percent = 26.739 Residual = 1.8195 Percent = 26.739 Residual = 1.7237 Percent = 27.198 Residual = 1.7237 Percent = 27.198 Residual = 1.628 Percent = 27.638 Residual = 1.628 Percent = 27.638 Residual = 1.5322 Percent = 28.06 Residual = 1.5322 Percent = 28.06 Residual = 1.4365 Percent = 28.462 Residual = 1.4365 Percent = 28.462 Residual = 1.3407 Percent = 28.844 Residual = 1.3407 Percent = 28.844 Residual = 1.2449 Percent = 29.204 Residual = 1.2449 Percent = 29.204 Residual = 1.1492 Percent = 29.541 Residual = 1.1492 Percent = 29.541 Residual = 1.0534 Percent = 29.854 Residual = 1.0534 Percent = 29.854 Residual = 0.9576 Percent = 30.144 Residual = 0.9576 Percent = 30.144 Residual = 0.8619 Percent = 30.408 Residual = 0.8619 Percent = 30.408 Residual = 0.7661 Percent = 30.646 Residual = 0.7661 Percent = 30.646 Residual = 0.6703 Percent = 30.858 Residual = 0.6703 Percent = 30.858 Residual = 0.5746 Percent = 31.043 Residual = 0.5746 Percent = 31.043 Residual = 0.4788 Percent = 31.2 Residual = 0.4788 Percent = 31.2 Residual = 0.3831 Percent = 31.329 Residual = 0.3831 Percent = 31.329 Residual = 0.2873 Percent = 31.43 Residual = 0.2873 Percent = 31.43 Residual = 0.1915 Percent = 31.502 Residual = 0.1915 Percent = 31.502 Residual = 0.0958 Percent = 31.545 Residual = 0.0958 Percent = 31.545 Residual = -1E-14 Percent = 31.56 Residual = -1E-14 Percent = 31.56 Residual = -0.096 Percent = 31.545 Residual = -0.096 Percent = 31.545 Residual = -0.192 Percent = 31.502 Residual = -0.192 Percent = 31.502 Residual = -0.287 Percent = 31.43 Residual = -0.287 Percent = 31.43 Residual = -0.383 Percent = 31.329 Residual = -0.383 Percent = 31.329 Residual = -0.479 Percent = 31.2 Residual = -0.479 Percent = 31.2 Residual = -0.575 Percent = 31.043 Residual = -0.575 Percent = 31.043 Residual = -0.67 Percent = 30.858 Residual = -0.67 Percent = 30.858 Residual = -0.766 Percent = 30.646 Residual = -0.766 Percent = 30.646 Residual = -0.862 Percent = 30.408 Residual = -0.862 Percent = 30.408 Residual = -0.958 Percent = 30.144 Residual = -0.958 Percent = 30.144 Residual = -1.053 Percent = 29.854 Residual = -1.053 Percent = 29.854 Residual = -1.149 Percent = 29.541 Residual = -1.149 Percent = 29.541 Residual = -1.245 Percent = 29.204 Residual = -1.245 Percent = 29.204 Residual = -1.341 Percent = 28.844 Residual = -1.341 Percent = 28.844 Residual = -1.436 Percent = 28.462 Residual = -1.436 Percent = 28.462 Residual = -1.532 Percent = 28.06 Residual = -1.532 Percent = 28.06 Residual = -1.628 Percent = 27.638 Residual = -1.628 Percent = 27.638 Residual = -1.724 Percent = 27.198 Residual = -1.724 Percent = 27.198 Residual = -1.82 Percent = 26.739 Residual = -1.82 Percent = 26.739 Residual = -1.915 Percent = 26.265 Residual = -1.915 Percent = 26.265 Residual = -2.107 Percent = 25.271 Residual = -2.107 Percent = 25.271 Residual = -2.298 Percent = 24.226 Residual = -2.298 Percent = 24.226 Residual = -3.447 Percent = 17.407 Residual = -3.447 Percent = 17.407 Residual = -3.831 Percent = 15.139 Residual = -3.831 Percent = 15.139 Residual = -4.118 Percent = 13.503 Residual = -4.118 Percent = 13.503 Residual = -4.309 Percent = 12.455 Residual = -4.309 Percent = 12.455 Residual = -4.501 Percent = 11.446 Residual = -4.501 Percent = 11.446 Residual = -4.692 Percent = 10.48 Residual = -4.692 Percent = 10.48 Residual = -4.884 Percent = 9.5608 Residual = -4.884 Percent = 9.5608 Residual = -5.075 Percent = 8.69 Residual = -5.075 Percent = 8.69 Residual = -5.171 Percent = 8.2734 Residual = -5.171 Percent = 8.2734 Residual = -5.267 Percent = 7.8695 Residual = -5.267 Percent = 7.8695 Residual = -5.363 Percent = 7.4785 Residual = -5.363 Percent = 7.4785 Residual = -5.459 Percent = 7.1004 Residual = -5.459 Percent = 7.1004 Residual = -5.554 Percent = 6.7352 Residual = -5.554 Percent = 6.7352 Residual = -5.65 Percent = 6.383 Residual = -5.65 Percent = 6.383 Residual = -5.746 Percent = 6.0436 Residual = -5.746 Percent = 6.0436 Residual = -5.842 Percent = 5.717 Residual = -5.842 Percent = 5.717 Residual = -5.937 Percent = 5.4031 Residual = -5.937 Percent = 5.4031 Residual = -6.033 Percent = 5.1017 Residual = -6.033 Percent = 5.1017 Residual = -6.129 Percent = 4.8127 Residual = -6.129 Percent = 4.8127 Residual = -6.225 Percent = 4.5359 Residual = -6.225 Percent = 4.5359 Residual = -6.32 Percent = 4.2712 Residual = -6.32 Percent = 4.2712 Residual = -6.416 Percent = 4.0182 Residual = -6.416 Percent = 4.0182 Residual = -6.512 Percent = 3.7767 Residual = -6.512 Percent = 3.7767 Residual = -6.608 Percent = 3.5464 Residual = -6.608 Percent = 3.5464 Residual = -6.703 Percent = 3.3272 Residual = -6.703 Percent = 3.3272 Residual = -6.799 Percent = 3.1186 Residual = -6.799 Percent = 3.1186 Residual = -6.895 Percent = 2.9204 Residual = -6.895 Percent = 2.9204 Residual = -6.991 Percent = 2.7323 Residual = -6.991 Percent = 2.7323 Residual = -7.087 Percent = 2.554 Residual = -7.087 Percent = 2.554 Residual = -7.182 Percent = 2.3851 Residual = -7.182 Percent = 2.3851 Residual = -7.278 Percent = 2.2253 Residual = -7.278 Percent = 2.2253 Residual = -7.374 Percent = 2.0744 Residual = -7.374 Percent = 2.0744 Residual = -7.47 Percent = 1.9319 Residual = -7.47 Percent = 1.9319 Residual = -7.565 Percent = 1.7975 Residual = -7.565 Percent = 1.7975 Residual = -7.661 Percent = 1.671 Residual = -7.661 Percent = 1.671 Residual = -7.757 Percent = 1.5519 Residual = -7.757 Percent = 1.5519 Residual = -7.853 Percent = 1.44 Residual = -7.853 Percent = 1.44 Residual = -7.948 Percent = 1.3349 Residual = -7.948 Percent = 1.3349 Residual = -8.044 Percent = 1.2364 Residual = -8.044 Percent = 1.2364 Residual = -8.14 Percent = 1.1441 Residual = -8.14 Percent = 1.1441 Residual = -8.236 Percent = 1.0577 Residual = -8.236 Percent = 1.0577 Residual = -8.331 Percent = 0.977 Residual = -8.331 Percent = 0.977 Residual = -8.427 Percent = 0.9015 Residual = -8.427 Percent = 0.9015 Residual = -8.523 Percent = 0.8312 Residual = -8.523 Percent = 0.8312 Residual = -8.619 Percent = 0.7656 Residual = -8.619 Percent = 0.7656 Residual = -8.714 Percent = 0.7045 Residual = -8.714 Percent = 0.7045 Residual = -8.81 Percent = 0.6478 Residual = -8.81 Percent = 0.6478 Residual = -8.906 Percent = 0.595 Residual = -8.906 Percent = 0.595 Residual = -9.002 Percent = 0.546 Residual = -9.002 Percent = 0.546 Residual = -9.098 Percent = 0.5007 Residual = -9.098 Percent = 0.5007 Residual = -9.193 Percent = 0.4586 Residual = -9.193 Percent = 0.4586 Residual = -9.289 Percent = 0.4197 Residual = -9.289 Percent = 0.4197 Residual = -9.385 Percent = 0.3838 Residual = -9.385 Percent = 0.3838 Residual = -9.481 Percent = 0.3506 Residual = 6.25 Percent = 4 Residual = 6.25 Percent = 4 Residual = 3.75 Percent = 16 Residual = 3.75 Percent = 16 Residual = 1.25 Percent = 32 Residual = 1.25 Percent = 32 Residual = -1.25 Percent = 26 Residual = -1.25 Percent = 26 Residual = -3.75 Percent = 14 Residual = -3.75 Percent = 14 Residual = -6.25 Percent = 8 Residual = -6.25 Percent = 8 Proportion Less = 0.9876 Fit-Mean = 21.383 Proportion Less = 0.9677 Fit-Mean = 19.996 Proportion Less = 0.9478 Fit-Mean = 13.805 Proportion Less = 0.9279 Fit-Mean = 11.561 Proportion Less = 0.908 Fit-Mean = 11.264 Proportion Less = 0.8881 Fit-Mean = 10.598 Proportion Less = 0.8682 Fit-Mean = 10.585 Proportion Less = 0.8483 Fit-Mean = 10.498 Proportion Less = 0.8284 Fit-Mean = 10.148 Proportion Less = 0.8085 Fit-Mean = 8.4593 Proportion Less = 0.7886 Fit-Mean = 7.9935 Proportion Less = 0.7687 Fit-Mean = 6.6169 Proportion Less = 0.7488 Fit-Mean = 5.1657 Proportion Less = 0.7289 Fit-Mean = 5.1476 Proportion Less = 0.709 Fit-Mean = 4.9885 Proportion Less = 0.6891 Fit-Mean = 4.7196 Proportion Less = 0.6692 Fit-Mean = 3.0133 Proportion Less = 0.6493 Fit-Mean = 2.3761 Proportion Less = 0.6294 Fit-Mean = 2.1959 Proportion Less = 0.6095 Fit-Mean = 1.6783 Proportion Less = 0.5896 Fit-Mean = 1.2399 Proportion Less = 0.5697 Fit-Mean = 1.0865 Proportion Less = 0.5498 Fit-Mean = -0.076 Proportion Less = 0.5299 Fit-Mean = -0.447 Proportion Less = 0.51 Fit-Mean = -0.886 Proportion Less = 0.49 Fit-Mean = -0.973 Proportion Less = 0.4701 Fit-Mean = -1.645 Proportion Less = 0.4502 Fit-Mean = -1.739 Proportion Less = 0.4303 Fit-Mean = -2.859 Proportion Less = 0.4104 Fit-Mean = -3.245 Proportion Less = 0.3905 Fit-Mean = -3.696 Proportion Less = 0.3706 Fit-Mean = -3.766 Proportion Less = 0.3507 Fit-Mean = -3.792 Proportion Less = 0.3308 Fit-Mean = -3.945 Proportion Less = 0.3109 Fit-Mean = -3.995 Proportion Less = 0.291 Fit-Mean = -4.308 Proportion Less = 0.2711 Fit-Mean = -4.601 Proportion Less = 0.2512 Fit-Mean = -5.029 Proportion Less = 0.2313 Fit-Mean = -5.226 Proportion Less = 0.2114 Fit-Mean = -6.886 Proportion Less = 0.1915 Fit-Mean = -7.115 Proportion Less = 0.1716 Fit-Mean = -8.905 Proportion Less = 0.1517 Fit-Mean = -9.415 Proportion Less = 0.1318 Fit-Mean = -10.73 Proportion Less = 0.1119 Fit-Mean = -10.81 Proportion Less = 0.092 Fit-Mean = -10.82 Proportion Less = 0.0721 Fit-Mean = -11.23 Proportion Less = 0.0522 Fit-Mean = -13.79 Proportion Less = 0.0323 Fit-Mean = -13.82 Proportion Less = 0.0124 Fit-Mean = -20.76 Proportion Less = 0.9876 Residual = 6.9324 Proportion Less = 0.9677 Residual = 6.6969 Proportion Less = 0.9478 Residual = 4.846 Proportion Less = 0.9279 Residual = 4.1954 Proportion Less = 0.908 Residual = 3.9664 Proportion Less = 0.8881 Residual = 3.4824 Proportion Less = 0.8682 Residual = 3.0865 Proportion Less = 0.8483 Residual = 2.9935 Proportion Less = 0.8284 Residual = 2.9853 Proportion Less = 0.8085 Residual = 2.6806 Proportion Less = 0.7886 Residual = 2.3885 Proportion Less = 0.7687 Residual = 2.0254 Proportion Less = 0.7488 Residual = 1.9665 Proportion Less = 0.7289 Residual = 1.9392 Proportion Less = 0.709 Residual = 1.9018 Proportion Less = 0.6891 Residual = 1.8884 Proportion Less = 0.6692 Residual = 1.8122 Proportion Less = 0.6493 Residual = 1.3115 Proportion Less = 0.6294 Residual = 1.0842 Proportion Less = 0.6095 Residual = 0.9021 Proportion Less = 0.5896 Residual = 0.8159 Proportion Less = 0.5697 Residual = 0.4631 Proportion Less = 0.5498 Residual = 0.3604 Proportion Less = 0.5299 Residual = 0.3063 Proportion Less = 0.51 Residual = 0.2755 Proportion Less = 0.49 Residual = 0.0667 Proportion Less = 0.4701 Residual = -0.086 Proportion Less = 0.4502 Residual = -0.116 Proportion Less = 0.4303 Residual = -0.161 Proportion Less = 0.4104 Residual = -0.379 Proportion Less = 0.3905 Residual = -0.505 Proportion Less = 0.3706 Residual = -0.675 Proportion Less = 0.3507 Residual = -0.908 Proportion Less = 0.3308 Residual = -1.128 Proportion Less = 0.3109 Residual = -1.16 Proportion Less = 0.291 Residual = -1.224 Proportion Less = 0.2711 Residual = -1.275 Proportion Less = 0.2512 Residual = -1.418 Proportion Less = 0.2313 Residual = -2.473 Proportion Less = 0.2114 Residual = -2.844 Proportion Less = 0.1915 Residual = -3.181 Proportion Less = 0.1716 Residual = -3.505 Proportion Less = 0.1517 Residual = -3.891 Proportion Less = 0.1318 Residual = -3.925 Proportion Less = 0.1119 Residual = -4.068 Proportion Less = 0.092 Residual = -4.128 Proportion Less = 0.0721 Residual = -5.296 Proportion Less = 0.0522 Residual = -5.481 Proportion Less = 0.0323 Residual = -6.598 Proportion Less = 0.0124 Residual = -6.947
Panel of fit diagnostics for Run_Pulse.

Residual Plots

Panel 1

Residual = 3.0865 Age = 79 Observation Number = 50 Residual = -6.598 Age = 31 Observation Number = 49 Residual = 0.2755 Age = 46 Observation Number = 48 Residual = 0.3063 Age = 59 Observation Number = 47 Residual = -3.891 Age = 31 Observation Number = 46 Residual = -0.116 Age = 49 Observation Number = 45 Residual = 1.3115 Age = 52 Observation Number = 44 Residual = -0.161 Age = 49 Observation Number = 43 Residual = 6.9324 Age = 34 Observation Number = 42 Residual = -1.418 Age = 41 Observation Number = 41 Residual = -1.224 Age = 55 Observation Number = 40 Residual = -0.086 Age = 56 Observation Number = 39 Residual = 2.6806 Age = 31 Observation Number = 38 Residual = 6.6969 Age = 64 Observation Number = 37 Residual = 3.4824 Age = 64 Observation Number = 36 Residual = -0.675 Age = 60 Observation Number = 35 Residual = 1.9392 Age = 69 Observation Number = 34 Residual = 1.9665 Age = 48 Observation Number = 33 Residual = 1.8122 Age = 44 Observation Number = 32 Residual = 3.9664 Age = 26 Observation Number = 31 Residual = 1.8884 Age = 23 Observation Number = 30 Residual = -4.068 Age = 53 Observation Number = 29 Residual = 4.846 Age = 57 Observation Number = 28 Residual = -3.505 Age = 68 Observation Number = 27 Residual = -3.925 Age = 43 Observation Number = 26 Residual = 2.3885 Age = 73 Observation Number = 25 Residual = 2.9935 Age = 36 Observation Number = 24 Residual = 0.0667 Age = 73 Observation Number = 23 Residual = -3.181 Age = 84 Observation Number = 22 Residual = -4.128 Age = 26 Observation Number = 21 Residual = -5.481 Age = 81 Observation Number = 20 Residual = 1.9018 Age = 31 Observation Number = 19 Residual = 0.4631 Age = 43 Observation Number = 18 Residual = -1.16 Age = 49 Observation Number = 17 Residual = -0.908 Age = 48 Observation Number = 16 Residual = 2.0254 Age = 54 Observation Number = 15 Residual = -1.275 Age = 51 Observation Number = 14 Residual = -5.296 Age = 19 Observation Number = 13 Residual = 0.8159 Age = 63 Observation Number = 12 Residual = 0.9021 Age = 63 Observation Number = 11 Residual = 1.0842 Age = 49 Observation Number = 10 Residual = 2.9853 Age = 35 Observation Number = 9 Residual = -2.844 Age = 30 Observation Number = 8 Residual = -0.505 Age = 64 Observation Number = 7 Residual = 0.3604 Age = 57 Observation Number = 6 Residual = -2.473 Age = 55 Observation Number = 5 Residual = -1.128 Age = 44 Observation Number = 4 Residual = -6.947 Age = 76 Observation Number = 3 Residual = 4.1954 Age = 64 Observation Number = 2 Residual = -0.379 Age = 68 Observation Number = 1 Y = 0 Residual = 3.0865 Pushups = 10 Observation Number = 50 Residual = -6.598 Pushups = 22 Observation Number = 49 Residual = 0.2755 Pushups = 19 Observation Number = 48 Residual = 0.3063 Pushups = 25 Observation Number = 47 Residual = -3.891 Pushups = 48 Observation Number = 46 Residual = -0.116 Pushups = 22 Observation Number = 45 Residual = 1.3115 Pushups = 27 Observation Number = 44 Residual = -0.161 Pushups = 33 Observation Number = 43 Residual = 6.9324 Pushups = 38 Observation Number = 42 Residual = -1.418 Pushups = 17 Observation Number = 41 Residual = -1.224 Pushups = 21 Observation Number = 40 Residual = -0.086 Pushups = 8 Observation Number = 39 Residual = 2.6806 Pushups = 30 Observation Number = 38 Residual = 6.6969 Pushups = 20 Observation Number = 37 Residual = 3.4824 Pushups = 22 Observation Number = 36 Residual = -0.675 Pushups = 36 Observation Number = 35 Residual = 1.9392 Pushups = 26 Observation Number = 34 Residual = 1.9665 Pushups = 21 Observation Number = 33 Residual = 1.8122 Pushups = 1 Observation Number = 32 Residual = 3.9664 Pushups = 40 Observation Number = 31 Residual = 1.8884 Pushups = 30 Observation Number = 30 Residual = -4.068 Pushups = 9 Observation Number = 29 Residual = 4.846 Pushups = 31 Observation Number = 28 Residual = -3.505 Pushups = 32 Observation Number = 27 Residual = -3.925 Pushups = 33 Observation Number = 26 Residual = 2.3885 Pushups = 8 Observation Number = 25 Residual = 2.9935 Pushups = 25 Observation Number = 24 Residual = 0.0667 Pushups = 12 Observation Number = 23 Residual = -3.181 Pushups = 11 Observation Number = 22 Residual = -4.128 Pushups = 52 Observation Number = 21 Residual = -5.481 Pushups = 16 Observation Number = 20 Residual = 1.9018 Pushups = 50 Observation Number = 19 Residual = 0.4631 Pushups = 29 Observation Number = 18 Residual = -1.16 Pushups = 11 Observation Number = 17 Residual = -0.908 Pushups = 43 Observation Number = 16 Residual = 2.0254 Pushups = 7 Observation Number = 15 Residual = -1.275 Pushups = 23 Observation Number = 14 Residual = -5.296 Pushups = 34 Observation Number = 13 Residual = 0.8159 Pushups = 30 Observation Number = 12 Residual = 0.9021 Pushups = 51 Observation Number = 11 Residual = 1.0842 Pushups = 9 Observation Number = 10 Residual = 2.9853 Pushups = 25 Observation Number = 9 Residual = -2.844 Pushups = 48 Observation Number = 8 Residual = -0.505 Pushups = 21 Observation Number = 7 Residual = 0.3604 Pushups = 14 Observation Number = 6 Residual = -2.473 Pushups = 24 Observation Number = 5 Residual = -1.128 Pushups = 35 Observation Number = 4 Residual = -6.947 Pushups = 11 Observation Number = 3 Residual = 4.1954 Pushups = 36 Observation Number = 2 Residual = -0.379 Pushups = 19 Observation Number = 1 Y = 0 Residual = 3.0865 Max_Pulse = 124 Observation Number = 50 Residual = -6.598 Max_Pulse = 118 Observation Number = 49 Residual = 0.2755 Max_Pulse = 130 Observation Number = 48 Residual = 0.3063 Max_Pulse = 110 Observation Number = 47 Residual = -3.891 Max_Pulse = 109 Observation Number = 46 Residual = -0.116 Max_Pulse = 118 Observation Number = 45 Residual = 1.3115 Max_Pulse = 104 Observation Number = 44 Residual = -0.161 Max_Pulse = 94 Observation Number = 43 Residual = 6.9324 Max_Pulse = 120 Observation Number = 42 Residual = -1.418 Max_Pulse = 127 Observation Number = 41 Residual = -1.224 Max_Pulse = 112 Observation Number = 40 Residual = -0.086 Max_Pulse = 122 Observation Number = 39 Residual = 2.6806 Max_Pulse = 111 Observation Number = 38 Residual = 6.6969 Max_Pulse = 137 Observation Number = 37 Residual = 3.4824 Max_Pulse = 126 Observation Number = 36 Residual = -0.675 Max_Pulse = 111 Observation Number = 35 Residual = 1.9392 Max_Pulse = 112 Observation Number = 34 Residual = 1.9665 Max_Pulse = 109 Observation Number = 33 Residual = 1.8122 Max_Pulse = 107 Observation Number = 32 Residual = 3.9664 Max_Pulse = 114 Observation Number = 31 Residual = 1.8884 Max_Pulse = 105 Observation Number = 30 Residual = -4.068 Max_Pulse = 127 Observation Number = 29 Residual = 4.846 Max_Pulse = 111 Observation Number = 28 Residual = -3.505 Max_Pulse = 125 Observation Number = 27 Residual = -3.925 Max_Pulse = 111 Observation Number = 26 Residual = 2.3885 Max_Pulse = 112 Observation Number = 25 Residual = 2.9935 Max_Pulse = 117 Observation Number = 24 Residual = 0.0667 Max_Pulse = 119 Observation Number = 23 Residual = -3.181 Max_Pulse = 114 Observation Number = 22 Residual = -4.128 Max_Pulse = 100 Observation Number = 21 Residual = -5.481 Max_Pulse = 127 Observation Number = 20 Residual = 1.9018 Max_Pulse = 100 Observation Number = 19 Residual = 0.4631 Max_Pulse = 122 Observation Number = 18 Residual = -1.16 Max_Pulse = 118 Observation Number = 17 Residual = -0.908 Max_Pulse = 119 Observation Number = 16 Residual = 2.0254 Max_Pulse = 113 Observation Number = 15 Residual = -1.275 Max_Pulse = 114 Observation Number = 14 Residual = -5.296 Max_Pulse = 118 Observation Number = 13 Residual = 0.8159 Max_Pulse = 126 Observation Number = 12 Residual = 0.9021 Max_Pulse = 102 Observation Number = 11 Residual = 1.0842 Max_Pulse = 137 Observation Number = 10 Residual = 2.9853 Max_Pulse = 107 Observation Number = 9 Residual = -2.844 Max_Pulse = 114 Observation Number = 8 Residual = -0.505 Max_Pulse = 106 Observation Number = 7 Residual = 0.3604 Max_Pulse = 121 Observation Number = 6 Residual = -2.473 Max_Pulse = 115 Observation Number = 5 Residual = -1.128 Max_Pulse = 111 Observation Number = 4 Residual = -6.947 Max_Pulse = 115 Observation Number = 3 Residual = 4.1954 Max_Pulse = 107 Observation Number = 2 Residual = -0.379 Max_Pulse = 124 Observation Number = 1 Y = 0
Panel of scatterplots of residuals by regressors for Run_Pulse.
  • This initial Linear Regression model’s R-square .8869 and adjusted R-square .8768 appear highly significant, but once when we look at the parameter estimates we see that only Max_Pulse looks significant. Also, a negative parameter estimate for Rest_Pulse also looks off.
  • “VIF is a popular diagnostic test for multi-collinearity, and large values of VIF indicate multi-collinearity problems.”
  • Rest_Pulse has the highest value for Variance Inflation (VIF) at 4.30537, so we drop this parameter and rerun the regression.
  • The revised Linear Regression model’s parameter estimates Variance Inflation (VIF) values are lower after Rest_Pulse is removed.

Stepwise Multiple Regression.

SAS Code, click to expand

SAS Code:

#  (&path1 and biostats libname previously defined)
/* Stepwise Multiple Regression - generated code - start */

/* Create 25 pct sample without replacement using random seed 13579 */
title1 "Multiple Regression - Create 25% Sample of Birth Weights Data"; 
proc surveyselect data=biostats.bweight out=work.Birth_Wt_Sample method=srs 
        samprate=0.25 seed=13579;
run;

title1 "Multiple Regression - Stepwise Selection using R-Square"; 
proc glmselect data=work.Birth_Wt_Sample 
        outdesign(addinputvars)=work.reg_design plots=(criterionpanel);
    class Black MomSmoke / param=glm;
    model Weight=MomAge MomWtGain Black MomSmoke / showpvalues 
        selection=stepwise (select=rsquare);
run;
proc reg data=work.reg_design alpha=0.05 
  plots(only maxpoints=none)=(diagnostics residuals observedbypredicted);
    where Black is not missing and MomSmoke is not missing;
    ods select ParameterEstimates DiagnosticsPanel ResidualPlot 
        ObservedByPredicted;
    model Weight=&_GLSMOD / vif;
    run;
quit;
proc delete data=work.reg_design;
run;

/* "Using the 25% random sample of birth weights from the SASHELP data set Bweight, we demonstrate stepwise multiple regression using the stepwise selection method specifying add/remove effect with R-square."

"The dependent variable is Weight; use the two variables Black (1=black, 0=non-black) and MomSmoke (1=yes, 0=no) as classification variables and the two variables MomAge (mother's age) and MomWtGain (mom's weight gain) as continuous variables."

"The stepwise selection summary shows which variables were entered into the models as well as the order of entry.  All four variables were entered into the model.  The last column, labeled Model R-Square, shows the model R-square as each variable is entered into the model."  

"AIC (Akaike's information criteria) and a modified version AICC are displayed in the top two graphs.  The stars on the plots indicate that the four-variable model is the "best" model as defined by each criterion.  SBC (Schwarz Bayesian Information Criterion) is displayed on the bottom left, and the adjusted R-square is displayed on the bottom right.  Although all four criteria selected the same model, this is not always the case." 

"The overall p-value for this model is low; but with 12,500 observations in this 25% random sample, even small effects can be significant.  Looking at the parameter estimates along with the t and p-values, we see only two levels of the classification variables.  The estimate for Black 0 (non-black) is about 218, which means that after all the other variables are adjusted for, babies of a non-black mother are 218 grams heavier than babies where the mother is black.  Because smoking is a risk factor for low birth weight babies, you see that if a mother does not smoke (MomSmoke = 0), the babies are almost 253 grams heavier than if the mother smokes." 
*/

title1; 
/* Stepwise Multiple Regression - generated code - end */

SAS Output

Results: biostats_by_ex_SAScode.sas

Results: biostats_by_ex_SAScode.sas

Multiple Regression - Create 25% Sample of Birth Weights Data

The Surveyselect Procedure

Sample Selection Method

Selection Method Simple Random Sampling

Sample Selection Summary

Input Data Set BWEIGHT
Random Number Seed 13579
Sampling Rate 0.25
Sample Size 12500
Selection Probability 0.25
Sampling Weight 4
Output Data Set BIRTH_WT_SAMPLE

Multiple Regression - Stepwise Selection using R-Square

The GLMSelect Procedure

Model Information

Data Set WORK.BIRTH_WT_SAMPLE
Dependent Variable Weight
Selection Method Stepwise
Select Criterion R-Square
Stop Criterion R-Square
Effect Hierarchy Enforced None

Number of Observations

Number of Observations Read 12500
Number of Observations Used 12500

Class Level Information

Class Level Information
Class Levels Values
Black 2 0 1
MomSmoke 2 0 1

Dimensions

Dimensions
Number of Effects 5
Number of Parameters 7

Multiple Regression - Stepwise Selection using R-Square

Model Building Summary

Stepwise Selection Summary

Stepwise Selection Summary
Step Effect
Entered		 Effect
Removed		 Number
Effects In		 Number
Parms In		 Model
R-Square
0 Intercept   1 1 0.0000
1 MomWtGain   2 2 0.0423
2 MomSmoke   3 3 0.0657
3 Black   4 4 0.0882
4 MomAge   5 5 0.0946

Stop Reason

Selection stopped because all effects are in the final model.

Criterion Panel

Optimal Step = 4+MomAge Optimal Value = 169544 Step = 4 Effect Sequence = 4+MomAge AIC = 169544.016 Step = 3 Effect Sequence = 3+Black AIC = 169630.057 Step = 2 Effect Sequence = 2+MomSmoke AIC = 169932.373 Step = 1 Effect Sequence = 1+MomWtGain AIC = 170239.952 Step = 0 Effect Sequence = Intercept AIC = 170778.168 Step = 4 Effect Sequence = 4+MomAge AIC = 169544.016 Step = 3 Effect Sequence = 3+Black AIC = 169630.057 Step = 3 Effect Sequence = 3+Black AIC = 169630.057 Step = 2 Effect Sequence = 2+MomSmoke AIC = 169932.373 Step = 2 Effect Sequence = 2+MomSmoke AIC = 169932.373 Step = 1 Effect Sequence = 1+MomWtGain AIC = 170239.952 Step = 1 Effect Sequence = 1+MomWtGain AIC = 170239.952 Step = 0 Effect Sequence = Intercept AIC = 170778.168 X = 4+MomAge Optimal Step = 4+MomAge Optimal Value = 169544 Step = 4 Effect Sequence = 4+MomAge AICC = 169544.023 Step = 3 Effect Sequence = 3+Black AICC = 169630.062 Step = 2 Effect Sequence = 2+MomSmoke AICC = 169932.376 Step = 1 Effect Sequence = 1+MomWtGain AICC = 170239.954 Step = 0 Effect Sequence = Intercept AICC = 170778.169 Step = 4 Effect Sequence = 4+MomAge AICC = 169544.023 Step = 3 Effect Sequence = 3+Black AICC = 169630.062 Step = 3 Effect Sequence = 3+Black AICC = 169630.062 Step = 2 Effect Sequence = 2+MomSmoke AICC = 169932.376 Step = 2 Effect Sequence = 2+MomSmoke AICC = 169932.376 Step = 1 Effect Sequence = 1+MomWtGain AICC = 170239.954 Step = 1 Effect Sequence = 1+MomWtGain AICC = 170239.954 Step = 0 Effect Sequence = Intercept AICC = 170778.169 X = 4+MomAge Optimal Step = 4+MomAge Optimal Value = 157079 Step = 4 Effect Sequence = 4+MomAge SBC = 157079.183 Step = 3 Effect Sequence = 3+Black SBC = 157157.791 Step = 2 Effect Sequence = 2+MomSmoke SBC = 157452.674 Step = 1 Effect Sequence = 1+MomWtGain SBC = 157752.819 Step = 0 Effect Sequence = Intercept SBC = 158283.601 Step = 4 Effect Sequence = 4+MomAge SBC = 157079.183 Step = 3 Effect Sequence = 3+Black SBC = 157157.791 Step = 3 Effect Sequence = 3+Black SBC = 157157.791 Step = 2 Effect Sequence = 2+MomSmoke SBC = 157452.674 Step = 2 Effect Sequence = 2+MomSmoke SBC = 157452.674 Step = 1 Effect Sequence = 1+MomWtGain SBC = 157752.819 Step = 1 Effect Sequence = 1+MomWtGain SBC = 157752.819 Step = 0 Effect Sequence = Intercept SBC = 158283.601 X = 4+MomAge Optimal Step = 4+MomAge Optimal Value = 0.0943 Step = 4 Effect Sequence = 4+MomAge Adj R-Sq = 0.0943 Step = 3 Effect Sequence = 3+Black Adj R-Sq = 0.088 Step = 2 Effect Sequence = 2+MomSmoke Adj R-Sq = 0.0656 Step = 1 Effect Sequence = 1+MomWtGain Adj R-Sq = 0.0422 Step = 0 Effect Sequence = Intercept Adj R-Sq = 0 Step = 4 Effect Sequence = 4+MomAge Adj R-Sq = 0.0943 Step = 3 Effect Sequence = 3+Black Adj R-Sq = 0.088 Step = 3 Effect Sequence = 3+Black Adj R-Sq = 0.088 Step = 2 Effect Sequence = 2+MomSmoke Adj R-Sq = 0.0656 Step = 2 Effect Sequence = 2+MomSmoke Adj R-Sq = 0.0656 Step = 1 Effect Sequence = 1+MomWtGain Adj R-Sq = 0.0422 Step = 1 Effect Sequence = 1+MomWtGain Adj R-Sq = 0.0422 Step = 0 Effect Sequence = Intercept Adj R-Sq = 0 X = 4+MomAge
Panel showing how selection criteria change with the effect sequence.

Selected Model

Multiple Regression - Stepwise Selection using R-Square

Selected Model

The selected model is the model at the last step (Step 4).

Selected Effects

Effects: Intercept MomAge MomWtGain Black MomSmoke

Note:The p-values for parameters and effects are not adjusted for the fact that the terms in the model have been selected and so are generally liberal.

ANOVA

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 4 373063503 93265876 326.36 <.0001
Error 12495 3570763188 285775    
Corrected Total 12499 3943826691      

Fit Statistics

Root MSE 534.57962
Dependent Mean 3373.25448
R-Square 0.0946
Adj R-Sq 0.0943
AIC 169544
AICC 169544
SBC 157079

Parameter Estimates

Parameter Estimates
Parameter DF Estimate Standard
Error		 t Value Pr > |t|
Intercept 1 2961.598722 17.629377 167.99 <.0001
MomAge 1 7.963514 0.847390 9.40 <.0001
MomWtGain 1 8.677708 0.374621 23.16 <.0001
Black 0 1 218.282338 13.219116 16.51 <.0001
Black 1 0 0 . . .
MomSmoke 0 1 252.807537 14.202584 17.80 <.0001
MomSmoke 1 0 0 . . .

Multiple Regression - Stepwise Selection using R-Square

Model: MODEL1

Dependent Variable: Weight Infant Birth Weight

The Reg Procedure

MODEL1

Fit

Weight

Parameter Estimates

Parameter Estimates
Variable Label DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t| Variance
Inflation
Intercept Intercept B 2961.59872 17.62938 167.99 <.0001 0
MomAge MomAge 1 7.96351 0.84739 9.40 <.0001 1.02152
MomWtGain MomWtGain 1 8.67771 0.37462 23.16 <.0001 1.00806
Black 0 Black 0 B 218.28234 13.21912 16.51 <.0001 1.01602
Black 1 Black 1 0 0 . . . .
MomSmoke 0 MomSmoke 0 B 252.80754 14.20258 17.80 <.0001 1.01039
MomSmoke 1 MomSmoke 1 0 0 . . . .

Multiple Regression - Stepwise Selection using R-Square

Model: MODEL1

Dependent Variable: Weight Infant Birth Weight

Observation-wise Statistics

Weight

Diagnostic Plots

Observed by Predicted

Slope = 1 Y = 0
Scatter plot of observed by predicted values for Weight.

Fit Diagnostics

Y = 0 Y = 2 Y = -2 X = 0.0008 Y = -2 Y = 2 Slope = 534.49 Y = 16E-14 Slope = 1 Y = 0 Y = .00032 Residual = 2400 Percent = .00047 Residual = 2372 Percent = .00059 Residual = 2372 Percent = .00059 Residual = 2343.9 Percent = .00075 Residual = 2343.9 Percent = .00075 Residual = 2315.9 Percent = .00094 Residual = 2315.9 Percent = .00094 Residual = 2287.9 Percent = 0.0012 Residual = 2287.9 Percent = 0.0012 Residual = 2259.8 Percent = 0.0015 Residual = 2259.8 Percent = 0.0015 Residual = 2231.8 Percent = 0.0018 Residual = 2231.8 Percent = 0.0018 Residual = 2203.8 Percent = 0.0023 Residual = 2203.8 Percent = 0.0023 Residual = 2175.8 Percent = 0.0028 Residual = 2175.8 Percent = 0.0028 Residual = 2147.7 Percent = 0.0035 Residual = 2147.7 Percent = 0.0035 Residual = 2119.7 Percent = 0.0043 Residual = 2119.7 Percent = 0.0043 Residual = 2091.7 Percent = 0.0053 Residual = 2091.7 Percent = 0.0053 Residual = 2063.6 Percent = 0.0065 Residual = 2063.6 Percent = 0.0065 Residual = 2035.6 Percent = 0.0079 Residual = 2035.6 Percent = 0.0079 Residual = 2007.6 Percent = 0.0097 Residual = 2007.6 Percent = 0.0097 Residual = 1979.5 Percent = 0.0118 Residual = 1979.5 Percent = 0.0118 Residual = 1951.5 Percent = 0.0143 Residual = 1951.5 Percent = 0.0143 Residual = 1923.5 Percent = 0.0173 Residual = 1923.5 Percent = 0.0173 Residual = 1895.5 Percent = 0.0208 Residual = 1895.5 Percent = 0.0208 Residual = 1867.4 Percent = 0.025 Residual = 1867.4 Percent = 0.025 Residual = 1839.4 Percent = 0.03 Residual = 1839.4 Percent = 0.03 Residual = 1811.4 Percent = 0.0359 Residual = 1811.4 Percent = 0.0359 Residual = 1783.3 Percent = 0.0428 Residual = 1783.3 Percent = 0.0428 Residual = 1755.3 Percent = 0.0509 Residual = 1755.3 Percent = 0.0509 Residual = 1727.3 Percent = 0.0604 Residual = 1727.3 Percent = 0.0604 Residual = 1699.2 Percent = 0.0715 Residual = 1699.2 Percent = 0.0715 Residual = 1671.2 Percent = 0.0844 Residual = 1671.2 Percent = 0.0844 Residual = 1643.2 Percent = 0.0993 Residual = 1643.2 Percent = 0.0993 Residual = 1615.2 Percent = 0.1165 Residual = 1615.2 Percent = 0.1165 Residual = 1587.1 Percent = 0.1363 Residual = 1587.1 Percent = 0.1363 Residual = 1559.1 Percent = 0.159 Residual = 1559.1 Percent = 0.159 Residual = 1531.1 Percent = 0.185 Residual = 1531.1 Percent = 0.185 Residual = 1503 Percent = 0.2147 Residual = 1503 Percent = 0.2147 Residual = 1475 Percent = 0.2485 Residual = 1475 Percent = 0.2485 Residual = 1447 Percent = 0.2868 Residual = 1447 Percent = 0.2868 Residual = 1418.9 Percent = 0.3301 Residual = 1418.9 Percent = 0.3301 Residual = 1390.9 Percent = 0.3789 Residual = 1390.9 Percent = 0.3789 Residual = 1362.9 Percent = 0.4337 Residual = 1362.9 Percent = 0.4337 Residual = 1334.8 Percent = 0.4951 Residual = 1334.8 Percent = 0.4951 Residual = 1306.8 Percent = 0.5636 Residual = 1306.8 Percent = 0.5636 Residual = 1278.8 Percent = 0.6398 Residual = 1278.8 Percent = 0.6398 Residual = 1250.8 Percent = 0.7244 Residual = 1250.8 Percent = 0.7244 Residual = 1222.7 Percent = 0.8178 Residual = 1222.7 Percent = 0.8178 Residual = 1194.7 Percent = 0.9208 Residual = 1194.7 Percent = 0.9208 Residual = 1166.7 Percent = 1.0339 Residual = 1166.7 Percent = 1.0339 Residual = 1138.6 Percent = 1.1577 Residual = 1138.6 Percent = 1.1577 Residual = 1110.6 Percent = 1.2928 Residual = 1110.6 Percent = 1.2928 Residual = 1082.6 Percent = 1.4396 Residual = 1082.6 Percent = 1.4396 Residual = 1054.5 Percent = 1.5988 Residual = 1054.5 Percent = 1.5988 Residual = 1026.5 Percent = 1.7706 Residual = 1026.5 Percent = 1.7706 Residual = 998.48 Percent = 1.9555 Residual = 998.48 Percent = 1.9555 Residual = 970.45 Percent = 2.1538 Residual = 970.45 Percent = 2.1538 Residual = 942.42 Percent = 2.3657 Residual = 942.42 Percent = 2.3657 Residual = 914.39 Percent = 2.5914 Residual = 914.39 Percent = 2.5914 Residual = 886.36 Percent = 2.8307 Residual = 886.36 Percent = 2.8307 Residual = 858.33 Percent = 3.0837 Residual = 858.33 Percent = 3.0837 Residual = 830.3 Percent = 3.35 Residual = 830.3 Percent = 3.35 Residual = 802.27 Percent = 3.6294 Residual = 802.27 Percent = 3.6294 Residual = 774.24 Percent = 3.9212 Residual = 774.24 Percent = 3.9212 Residual = 746.21 Percent = 4.2249 Residual = 746.21 Percent = 4.2249 Residual = 718.18 Percent = 4.5395 Residual = 718.18 Percent = 4.5395 Residual = 690.15 Percent = 4.8643 Residual = 690.15 Percent = 4.8643 Residual = 634.09 Percent = 5.5392 Residual = 634.09 Percent = 5.5392 Residual = 521.97 Percent = 6.9497 Residual = 521.97 Percent = 6.9497 Residual = 437.88 Percent = 8.0042 Residual = 437.88 Percent = 8.0042 Residual = 381.82 Percent = 8.6746 Residual = 381.82 Percent = 8.6746 Residual = 353.79 Percent = 8.9933 Residual = 353.79 Percent = 8.9933 Residual = 325.76 Percent = 9.2982 Residual = 325.76 Percent = 9.2982 Residual = 297.73 Percent = 9.587 Residual = 297.73 Percent = 9.587 Residual = 269.7 Percent = 9.8576 Residual = 269.7 Percent = 9.8576 Residual = 241.67 Percent = 10.108 Residual = 241.67 Percent = 10.108 Residual = 213.64 Percent = 10.336 Residual = 213.64 Percent = 10.336 Residual = 185.61 Percent = 10.541 Residual = 185.61 Percent = 10.541 Residual = 157.58 Percent = 10.72 Residual = 157.58 Percent = 10.72 Residual = 129.55 Percent = 10.872 Residual = 129.55 Percent = 10.872 Residual = 101.52 Percent = 10.996 Residual = 101.52 Percent = 10.996 Residual = 73.485 Percent = 11.091 Residual = 73.485 Percent = 11.091 Residual = 45.455 Percent = 11.155 Residual = 45.455 Percent = 11.155 Residual = 17.424 Percent = 11.19 Residual = 17.424 Percent = 11.19 Residual = 16E-14 Percent = 11.196 Residual = 16E-14 Percent = 11.196 Residual = -10.61 Percent = 11.194 Residual = -10.61 Percent = 11.194 Residual = -38.64 Percent = 11.167 Residual = -38.64 Percent = 11.167 Residual = -66.67 Percent = 11.109 Residual = -66.67 Percent = 11.109 Residual = -94.7 Percent = 11.022 Residual = -94.7 Percent = 11.022 Residual = -122.7 Percent = 10.905 Residual = -122.7 Percent = 10.905 Residual = -150.8 Percent = 10.759 Residual = -150.8 Percent = 10.759 Residual = -178.8 Percent = 10.587 Residual = -178.8 Percent = 10.587 Residual = -206.8 Percent = 10.388 Residual = -206.8 Percent = 10.388 Residual = -234.8 Percent = 10.166 Residual = -234.8 Percent = 10.166 Residual = -262.9 Percent = 9.9205 Residual = -262.9 Percent = 9.9205 Residual = -290.9 Percent = 9.6546 Residual = -290.9 Percent = 9.6546 Residual = -318.9 Percent = 9.37 Residual = -318.9 Percent = 9.37 Residual = -347 Percent = 9.0688 Residual = -347 Percent = 9.0688 Residual = -375 Percent = 8.7533 Residual = -375 Percent = 8.7533 Residual = -599.2 Percent = 5.9719 Residual = -599.2 Percent = 5.9719 Residual = -655.3 Percent = 5.2803 Residual = -655.3 Percent = 5.2803 Residual = -711.4 Percent = 4.6176 Residual = -711.4 Percent = 4.6176 Residual = -739.4 Percent = 4.3004 Residual = -739.4 Percent = 4.3004 Residual = -767.4 Percent = 3.994 Residual = -767.4 Percent = 3.994 Residual = -795.5 Percent = 3.6992 Residual = -795.5 Percent = 3.6992 Residual = -823.5 Percent = 3.4168 Residual = -823.5 Percent = 3.4168 Residual = -851.5 Percent = 3.1472 Residual = -851.5 Percent = 3.1472 Residual = -879.5 Percent = 2.891 Residual = -879.5 Percent = 2.891 Residual = -907.6 Percent = 2.6483 Residual = -907.6 Percent = 2.6483 Residual = -935.6 Percent = 2.4194 Residual = -935.6 Percent = 2.4194 Residual = -963.6 Percent = 2.2041 Residual = -963.6 Percent = 2.2041 Residual = -991.7 Percent = 2.0025 Residual = -991.7 Percent = 2.0025 Residual = -1020 Percent = 1.8144 Residual = -1020 Percent = 1.8144 Residual = -1048 Percent = 1.6394 Residual = -1048 Percent = 1.6394 Residual = -1076 Percent = 1.4772 Residual = -1076 Percent = 1.4772 Residual = -1104 Percent = 1.3274 Residual = -1104 Percent = 1.3274 Residual = -1132 Percent = 1.1895 Residual = -1132 Percent = 1.1895 Residual = -1160 Percent = 1.063 Residual = -1160 Percent = 1.063 Residual = -1188 Percent = 0.9474 Residual = -1188 Percent = 0.9474 Residual = -1216 Percent = 0.842 Residual = -1216 Percent = 0.842 Residual = -1244 Percent = 0.7463 Residual = -1244 Percent = 0.7463 Residual = -1272 Percent = 0.6596 Residual = -1272 Percent = 0.6596 Residual = -1300 Percent = 0.5814 Residual = -1300 Percent = 0.5814 Residual = -1328 Percent = 0.5111 Residual = -1328 Percent = 0.5111 Residual = -1356 Percent = 0.448 Residual = -1356 Percent = 0.448 Residual = -1384 Percent = 0.3917 Residual = -1384 Percent = 0.3917 Residual = -1412 Percent = 0.3415 Residual = -1412 Percent = 0.3415 Residual = -1440 Percent = 0.2969 Residual = -1440 Percent = 0.2969 Residual = -1468 Percent = 0.2574 Residual = -1468 Percent = 0.2574 Residual = -1496 Percent = 0.2226 Residual = -1496 Percent = 0.2226 Residual = -1524 Percent = 0.1919 Residual = -1524 Percent = 0.1919 Residual = -1552 Percent = 0.165 Residual = -1552 Percent = 0.165 Residual = -1580 Percent = 0.1415 Residual = -1580 Percent = 0.1415 Residual = -1608 Percent = 0.121 Residual = -1608 Percent = 0.121 Residual = -1636 Percent = 0.1032 Residual = -1636 Percent = 0.1032 Residual = -1664 Percent = 0.0878 Residual = -1664 Percent = 0.0878 Residual = -1692 Percent = 0.0745 Residual = -1692 Percent = 0.0745 Residual = -1720 Percent = 0.063 Residual = -1720 Percent = 0.063 Residual = -1748 Percent = 0.0531 Residual = -1748 Percent = 0.0531 Residual = -1777 Percent = 0.0447 Residual = -1777 Percent = 0.0447 Residual = -1805 Percent = 0.0375 Residual = -1805 Percent = 0.0375 Residual = -1833 Percent = 0.0314 Residual = -1833 Percent = 0.0314 Residual = -1861 Percent = 0.0262 Residual = -1861 Percent = 0.0262 Residual = -1889 Percent = 0.0218 Residual = -1889 Percent = 0.0218 Residual = -1917 Percent = 0.0181 Residual = -1917 Percent = 0.0181 Residual = -1945 Percent = 0.0149 Residual = -1945 Percent = 0.0149 Residual = -1973 Percent = 0.0123 Residual = -1973 Percent = 0.0123 Residual = -2001 Percent = 0.0101 Residual = -2001 Percent = 0.0101 Residual = -2029 Percent = 0.0083 Residual = -2029 Percent = 0.0083 Residual = -2057 Percent = 0.0068 Residual = -2057 Percent = 0.0068 Residual = -2085 Percent = 0.0056 Residual = -2085 Percent = 0.0056 Residual = -2113 Percent = 0.0045 Residual = -2113 Percent = 0.0045 Residual = -2141 Percent = 0.0037 Residual = -2141 Percent = 0.0037 Residual = -2169 Percent = 0.003 Residual = -2169 Percent = 0.003 Residual = -2197 Percent = 0.0024 Residual = -2197 Percent = 0.0024 Residual = -2225 Percent = 0.0019 Residual = -2225 Percent = 0.0019 Residual = -2253 Percent = 0.0016 Residual = -2253 Percent = 0.0016 Residual = -2281 Percent = 0.0012 Residual = -2281 Percent = 0.0012 Residual = -2309 Percent = .00099 Residual = -2309 Percent = .00099 Residual = -2337 Percent = .00079 Residual = -2337 Percent = .00079 Residual = -2365 Percent = .00063 Residual = -2365 Percent = .00063 Residual = -2393 Percent = 0.0005 Residual = -2393 Percent = 0.0005 Residual = -2421 Percent = .00039 Residual = -2421 Percent = .00039 Residual = -2449 Percent = .00031 Residual = -2449 Percent = .00031 Residual = -2477 Percent = .00024 Residual = -2477 Percent = .00024 Residual = -2505 Percent = .00019 Residual = -2505 Percent = .00019 Residual = -2533 Percent = .00015 Residual = -2533 Percent = .00015 Residual = -2561 Percent = .00012 Residual = -2561 Percent = .00012 Residual = -2589 Percent = .00009 Residual = -2589 Percent = .00009 Residual = -2617 Percent = 6.9E-5 Residual = -2617 Percent = 6.9E-5 Residual = -2645 Percent = 5.4E-5 Residual = -2645 Percent = 5.4E-5 Residual = -2673 Percent = 4.1E-5 Residual = -2673 Percent = 4.1E-5 Residual = -2702 Percent = 3.2E-5 Residual = -2702 Percent = 3.2E-5 Residual = -2730 Percent = 2.4E-5 Residual = -2730 Percent = 2.4E-5 Residual = -2758 Percent = 1.9E-5 Residual = -2758 Percent = 1.9E-5 Residual = -2786 Percent = 1.4E-5 Residual = -2786 Percent = 1.4E-5 Residual = -2814 Percent = 1.1E-5 Residual = -2814 Percent = 1.1E-5 Residual = -2842 Percent = 8.2E-6 Residual = -2842 Percent = 8.2E-6 Residual = -2870 Percent = 6.2E-6 Residual = -2870 Percent = 6.2E-6 Residual = -2898 Percent = 4.6E-6 Residual = -2898 Percent = 4.6E-6 Residual = -2926 Percent = 3.5E-6 Residual = -2926 Percent = 3.5E-6 Residual = -2954 Percent = 2.6E-6 Residual = -2954 Percent = 2.6E-6 Residual = -2982 Percent = 2E-6 Residual = -2982 Percent = 2E-6 Residual = -3010 Percent = 1.5E-6 Residual = -3010 Percent = 1.5E-6 Residual = -3038 Percent = 1.1E-6 Residual = -3038 Percent = 1.1E-6 Residual = -3066 Percent = 8E-7 Residual = -3066 Percent = 8E-7 Residual = -3094 Percent = 5.9E-7 Residual = -3094 Percent = 5.9E-7 Residual = -3122 Percent = 4.4E-7 Residual = -3122 Percent = 4.4E-7 Residual = -3150 Percent = 3.2E-7 Residual = 2325 Percent = 0.008 Residual = 2325 Percent = 0.008 Residual = 2175 Percent = 0 Residual = 2175 Percent = 0 Residual = 2025 Percent = 0 Residual = 2025 Percent = 0 Residual = 1875 Percent = 0.04 Residual = 1875 Percent = 0.04 Residual = 1725 Percent = 0.032 Residual = 1725 Percent = 0.032 Residual = 1575 Percent = 0.128 Residual = 1575 Percent = 0.128 Residual = 1425 Percent = 0.232 Residual = 1425 Percent = 0.232 Residual = 1275 Percent = 0.456 Residual = 1275 Percent = 0.456 Residual = 1125 Percent = 1.032 Residual = 1125 Percent = 1.032 Residual = 975 Percent = 1.408 Residual = 975 Percent = 1.408 Residual = 825 Percent = 2.976 Residual = 825 Percent = 2.976 Residual = 675 Percent = 4.232 Residual = 675 Percent = 4.232 Residual = 525 Percent = 7.144 Residual = 525 Percent = 7.144 Residual = 375 Percent = 9.768 Residual = 375 Percent = 9.768 Residual = 225 Percent = 11.08 Residual = 225 Percent = 11.08 Residual = 75 Percent = 13.328 Residual = 75 Percent = 13.328 Residual = -75 Percent = 12.552 Residual = -75 Percent = 12.552 Residual = -225 Percent = 11.312 Residual = -225 Percent = 11.312 Residual = -375 Percent = 8.208 Residual = -375 Percent = 8.208 Residual = -525 Percent = 5.8 Residual = -525 Percent = 5.8 Residual = -675 Percent = 3.64 Residual = -675 Percent = 3.64 Residual = -825 Percent = 2.312 Residual = -825 Percent = 2.312 Residual = -975 Percent = 1.312 Residual = -975 Percent = 1.312 Residual = -1125 Percent = 0.784 Residual = -1125 Percent = 0.784 Residual = -1275 Percent = 0.464 Residual = -1275 Percent = 0.464 Residual = -1425 Percent = 0.392 Residual = -1425 Percent = 0.392 Residual = -1575 Percent = 0.208 Residual = -1575 Percent = 0.208 Residual = -1725 Percent = 0.24 Residual = -1725 Percent = 0.24 Residual = -1875 Percent = 0.224 Residual = -1875 Percent = 0.224 Residual = -2025 Percent = 0.136 Residual = -2025 Percent = 0.136 Residual = -2175 Percent = 0.192 Residual = -2175 Percent = 0.192 Residual = -2325 Percent = 0.096 Residual = -2325 Percent = 0.096 Residual = -2475 Percent = 0.096 Residual = -2475 Percent = 0.096 Residual = -2625 Percent = 0.08 Residual = -2625 Percent = 0.08 Residual = -2775 Percent = 0.032 Residual = -2775 Percent = 0.032 Residual = -2925 Percent = 0.04 Residual = -2925 Percent = 0.04 Residual = -3075 Percent = 0.016 Residual = -3075 Percent = 0.016
Panel of fit diagnostics for Weight.

Residual Plots

Panel 1

Y = 0 Y = 0 Y = 0 Y = 0 Y = 0 Y = 0
Panel of scatterplots of residuals by regressors for Weight.

  • “Using the 25% random sample of birth weights from the SASHELP data set Bweight, we demonstrate stepwise multiple regression using the stepwise selection method specifying add/remove effect with R-square.”

  • “The dependent variable is Weight; use the two variables Black (1=black, 0=non-black) and MomSmoke (1=yes, 0=no) as classification variables and the two variables MomAge (mother’s age) and MomWtGain (mom’s weight gain) as continuous variables.”

  • “The stepwise selection summary shows which variables were entered into the models as well as the order of entry. All four variables were entered into the model. The last column, labeled Model R-Square, shows the model R-square as each variable is entered into the model.”

  • “AIC (Akaike’s information criteria) and a modified version AICC are displayed in the top two graphs. The stars on the plots indicate that the four-variable model is the”best” model as defined by each criterion. SBC (Schwarz Bayesian Information Criterion) is displayed on the bottom left, and the adjusted R-square is displayed on the bottom right. Although all four criteria selected the same model, this is not always the case.”

  • “The overall p-value for this model is low; but with 12,500 observations in this 25% random sample, even small effects can be significant. Looking at the parameter estimates along with the t and p-values, we see only two levels of the classification variables. The estimate for Black 0 (non-black) is about 218, which means that after all the other variables are adjusted for, babies of a non-black mother are 218 grams heavier than babies where the mother is black. Because smoking is a risk factor for low birth weight babies, you see that if a mother does not smoke (MomSmoke = 0), the babies are almost 253 grams heavier than if the mother smokes.”

Chapter 12: Binary Logistic Regression

Logistic Regression.

SAS Code, click to expand

SAS Code:

#  (&path1 and biostats libname previously defined)
/* Logistic Regression - generated code - start */
ods noproctitle;
ods graphics / imagemap=on;
title1 "Binary Logistic Regression - Reference Coding"; 
proc logistic data=WORK.HIGH_LOW;
    class Black MomSmoke / param=ref;
    model Wt_Group(event='1')=MomAge MomWtGain Black MomSmoke / link=logit 
        technique=fisher;
run;

/* specify reference levels by using values in quotes:
  class Black(ref='0') MomSmoke(ref='0') / param=ref;
  which impacts the Odds Ratio Estimates: Black 1 vs 0 = 2.038, MomSmoke 1 vs 0 = 2.295
*/

/*
"The model fit statistics section is useful when comparing models.  Smaller values of AIC (Akaike's information criteria) indicate better models.  The criterion labeled SC (Schwarz Criterion) is based on the value of AIC but adjusts for the number of variables entered into the model.  As with AIC, smaller values of SC  indicate better models.  The Schwarz Criterion is probably better to use than the AIC if you want a parsimonious model (fewer predictor variables)."  

"The global test of the null hypothesis shows all three tests of the null hypothesis reject it with very low p-values."  

"The table of p-values for each of the predictor variables (both classification variables and continuous variables) shows that all variables are significant."  

"The odds ratios for the two classification variables show that: 
 - for Black (0 versus 1), you see a point estimate of .491.  (Because you didn't select a reference level for the two classification variables, the task selected the higher value (1) as the reference level.)  You conclude that a person who is non-black (0) is less likely to have a baby whose weight is below the median value. If you take the reciprocal of this value (1/.491 or about 2.037), you could say that based on this model, that the odds of a black mother having a baby whose weight is below the median is 2.037 times higher than for a non-black mother.  The 95% confidence limits indicate that you are 95% confident that your estimate of the odds ratio is between those two limits.  Because both classification variables were significant, these limits do not include 1 (meaning that the odds are equal for each outcome).  
 - for MomSmoke (0 versus 1), you see a point estimate of .436, which means that non-smoking moms are less likely to have babies with birth weights below the median.  Based on this model, that the odds of a smoking mother having a baby whose weight is below the median is [1/.436 or] 2.294 times higher than for a non-smoking mother."
  
"The odds ratios for the continuous variables show the odds for each year (for MomAge) or each pound (for MomWtGain)."  
*/
title1 ; 
/* Logistic Regression - generated code - end */

SAS Output

Results: biostats_by_ex_SAScode.sas

Results: biostats_by_ex_SAScode.sas

Binary Logistic Regression - Reference Coding

The Logistic Procedure

Model Information

Model Information
Data Set WORK.HIGH_LOW
Response Variable Wt_Group
Number of Response Levels 2
Model binary logit
Optimization Technique Fisher's scoring

Observations Summary

Number of Observations Read 12500
Number of Observations Used 12500

Response Profile

Response Profile
Ordered
Value		 Wt_Group Total
Frequency
1 0 6325
2 1 6175

Probability modeled is Wt_Group=1.

Class Level Information

Class Level Information
Class Value Design Variables
Black 0 1
  1 0
MomSmoke 0 1
  1 0

Convergence Status

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Fit Statistics

Model Fit Statistics
Criterion Intercept Only Intercept and Covariates
AIC 17328.879 16490.398
SC 17336.313 16527.565
-2 Log L 17326.879 16480.398

Global Tests

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 846.4819 4 <.0001
Score 816.2735 4 <.0001
Wald 761.0124 4 <.0001

Type 3 Tests

Type 3 Analysis of Effects
Effect DF Wald
Chi-Square		 Pr > ChiSq
MomAge 1 83.0882 <.0001
MomWtGain 1 291.4380 <.0001
Black 1 183.9687 <.0001
MomSmoke 1 210.9599 <.0001

Parameter Estimates

Analysis of Maximum Likelihood Estimates
Parameter   DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept   1 1.3296 0.0718 342.7422 <.0001
MomAge   1 -0.0300 0.00329 83.0882 <.0001
MomWtGain   1 -0.0256 0.00150 291.4380 <.0001
Black 0 1 -0.7119 0.0525 183.9687 <.0001
MomSmoke 0 1 -0.8308 0.0572 210.9599 <.0001

Odds Ratios

Odds Ratio Estimates
Effect Point Estimate 95% Wald
Confidence Limits
MomAge 0.970 0.964 0.977
MomWtGain 0.975 0.972 0.978
Black 0 vs 1 0.491 0.443 0.544
MomSmoke 0 vs 1 0.436 0.389 0.487

Association Statistics

Association of Predicted Probabilities and Observed Responses
Percent Concordant 64.7 Somers' D 0.296
Percent Discordant 35.2 Gamma 0.296
Percent Tied 0.1 Tau-a 0.148
Pairs 39056875 c 0.648
  • “The model fit statistics section is useful when comparing models. Smaller values of AIC (Akaike’s information criteria) indicate better models. The criterion labeled SC (Schwarz Criterion) is based on the value of AIC but adjusts for the number of variables entered into the model. As with AIC, smaller values of SC indicate better models. The Schwarz Criterion is probably better to use than the AIC if you want a parsimonious model (fewer predictor variables).”
  • “The global test of the null hypothesis shows all three tests of the null hypothesis reject it with very low p-values.”
  • “The table of p-values for each of the predictor variables (both classification variables and continuous variables) shows that all variables are significant.”
  • “The odds ratios for the two classification variables show that:
    – for Black (0 versus 1), you see a point estimate of .491. (Because you didn’t select a reference level for the two classification variables, the task selected the higher value (1) as the reference level.) You conclude that a person who is non-black (0) is less likely to have a baby whose weight is below the median value. If you take the reciprocal of this value (1/.491 or about 2.037), you could say that based on this model, that the odds of a black mother having a baby whose weight is below the median is 2.037 times higher than for a non-black mother. The 95% confidence limits indicate that you are 95% confident that your estimate of the odds ratio is between those two limits. Because both classification variables were significant, these limits do not include 1 (meaning that the odds are equal for each outcome).
    – for MomSmoke (0 versus 1), you see a point estimate of .436, which means that non-smoking moms are less likely to have babies with birth weights below the median. Based on this model, that the odds of a smoking mother having a baby whose weight is below the median is [1/.436 or] 2.294 times higher than for a non-smoking mother.”
  • “The odds ratios for the continuous variables show the odds for each year (for MomAge) or each pound (for MomWtGain).”

Chapter 13: Analyzing Categorical Data

Two-Way Tables for Categorical Data.

SAS Code, click to expand

SAS Code:

#  (&path1 and biostats libname previously defined)
/* Two-Way Tables for Heart_Attack - start */
title1 "Two-Way Tables for Categorical Data - Heart_Attack";
ods noproctitle;
proc freq data=WORK.HEART_ATTACK order=formatted;
    tables  (Gender Age_Group High_Chol) * (Heart_Attack) 
    / chisq relrisk fisher nopercent nocum plots=none;
  run;

/*
  - "Looking at the output, the first section is the Table of Gender by Heart_Attack where each box has 3 values: frequency count, row percentage, and column percentage.  There are 41 subjects who are Male and had a Heart Attack.  These represent 16.40% of Males (row), and 70.69% of those who had a Heart Attack (column). Row and Column total frequencies are also displayed."  
  
  - "The next section is the Statistics for Table of Gender by Heart_Attack which shows various measures with very low p-values."  
  
  - "The Odds Ratio and Relative Risks section shows the risk of having a Heart Attack if you are Male.  If you conducted a case-control study, you would have used the Odds Ratio.  Since this is a cohort study, we use the Relative Risk.  A person is 2.4118 times more likely to suffer a heart attack if he is Male.  The table also shows the confidence limits for the odds ratio and relative risks; note that these intervals do not include 1.  An odds ratio or relative risk of 1 would mean that a Male person was not at a higher or lower risk of having a heart attack.  You expect this because of the significant chi-square value."  
  
  - "When Analyzing Tables with Low Expected Values (e.g., 2-by-2 tables with expected values less than 5) a popular alternative to chi-square is Fisher's Exact test.   There are statisticians who prefer chi-square with a correction for continuity instead, and we have both statistics (see Statistics for Table of Gender by Heart_Attack):  
  - Continuity Adj. Chi-Square value = 10.3175, p = .0013;  
  - Fisher's Exact test - Two-sided Pr <= P = 0.0012."    
*/

title1;
/* Two-Way Tables for Heart_Attack - end */

SAS Output

Results: biostats_by_ex_SAScode.sas

Results: biostats_by_ex_SAScode.sas

Two-Way Tables for Categorical Data - Heart_Attack

The Freq Procedure

Table Gender * Heart_Attack

Cross-Tabular Freq Table

Frequency
Row Pct
Col Pct
Table of Gender by Heart_Attack
Gender(Gender) Heart_Attack(Heart_Attack)
1:Yes 2:No Total
1:Male
41
16.40
70.69
209
83.60
47.29
250
 
 
2:Female
17
6.80
29.31
233
93.20
52.71
250
 
 
Total
58
442
500

Statistics for Table of Gender by Heart_Attack

Chi-Square Tests

Statistic DF Value Prob
Chi-Square 1 11.2342 0.0008
Likelihood Ratio Chi-Square 1 11.5397 0.0007
Continuity Adj. Chi-Square 1 10.3175 0.0013
Mantel-Haenszel Chi-Square 1 11.2117 0.0008
Phi Coefficient   0.1499  
Contingency Coefficient   0.1482  
Cramer's V   0.1499  

Fisher's Exact Test

Fisher's Exact Test
Cell (1,1) Frequency (F) 41
Left-sided Pr <= F 0.9998
Right-sided Pr >= F 0.0006
   
Table Probability (P) 0.0004
Two-sided Pr <= P 0.0012

Relative Risk Estimates

Odds Ratio and Relative Risks
Statistic Value 95% Confidence Limits
Odds Ratio 2.6887 1.4824 4.8768
Relative Risk (Column 1) 2.4118 1.4089 4.1284
Relative Risk (Column 2) 0.8970 0.8411 0.9566

Sample Size = 500

Table Age_Group * Heart_Attack

Cross-Tabular Freq Table

Frequency
Row Pct
Col Pct
Table of Age_Group by Heart_Attack
Age_Group(Age_Group) Heart_Attack(Heart_Attack)
1:Yes 2:No Total
60-70
23
12.78
39.66
157
87.22
35.52
180
 
 
71+
30
17.24
51.72
144
82.76
32.58
174
 
 
< 60
5
3.42
8.62
141
96.58
31.90
146
 
 
Total
58
442
500

Statistics for Table of Age_Group by Heart_Attack

Chi-Square Tests

Statistic DF Value Prob
Chi-Square 2 15.1597 0.0005
Likelihood Ratio Chi-Square 2 17.7666 0.0001
Mantel-Haenszel Chi-Square 1 14.4611 0.0001
Phi Coefficient   0.1741  
Contingency Coefficient   0.1715  
Cramer's V   0.1741  

Fisher's Exact Test

Fisher's Exact Test
Table Probability (P) <.0001
Pr <= P 0.0002

Sample Size = 500

Table High_Chol * Heart_Attack

Cross-Tabular Freq Table

Frequency
Row Pct
Col Pct
Table of High_Chol by Heart_Attack
High_Chol(High_Chol) Heart_Attack(Heart_Attack)
1:Yes 2:No Total
1:Yes
44
17.25
75.86
211
82.75
47.74
255
 
 
2:No
14
5.71
24.14
231
94.29
52.26
245
 
 
Total
58
442
500

Statistics for Table of High_Chol by Heart_Attack

Chi-Square Tests

Statistic DF Value Prob
Chi-Square 1 16.2287 <.0001
Likelihood Ratio Chi-Square 1 17.0012 <.0001
Continuity Adj. Chi-Square 1 15.1228 0.0001
Mantel-Haenszel Chi-Square 1 16.1963 <.0001
Phi Coefficient   0.1802  
Contingency Coefficient   0.1773  
Cramer's V   0.1802  

Fisher's Exact Test

Fisher's Exact Test
Cell (1,1) Frequency (F) 44
Left-sided Pr <= F 1.0000
Right-sided Pr >= F <.0001
   
Table Probability (P) <.0001
Two-sided Pr <= P <.0001

Relative Risk Estimates

Odds Ratio and Relative Risks
Statistic Value 95% Confidence Limits
Odds Ratio 3.4408 1.8331 6.4585
Relative Risk (Column 1) 3.0196 1.6987 5.3678
Relative Risk (Column 2) 0.8776 0.8232 0.9356

Sample Size = 500

  • “Looking at the output, the first section is the Table of Gender by Heart_Attack where each box has 3 values: frequency count, row percentage, and column percentage. There are 41 subjects who are Male and had a Heart Attack. These represent 16.40% of Males (row), and 70.69% of those who had a Heart Attack (column). Row and Column total frequencies are also displayed.”

  • “The next section is the Statistics for Table of Gender by Heart_Attack which shows various measures with very low p-values.”

  • “The Odds Ratio and Relative Risks section shows the risk of having a Heart Attack if you are Male. If you conducted a case-control study, you would have used the Odds Ratio. Since this is a cohort study, we use the Relative Risk. A person is 2.4118 times more likely to suffer a heart attack if he is Male. The table also shows the confidence limits for the odds ratio and relative risks; note that these intervals do not include 1. An odds ratio or relative risk of 1 would mean that a Male person was not at a higher or lower risk of having a heart attack. You expect this because of the significant chi-square value.”

  • “When Analyzing Tables with Low Expected Values (e.g., 2-by-2 tables with expected values less than 5) a popular alternative to chi-square is Fisher’s Exact test. There are statisticians who prefer chi-square with a correction for continuity instead, and we have both statistics (see Statistics for Table of Gender by Heart_Attack):

  • Continuity Adj. Chi-Square value = 10.3175, p = .0013;

  • Fisher’s Exact test - Two-sided Pr <= P = 0.0012.”

Chapter 14: Computing Power and Sample Size

Computing Sample Size for a t Test.

SAS Code, click to expand

SAS Code:

#  (&path1 and biostats libname previously defined)
/* Computing Sample Size for a t Test - start */
title1 "Computing Sample Size for a t Test";
ods noproctitle;
ods graphics / imagemap=on;
proc power;
    twosamplemeans test=diff sides=2 groupmeans=(130 120) (130 125) stddev=10 
        power=0.8 0.9 alpha=0.05 npergroup=.;
    plot x=power;
run;
/*
"Assume we will conduct a simple study to compare blood pressure in a group of borderline hypertensive subjects.  You want to see if a low dose of a beta blocker will reduce blood pressure.  Because these subjects are borderline hypertensive and the trial will be relatively short, you decide that it is ethical to use a placebo as your control.  What information do you need to decide how many subjects you need to recruit in order to have a power of 80%?  We assume equal variances in the two groups, and select a two-sided test with equal (pooled) variances. 
We enter the expected mean for each group to compute sample sizes; one for means of 130 versus 120 (a 10-point difference) and another for means of 130 versus 125 (a 5-point difference).  We provide an estimate of 10 for standard deviation, and entered the desired power(s): .8 and .9. 
  
  - Sample Size per Group in Table Form: Notice the large sample sizes necessary to detect a small difference of 5 points.  The lowest sample size per group (n per group = 17) is for the largest difference (130 versus 120) and the lowest power (80%).   
  - Plot of Power versus Sample Size: The graph of sample size by power will contain a line for each combination of means, standard deviations, and powers that you entered.  The final decision of sample size is sometimes a compromise between how many subjects you can recruit (and pay for) and how large a difference you would like to be able to detect."  
*/
title1;
/* Computing Sample Size for a t Test - end */

SAS Output

Results: biostats_by_ex_SAScode.sas

Results: biostats_by_ex_SAScode.sas

Computing Sample Size for a t Test

Two-Sample t Test for Mean Difference

The Power Procedure

Two-Sample t Test for Mean Difference 1

Fixed Scenario Elements

Fixed Scenario Elements
Distribution Normal
Method Exact
Number of Sides 2
Alpha 0.05
Standard Deviation 10
Null Difference 0

Output

Computed N per Group
Index Mean1 Mean2 Nominal Power Actual Power N per Group
1 130 120 0.8 0.807 17
2 130 120 0.9 0.912 23
3 130 125 0.8 0.801 64
4 130 125 0.9 0.903 86

Computing Sample Size for a t Test

Two-Sample t Test for Mean Difference

Plot Statement 1

N per Group vs. Power

N per Group vs. Power

Power = 0.9032 N per Group = 86 Means = 130 125 Power = 0.8965 N per Group = 84 Means = 130 125 Power = 0.8929 N per Group = 83 Means = 130 125 Power = 0.8855 N per Group = 81 Means = 130 125 Power = 0.8816 N per Group = 80 Means = 130 125 Power = 0.8776 N per Group = 79 Means = 130 125 Power = 0.8692 N per Group = 77 Means = 130 125 Power = 0.8649 N per Group = 76 Means = 130 125 Power = 0.8604 N per Group = 75 Means = 130 125 Power = 0.8557 N per Group = 74 Means = 130 125 Power = 0.851 N per Group = 73 Means = 130 125 Power = 0.8461 N per Group = 72 Means = 130 125 Power = 0.841 N per Group = 71 Means = 130 125 Power = 0.8358 N per Group = 70 Means = 130 125 Power = 0.8305 N per Group = 69 Means = 130 125 Power = 0.825 N per Group = 68 Means = 130 125 Power = 0.8193 N per Group = 67 Means = 130 125 Power = 0.8135 N per Group = 66 Means = 130 125 Power = 0.8076 N per Group = 65 Means = 130 125 Power = 0.8015 N per Group = 64 Means = 130 125 Power = 0.9125 N per Group = 23 Means = 130 120 Power = 0.8997 N per Group = 22 Means = 130 120 Power = 0.8997 N per Group = 22 Means = 130 120 Power = 0.8853 N per Group = 21 Means = 130 120 Power = 0.8853 N per Group = 21 Means = 130 120 Power = 0.8853 N per Group = 21 Means = 130 120 Power = 0.869 N per Group = 20 Means = 130 120 Power = 0.869 N per Group = 20 Means = 130 120 Power = 0.869 N per Group = 20 Means = 130 120 Power = 0.869 N per Group = 20 Means = 130 120 Power = 0.8506 N per Group = 19 Means = 130 120 Power = 0.8506 N per Group = 19 Means = 130 120 Power = 0.8506 N per Group = 19 Means = 130 120 Power = 0.8506 N per Group = 19 Means = 130 120 Power = 0.83 N per Group = 18 Means = 130 120 Power = 0.83 N per Group = 18 Means = 130 120 Power = 0.83 N per Group = 18 Means = 130 120 Power = 0.83 N per Group = 18 Means = 130 120 Power = 0.807 N per Group = 17 Means = 130 120 Power = 0.807 N per Group = 17 Means = 130 120 Power = 0.9032 N per Group = 86 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8965 N per Group = 84 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8965 N per Group = 84 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8929 N per Group = 83 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8929 N per Group = 83 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8855 N per Group = 81 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8855 N per Group = 81 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8816 N per Group = 80 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8816 N per Group = 80 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8776 N per Group = 79 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8776 N per Group = 79 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8692 N per Group = 77 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8692 N per Group = 77 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8649 N per Group = 76 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8649 N per Group = 76 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8604 N per Group = 75 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8604 N per Group = 75 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8557 N per Group = 74 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8557 N per Group = 74 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.851 N per Group = 73 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.851 N per Group = 73 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8461 N per Group = 72 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8461 N per Group = 72 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.841 N per Group = 71 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.841 N per Group = 71 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8358 N per Group = 70 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8358 N per Group = 70 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8305 N per Group = 69 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8305 N per Group = 69 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.825 N per Group = 68 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.825 N per Group = 68 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8193 N per Group = 67 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8193 N per Group = 67 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8135 N per Group = 66 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8135 N per Group = 66 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8076 N per Group = 65 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8076 N per Group = 65 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.8015 N per Group = 64 Plot Curve = 2 Plot Color = 1 Line Entry = 130 125 Power = 0.9125 N per Group = 23 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.8997 N per Group = 22 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.8997 N per Group = 22 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.8997 N per Group = 22 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.8997 N per Group = 22 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.8853 N per Group = 21 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.8853 N per Group = 21 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.8853 N per Group = 21 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.8853 N per Group = 21 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.8853 N per Group = 21 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.8853 N per Group = 21 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.869 N per Group = 20 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.869 N per Group = 20 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.869 N per Group = 20 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.869 N per Group = 20 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.869 N per Group = 20 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.869 N per Group = 20 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.869 N per Group = 20 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.869 N per Group = 20 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.8506 N per Group = 19 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.8506 N per Group = 19 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.8506 N per Group = 19 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.8506 N per Group = 19 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.8506 N per Group = 19 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.8506 N per Group = 19 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.8506 N per Group = 19 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.8506 N per Group = 19 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.83 N per Group = 18 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.83 N per Group = 18 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.83 N per Group = 18 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.83 N per Group = 18 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.83 N per Group = 18 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.83 N per Group = 18 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.83 N per Group = 18 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.83 N per Group = 18 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.807 N per Group = 17 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.807 N per Group = 17 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120 Power = 0.807 N per Group = 17 Plot Curve = 1 Plot Color = 1 Line Entry = 130 120
N per Group vs. Power
  • “Assume we will conduct a simple study to compare blood pressure in a group of borderline hypertensive subjects. You want to see if a low dose of a beta blocker will reduce blood pressure. Because these subjects are borderline hypertensive and the trial will be relatively short, you decide that it is ethical to use a placebo as your control. What information do you need to decide how many subjects you need to recruit in order to have a power of 80%? We assume equal variances in the two groups, and select a two-sided test with equal (pooled) variances. We enter the expected mean for each group to compute sample sizes; one for means of 130 versus 120 (a 10-point difference) and another for means of 130 versus 125 (a 5-point difference). We provide an estimate of 10 for standard deviation, and entered the desired power(s): .8 and .9.
  • Sample Size per Group in Table Form: Notice the large sample sizes necessary to detect a small difference of 5 points. The lowest sample size per group (n per group = 17) is for the largest difference (130 versus 120) and the lowest power (80%).
  • Plot of Power versus Sample Size: The graph of sample size by power will contain a line for each combination of means, standard deviations, and powers that you entered. The final decision of sample size is sometimes a compromise between how many subjects you can recruit (and pay for) and how large a difference you would like to be able to detect.”

Calculating the Sample Size for a Test of Proportions.

SAS Code, click to expand

SAS Code:

#  (&path1 and biostats libname previously defined)
/* Calculating the Sample Size for a Test of Proportions - start */
title1 "Calculating the Sample Size for a Test of Proportions";
ods noproctitle;
ods graphics / imagemap=on;
proc power;
    twosamplefreq test=pchi sides=2 groupproportions=(0.7 0.8) (0.7 0.9) power=0.8 
        0.85 0.9 alpha=0.05 npergroup=.;
    plot x=power;
run;
/*
"Information needed to compute sample sizes for test of proportions:  
  - Conduct a one-sided or two-sided test? (Usually two-sided);  
  - Alpha level? (Usually ⍺ = .05);  
  - Proportion in the first group (usually a control group)?  If unsure, lean toward .5 (maximum variance);  
  - How large a difference in proportions do you want to be able to detect? (Or the proportion in group two);   
  - You decide to compute sample sizes for two different scenarios: one with proportions of .7 and .8, the other with proportions of .7 and .9;  
  - What power do you want? (You often enter several values such as .8, .85, and .9);  
  - The statistical test that you plan to use in the analysis: for most studies with fairly large n's, the Pearson chi-square test is a
good choice; if you believe that you will have small expected values in the study, you may choose Fisher's exact test.  
  
  - "Sample Size per Group in Table Form: If you look at the N per Group for comparing proportions of .7 and .8 with a power of 90%, you see that you need 392 subjects per group.  The smallest number of subjects per group (62) is for proportions of .7 versus .9 with 80% power.
  - Plot of Power versus Sample Size: When you compare proportions, you may have to lower your expectations of detecting small differences and design the study with larger differences in the two proportions and, perhaps, slightly lower power."  
*/
title1;
/* Calculating the Sample Size for a Test of Proportions - end */

SAS Output

Results: biostats_by_ex_SAScode.sas

Results: biostats_by_ex_SAScode.sas

Calculating the Sample Size for a Test of Proportions

Pearson Chi-square Test for Proportion Difference

The Power Procedure

Pearson Chi-square Test for Proportion Difference 1

Fixed Scenario Elements

Fixed Scenario Elements
Distribution Asymptotic normal
Method Normal approximation
Number of Sides 2
Alpha 0.05
Null Proportion Difference 0

Output

Computed N per Group
Index Proportion1 Proportion2 Nominal Power Actual Power N per Group
1 0.7 0.8 0.80 0.801 294
2 0.7 0.8 0.85 0.851 336
3 0.7 0.8 0.90 0.900 392
4 0.7 0.9 0.80 0.803 62
5 0.7 0.9 0.85 0.854 71
6 0.7 0.9 0.90 0.900 82

Calculating the Sample Size for a Test of Proportions

Pearson Chi-square Test for Proportion Difference

Plot Statement 1

N per Group vs. Power

N per Group vs. Power

Power = 0.9001 N per Group = 82 Proportions = 0.7 0.9 Power = 0.8965 N per Group = 81 Proportions = 0.7 0.9 Power = 0.8928 N per Group = 80 Proportions = 0.7 0.9 Power = 0.8851 N per Group = 78 Proportions = 0.7 0.9 Power = 0.881 N per Group = 77 Proportions = 0.7 0.9 Power = 0.8768 N per Group = 76 Proportions = 0.7 0.9 Power = 0.8724 N per Group = 75 Proportions = 0.7 0.9 Power = 0.8634 N per Group = 73 Proportions = 0.7 0.9 Power = 0.8586 N per Group = 72 Proportions = 0.7 0.9 Power = 0.8537 N per Group = 71 Proportions = 0.7 0.9 Power = 0.8487 N per Group = 70 Proportions = 0.7 0.9 Power = 0.8435 N per Group = 69 Proportions = 0.7 0.9 Power = 0.8381 N per Group = 68 Proportions = 0.7 0.9 Power = 0.8326 N per Group = 67 Proportions = 0.7 0.9 Power = 0.827 N per Group = 66 Proportions = 0.7 0.9 Power = 0.8211 N per Group = 65 Proportions = 0.7 0.9 Power = 0.8211 N per Group = 65 Proportions = 0.7 0.9 Power = 0.8151 N per Group = 64 Proportions = 0.7 0.9 Power = 0.809 N per Group = 63 Proportions = 0.7 0.9 Power = 0.8026 N per Group = 62 Proportions = 0.7 0.9 Power = 0.9 N per Group = 392 Proportions = 0.7 0.8 Power = 0.8948 N per Group = 385 Proportions = 0.7 0.8 Power = 0.8902 N per Group = 379 Proportions = 0.7 0.8 Power = 0.8845 N per Group = 372 Proportions = 0.7 0.8 Power = 0.8794 N per Group = 366 Proportions = 0.7 0.8 Power = 0.8741 N per Group = 360 Proportions = 0.7 0.8 Power = 0.8686 N per Group = 354 Proportions = 0.7 0.8 Power = 0.8639 N per Group = 349 Proportions = 0.7 0.8 Power = 0.858 N per Group = 343 Proportions = 0.7 0.8 Power = 0.853 N per Group = 338 Proportions = 0.7 0.8 Power = 0.8478 N per Group = 333 Proportions = 0.7 0.8 Power = 0.8424 N per Group = 328 Proportions = 0.7 0.8 Power = 0.8379 N per Group = 324 Proportions = 0.7 0.8 Power = 0.8323 N per Group = 319 Proportions = 0.7 0.8 Power = 0.8264 N per Group = 314 Proportions = 0.7 0.8 Power = 0.8216 N per Group = 310 Proportions = 0.7 0.8 Power = 0.8166 N per Group = 306 Proportions = 0.7 0.8 Power = 0.8116 N per Group = 302 Proportions = 0.7 0.8 Power = 0.8064 N per Group = 298 Proportions = 0.7 0.8 Power = 0.8011 N per Group = 294 Proportions = 0.7 0.8 Power = 0.9001 N per Group = 82 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8965 N per Group = 81 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8965 N per Group = 81 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8928 N per Group = 80 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8928 N per Group = 80 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8851 N per Group = 78 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8851 N per Group = 78 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.881 N per Group = 77 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.881 N per Group = 77 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8768 N per Group = 76 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8768 N per Group = 76 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8724 N per Group = 75 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8724 N per Group = 75 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8634 N per Group = 73 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8634 N per Group = 73 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8586 N per Group = 72 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8586 N per Group = 72 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8537 N per Group = 71 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8537 N per Group = 71 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8487 N per Group = 70 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8487 N per Group = 70 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8435 N per Group = 69 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8435 N per Group = 69 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8381 N per Group = 68 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8381 N per Group = 68 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8326 N per Group = 67 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8326 N per Group = 67 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.827 N per Group = 66 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.827 N per Group = 66 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8211 N per Group = 65 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8211 N per Group = 65 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8211 N per Group = 65 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8211 N per Group = 65 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8151 N per Group = 64 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8151 N per Group = 64 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.809 N per Group = 63 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.809 N per Group = 63 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.8026 N per Group = 62 Plot Curve = 2 Plot Color = 1 Line Entry = 0.7 0.9 Power = 0.9 N per Group = 392 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8948 N per Group = 385 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8948 N per Group = 385 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8902 N per Group = 379 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8902 N per Group = 379 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8845 N per Group = 372 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8845 N per Group = 372 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8794 N per Group = 366 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8794 N per Group = 366 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8741 N per Group = 360 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8741 N per Group = 360 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8686 N per Group = 354 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8686 N per Group = 354 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8639 N per Group = 349 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8639 N per Group = 349 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.858 N per Group = 343 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.858 N per Group = 343 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.853 N per Group = 338 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.853 N per Group = 338 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8478 N per Group = 333 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8478 N per Group = 333 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8424 N per Group = 328 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8424 N per Group = 328 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8379 N per Group = 324 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8379 N per Group = 324 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8323 N per Group = 319 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8323 N per Group = 319 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8264 N per Group = 314 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8264 N per Group = 314 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8216 N per Group = 310 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8216 N per Group = 310 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8166 N per Group = 306 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8166 N per Group = 306 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8116 N per Group = 302 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8116 N per Group = 302 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8064 N per Group = 298 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8064 N per Group = 298 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8 Power = 0.8011 N per Group = 294 Plot Curve = 1 Plot Color = 1 Line Entry = 0.7 0.8
N per Group vs. Power
  • “Information needed to compute sample sizes for test of proportions:
    – Conduct a one-sided or two-sided test? (Usually two-sided);
    – Alpha level? (Usually ⍺ = .05);
    – Proportion in the first group (usually a control group)? If unsure, lean toward .5 (maximum variance);
    – How large a difference in proportions do you want to be able to detect? (Or the proportion in group two);
    – You decide to compute sample sizes for two different scenarios: one with proportions of .7 and .8, the other with proportions of .7 and .9;
    – What power do you want? (You often enter several values such as .8, .85, and .9);
    – The statistical test that you plan to use in the analysis: for most studies with fairly large n’s, the Pearson chi-square test is a good choice; if you believe that you will have small expected values in the study, you may choose Fisher’s exact test.
  • Sample Size per Group in Table Form: If you look at the N per Group for comparing proportions of .7 and .8 with a power of 90%, you see that you need 392 subjects per group. The smallest number of subjects per group (62) is for proportions of .7 versus .9 with 80% power.
  • Plot of Power versus Sample Size: When you compare proportions, you may have to lower your expectations of detecting small differences and design the study with larger differences in the two proportions and, perhaps, slightly lower power.”

Computing Sample Size for a One-Way ANOVA Design.

SAS Code, click to expand

SAS Code:

#  (&path1 and biostats libname previously defined)
/* Computing Sample Size for a One-Way ANOVA Design - start */
title1 "Computing Sample Size for a One-Way ANOVA Design";
proc power;
   onewayanova
   groupmeans = 20 | 25 | 30 
   stddev = 8 10 
   power = .80 .90
   npergroup = .;
   plot x = power min = .70 max = .90;
run; 
/*
  - "3 means estimated to be 20, 25, and 30;  
  - Two estimates for standard deviation: 8 and 10;   
  - You want to compute sample size for powers of 80% and 90%;  
  - You want to compute the n-per-group (as compared to power for a given sample size);  
  - You would like a plot of Power (x-axis) versus sample size and the axes scaled to show powers from .7 to .9;  
  - You enter the group means following the key word GROUPMEANS, separating them using a vertical bar (also called a pipe symbol);  
  - Follow the keyword STDDEV with one or more estimates of the pooled standard deviation;  
  - You have a choice of computing power or sample size:  
   -- if you want to compute sample size, enter one or more values for your desired power, and enter a SAS numeric missing value (coded as a period) for the number of subjects per group;
   -- if you want to compute power for a given sample size, enter a period for the power and one or more values of sample size. 
  - Use a PLOT statement to indicate that you want power on the x axis, with values of power ranging from .7 to .9."  
*/
title1;
/* Computing Sample Size for a One-Way ANOVA Design - end */

SAS Output

Results: biostats_by_ex_SAScode.sas

Results: biostats_by_ex_SAScode.sas

Computing Sample Size for a One-Way ANOVA Design

Overall F Test for One-Way ANOVA

The Power Procedure

Overall F Test for One-Way ANOVA 1

Fixed Scenario Elements

Fixed Scenario Elements
Method Exact
Group Means 20 25 30
Alpha 0.05

Output

Computed N per Group
Index Std Dev Nominal Power Actual Power N per Group
1 8 0.8 0.820 14
2 8 0.9 0.913 18
3 10 0.8 0.815 21
4 10 0.9 0.908 27

Computing Sample Size for a One-Way ANOVA Design

Overall F Test for One-Way ANOVA

Plot Statement 1

N per Group vs. Power

N per Group vs. Power

Power = 0.9077 N per Group = 27 Std Dev = 10 Power = 0.8959 N per Group = 26 Std Dev = 10 Power = 0.8828 N per Group = 25 Std Dev = 10 Power = 0.8828 N per Group = 25 Std Dev = 10 Power = 0.8682 N per Group = 24 Std Dev = 10 Power = 0.8521 N per Group = 23 Std Dev = 10 Power = 0.8521 N per Group = 23 Std Dev = 10 Power = 0.8343 N per Group = 22 Std Dev = 10 Power = 0.8343 N per Group = 22 Std Dev = 10 Power = 0.8148 N per Group = 21 Std Dev = 10 Power = 0.8148 N per Group = 21 Std Dev = 10 Power = 0.7933 N per Group = 20 Std Dev = 10 Power = 0.7933 N per Group = 20 Std Dev = 10 Power = 0.7698 N per Group = 19 Std Dev = 10 Power = 0.7698 N per Group = 19 Std Dev = 10 Power = 0.7443 N per Group = 18 Std Dev = 10 Power = 0.7443 N per Group = 18 Std Dev = 10 Power = 0.7443 N per Group = 18 Std Dev = 10 Power = 0.7165 N per Group = 17 Std Dev = 10 Power = 0.7165 N per Group = 17 Std Dev = 10 Power = 0.9134 N per Group = 18 Std Dev = 8 Power = 0.8954 N per Group = 17 Std Dev = 8 Power = 0.8954 N per Group = 17 Std Dev = 8 Power = 0.8742 N per Group = 16 Std Dev = 8 Power = 0.8742 N per Group = 16 Std Dev = 8 Power = 0.8492 N per Group = 15 Std Dev = 8 Power = 0.8492 N per Group = 15 Std Dev = 8 Power = 0.8492 N per Group = 15 Std Dev = 8 Power = 0.8202 N per Group = 14 Std Dev = 8 Power = 0.8202 N per Group = 14 Std Dev = 8 Power = 0.8202 N per Group = 14 Std Dev = 8 Power = 0.7865 N per Group = 13 Std Dev = 8 Power = 0.7865 N per Group = 13 Std Dev = 8 Power = 0.7865 N per Group = 13 Std Dev = 8 Power = 0.7865 N per Group = 13 Std Dev = 8 Power = 0.7479 N per Group = 12 Std Dev = 8 Power = 0.7479 N per Group = 12 Std Dev = 8 Power = 0.7479 N per Group = 12 Std Dev = 8 Power = 0.7479 N per Group = 12 Std Dev = 8 Power = 0.7039 N per Group = 11 Std Dev = 8 Power = 0.9077 N per Group = 27 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.8959 N per Group = 26 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.8959 N per Group = 26 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.8828 N per Group = 25 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.8828 N per Group = 25 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.8828 N per Group = 25 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.8828 N per Group = 25 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.8682 N per Group = 24 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.8682 N per Group = 24 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.8521 N per Group = 23 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.8521 N per Group = 23 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.8521 N per Group = 23 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.8521 N per Group = 23 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.8343 N per Group = 22 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.8343 N per Group = 22 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.8343 N per Group = 22 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.8343 N per Group = 22 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.8148 N per Group = 21 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.8148 N per Group = 21 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.8148 N per Group = 21 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.8148 N per Group = 21 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.7933 N per Group = 20 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.7933 N per Group = 20 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.7933 N per Group = 20 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.7933 N per Group = 20 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.7698 N per Group = 19 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.7698 N per Group = 19 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.7698 N per Group = 19 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.7698 N per Group = 19 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.7443 N per Group = 18 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.7443 N per Group = 18 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.7443 N per Group = 18 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.7443 N per Group = 18 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.7443 N per Group = 18 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.7443 N per Group = 18 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.7165 N per Group = 17 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.7165 N per Group = 17 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.7165 N per Group = 17 Plot Curve = 2 Plot Color = 1 Line Entry = 10 Power = 0.9134 N per Group = 18 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.8954 N per Group = 17 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.8954 N per Group = 17 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.8954 N per Group = 17 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.8954 N per Group = 17 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.8742 N per Group = 16 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.8742 N per Group = 16 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.8742 N per Group = 16 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.8742 N per Group = 16 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.8492 N per Group = 15 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.8492 N per Group = 15 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.8492 N per Group = 15 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.8492 N per Group = 15 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.8492 N per Group = 15 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.8492 N per Group = 15 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.8202 N per Group = 14 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.8202 N per Group = 14 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.8202 N per Group = 14 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.8202 N per Group = 14 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.8202 N per Group = 14 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.8202 N per Group = 14 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.7865 N per Group = 13 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.7865 N per Group = 13 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.7865 N per Group = 13 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.7865 N per Group = 13 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.7865 N per Group = 13 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.7865 N per Group = 13 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.7865 N per Group = 13 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.7865 N per Group = 13 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.7479 N per Group = 12 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.7479 N per Group = 12 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.7479 N per Group = 12 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.7479 N per Group = 12 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.7479 N per Group = 12 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.7479 N per Group = 12 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.7479 N per Group = 12 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.7479 N per Group = 12 Plot Curve = 1 Plot Color = 1 Line Entry = 8 Power = 0.7039 N per Group = 11 Plot Curve = 1 Plot Color = 1 Line Entry = 8
N per Group vs. Power
  • “3 means estimated to be 20, 25, and 30;
  • Two estimates for standard deviation: 8 and 10;
  • You want to compute sample size for powers of 80% and 90%;
  • You want to compute the n-per-group (as compared to power for a given sample size);
  • You would like a plot of Power (x-axis) versus sample size and the axes scaled to show powers from .7 to .9;
  • You enter the group means following the key word GROUPMEANS, separating them using a vertical bar (also called a pipe symbol);
  • Follow the keyword STDDEV with one or more estimates of the pooled standard deviation;
  • You have a choice of computing power or sample size:
    – if you want to compute sample size, enter one or more values for your desired power, and enter a SAS numeric missing value (coded as a period) for the number of subjects per group;
    – if you want to compute power for a given sample size, enter a period for the power and one or more values of sample size.
  • Use a PLOT statement to indicate that you want power on the x axis, with values of power ranging from .7 to .9.”

Now, let’s use R!

library(tidyverse)
library(lubridate)
library(haven)
library(readxl)
library(Hmisc)
# library(kableExtra)
# library(car)
# library(scales)
# library(lsr)
# library(psych)
# library(broom)

Chapters 1 - 4: Data Import Basics

Read-in bult-in dataset, import from text and CSV files, work with various delimiters and header profiles. For example, the heart dataset was exported from the built-in SAS library into a physical SAS dataset, which is then imported by R using the haven package. Another dataset Bweight contains birth weights for 50,000 babies, along with several variables believed to be related to birth weight, such as race (coded as black=1 or not black=0), mother’s smoking status (smoking=1 or non-smoking=0), and marital status (not married=0 or married=1).

R Code:

# if you wrote the SAS dataset with validvarname v6, you might need to fill in the mainframe style field names
# heart <- haven::read_sas("heart.sas7bdat") %>%
#   rename(Status =     STATUS,
# DeathCause = DEATHCAU, # Cause of Death
# AgeCHDdiag = AGECHDDI, # Age CHD Diagnosed
# Sex = SEX, 
# AgeAtStart = AGEATSTA, # Age at Start
# Height = HEIGHT, 
# Weight = WEIGHT, 
# Diastolic = DIASTOLI, 
# Systolic = SYSTOLIC, 
# MRW = MRW, # Metropolitan Relative Weight
# Smoking = SMOKING, 
# AgeAtDeath = AGEATDEA, # Age at Death
# Cholesterol = CHOLESTE, 
# Chol_Status = CHOL_STA, # Cholesterol Status
# BP_Status = BP_STATU, # Blood Pressure Status
# Weight_Status = WEIGHT_S, # Weight Status
# Smoking_Status = SMOKING_)
# glimpse(heart)

# if you wrote the SAS dataset with validvarname v9, field names longer than 8 characters and mixed case are okay 
heart <- haven::read_sas("heart_v9.sas7bdat")
glimpse(heart)
## Rows: 5,209
## Columns: 17
## $ Status         <chr> "Dead", "Dead", "Alive", "Alive", "Alive", "Alive", "Al~
## $ DeathCause     <chr> "Other", "Cancer", "", "", "", "", "", "Other", "", "Ce~
## $ AgeCHDdiag     <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 57, 55, 79,~
## $ Sex            <chr> "Female", "Female", "Female", "Female", "Male", "Female~
## $ AgeAtStart     <dbl> 29, 41, 57, 39, 42, 58, 36, 53, 35, 52, 39, 33, 33, 57,~
## $ Height         <dbl> 62.50, 59.75, 62.25, 65.75, 66.00, 61.75, 64.75, 65.50,~
## $ Weight         <dbl> 140, 194, 132, 158, 156, 131, 136, 130, 194, 129, 179, ~
## $ Diastolic      <dbl> 78, 92, 90, 80, 76, 92, 80, 80, 68, 78, 76, 68, 90, 76,~
## $ Systolic       <dbl> 124, 144, 170, 128, 110, 176, 112, 114, 132, 124, 128, ~
## $ MRW            <dbl> 121, 183, 114, 123, 116, 117, 110, 99, 124, 106, 133, 1~
## $ Smoking        <dbl> 0, 0, 10, 0, 20, 0, 15, 0, 0, 5, 30, 0, 0, 15, 30, 10, ~
## $ AgeAtDeath     <dbl> 55, 57, NA, NA, NA, NA, NA, 77, NA, 82, NA, NA, NA, NA,~
## $ Cholesterol    <dbl> NA, 181, 250, 242, 281, 196, 196, 276, 211, 284, 225, 2~
## $ Chol_Status    <chr> "", "Desirable", "High", "High", "High", "Desirable", "~
## $ BP_Status      <chr> "Normal", "High", "High", "Normal", "Optimal", "High", ~
## $ Weight_Status  <chr> "Overweight", "Overweight", "Overweight", "Overweight",~
## $ Smoking_Status <chr> "Non-smoker", "Non-smoker", "Moderate (6-15)", "Non-smo~
fish <- haven::read_sas("fish.sas7bdat")
glimpse(heart)
## Rows: 5,209
## Columns: 17
## $ Status         <chr> "Dead", "Dead", "Alive", "Alive", "Alive", "Alive", "Al~
## $ DeathCause     <chr> "Other", "Cancer", "", "", "", "", "", "Other", "", "Ce~
## $ AgeCHDdiag     <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 57, 55, 79,~
## $ Sex            <chr> "Female", "Female", "Female", "Female", "Male", "Female~
## $ AgeAtStart     <dbl> 29, 41, 57, 39, 42, 58, 36, 53, 35, 52, 39, 33, 33, 57,~
## $ Height         <dbl> 62.50, 59.75, 62.25, 65.75, 66.00, 61.75, 64.75, 65.50,~
## $ Weight         <dbl> 140, 194, 132, 158, 156, 131, 136, 130, 194, 129, 179, ~
## $ Diastolic      <dbl> 78, 92, 90, 80, 76, 92, 80, 80, 68, 78, 76, 68, 90, 76,~
## $ Systolic       <dbl> 124, 144, 170, 128, 110, 176, 112, 114, 132, 124, 128, ~
## $ MRW            <dbl> 121, 183, 114, 123, 116, 117, 110, 99, 124, 106, 133, 1~
## $ Smoking        <dbl> 0, 0, 10, 0, 20, 0, 15, 0, 0, 5, 30, 0, 0, 15, 30, 10, ~
## $ AgeAtDeath     <dbl> 55, 57, NA, NA, NA, NA, NA, 77, NA, 82, NA, NA, NA, NA,~
## $ Cholesterol    <dbl> NA, 181, 250, 242, 281, 196, 196, 276, 211, 284, 225, 2~
## $ Chol_Status    <chr> "", "Desirable", "High", "High", "High", "Desirable", "~
## $ BP_Status      <chr> "Normal", "High", "High", "Normal", "Optimal", "High", ~
## $ Weight_Status  <chr> "Overweight", "Overweight", "Overweight", "Overweight",~
## $ Smoking_Status <chr> "Non-smoker", "Non-smoker", "Moderate (6-15)", "Non-smo~
bweight <- haven::read_sas("bweight.sas7bdat")
glimpse(bweight)
## Rows: 50,000
## Columns: 10
## $ Weight     <dbl> 4111, 3997, 3572, 1956, 3515, 3757, 2977, 3884, 3629, 3062,~
## $ Black      <dbl> 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,~
## $ Married    <dbl> 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1,~
## $ Boy        <dbl> 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0,~
## $ MomAge     <dbl> -3, 1, 0, -1, -6, 3, -5, -5, 6, -1, -2, -6, 0, 1, 1, 7, -4,~
## $ MomSmoke   <dbl> 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0,~
## $ CigsPerDay <dbl> 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 4, 0, 0, 10, 0, 0, 0, 0, 0, 0~
## $ MomWtGain  <dbl> -16, 2, -3, -5, -20, 0, 5, 0, -5, 6, 22, -1, 7, -6, 10, 15,~
## $ Visit      <dbl> 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,~
## $ MomEdLevel <dbl> 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1,~
# test reading local files 
# excel file import 
read_excel("Grades.xlsx") %>%
  glimpse()
## Rows: 3
## Columns: 8
## $ Name    <chr> "Jones", "Hildebrand", "O'Brien"
## $ ID      <dbl> 12345, 22222, 33333
## $ Quiz1   <dbl> 88, 95, 76
## $ Quiz2   <dbl> 80, 92, 78
## $ Midterm <dbl> 76, 91, 79
## $ Quiz3   <dbl> 88, 94, 81
## $ Quiz4   <dbl> 90, 90, 83
## $ Final   <dbl> 82, 96, 80
# excel file with odd fields names import - backticked
read_excel("Grades2.xlsx") %>%
  glimpse()
## Rows: 3
## Columns: 8
## $ `Stuent Name` <chr> "Jones", "Hildebrand", "O'Brien"
## $ ID            <dbl> 12345, 22222, 33333
## $ `Quiz 1`      <dbl> 88, 95, 76
## $ `Quiz 2`      <dbl> 80, 92, 78
## $ `Mid Term`    <dbl> 76, 91, 79
## $ `Quiz 3`      <dbl> 88, 94, 81
## $ `Quiz 4`      <dbl> 90, 90, 83
## $ `2015Final`   <dbl> 82, 96, 80
# excel file with odd fields names import - rename on the fly
read_excel("Grades2.xlsx") %>%
  rename(
    Quiz_1 = `Quiz 1`,
    Quiz_2 = `Quiz 2`,
    Midterm = `Mid Term`,
    Quiz_3 = `Quiz 3`,
    Quiz_4 = `Quiz 4`,
    Final_2015 = `2015Final`
    ) %>%
  glimpse()
## Rows: 3
## Columns: 8
## $ `Stuent Name` <chr> "Jones", "Hildebrand", "O'Brien"
## $ ID            <dbl> 12345, 22222, 33333
## $ Quiz_1        <dbl> 88, 95, 76
## $ Quiz_2        <dbl> 80, 92, 78
## $ Midterm       <dbl> 76, 91, 79
## $ Quiz_3        <dbl> 88, 94, 81
## $ Quiz_4        <dbl> 90, 90, 83
## $ Final_2015    <dbl> 82, 96, 80
# csv file import 
read_csv("Grades.csv") %>%
  glimpse()
## Rows: 3 Columns: 8
## -- Column specification --------------------------------------------------------
## Delimiter: ","
## chr (1): Name
## dbl (7): ID, Quiz1, Quiz2, Midterm, Quiz3, Quiz4, Final
## 
## i Use `spec()` to retrieve the full column specification for this data.
## i Specify the column types or set `show_col_types = FALSE` to quiet this message.
## Rows: 3
## Columns: 8
## $ Name    <chr> "Jones", "Hildebrand", "O'Brien"
## $ ID      <dbl> 12345, 22222, 33333
## $ Quiz1   <dbl> 88, 95, 76
## $ Quiz2   <dbl> 80, 92, 78
## $ Midterm <dbl> 76, 91, 79
## $ Quiz3   <dbl> 88, 94, 81
## $ Quiz4   <dbl> 90, 90, 83
## $ Final   <dbl> 82, 96, 80
# txt file import space delimiter treat multiples as one
# read_delim with delim = " " will trip up on multiple spaces
# added period in the na spec list as per SAS input text file
# columns has no headings, and rename default names
read_table("Health_List.txt",
  col_names = F, na = c("", "NA", ".")) %>%
  rename(
    Subj = X1,
    Gender = X2,
    Age = X3,
    Heart_Rate = X4,
    SBP = X5,
    DBP = X6,
    Chol = X7
    ) %>%
  glimpse()
## 
## -- Column specification --------------------------------------------------------
## cols(
##   X1 = col_character(),
##   X2 = col_character(),
##   X3 = col_double(),
##   X4 = col_double(),
##   X5 = col_double(),
##   X6 = col_double(),
##   X7 = col_double()
## )
## Rows: 6
## Columns: 7
## $ Subj       <chr> "001", "002", "003", "004", "005", "006"
## $ Gender     <chr> "M", "F", "F", "M", "F", "F"
## $ Age        <dbl> 23, 55, 18, 80, 34, 38
## $ Heart_Rate <dbl> 68, 72, 58, 82, 62, 78
## $ SBP        <dbl> 120, 180, 118, NA, 128, 108
## $ DBP        <dbl> 90, 90, 72, NA, 80, 68
## $ Chol       <dbl> 128, 170, 122, 220, NA, 220
# fixed width txt file import
read_fwf("Health.txt", 
  fwf_cols(
    Subj = 3, 
    Gender = 1,
    Age = 2,
    Heart_Rate = 2,
    SBP = 3,
    DBP = 3,
    Chol = 3
    )) %>%
  glimpse()
## Rows: 5 Columns: 7
## -- Column specification --------------------------------------------------------
## 
## chr (2): Subj, Gender
## dbl (5): Age, Heart_Rate, SBP, DBP, Chol
## 
## i Use `spec()` to retrieve the full column specification for this data.
## i Specify the column types or set `show_col_types = FALSE` to quiet this message.
## Rows: 5
## Columns: 7
## $ Subj       <chr> "001", "002", "003", "004", "005"
## $ Gender     <chr> "M", "F", "F", "M", "F"
## $ Age        <dbl> 23, 55, 18, 80, 34
## $ Heart_Rate <dbl> 68, 72, 58, 82, 62
## $ SBP        <dbl> 120, 180, 118, NA, 128
## $ DBP        <dbl> 90, 90, 72, NA, 80
## $ Chol       <dbl> 128, 170, 122, 220, NA
# tab delimited text file with no column names
read_tsv("Blood_Pressure.txt",
  col_names = F) %>%
  rename(
    Drug = X1,
    Subj = X2,
    Gender = X3,
    SBP = X4,
    DBP = X5
    ) %>%
  glimpse()
## Rows: 60 Columns: 5
## -- Column specification --------------------------------------------------------
## Delimiter: "\t"
## chr (2): X1, X3
## dbl (3): X2, X4, X5
## 
## i Use `spec()` to retrieve the full column specification for this data.
## i Specify the column types or set `show_col_types = FALSE` to quiet this message.
## Rows: 60
## Columns: 5
## $ Drug   <chr> "Placebo", "Placebo", "Placebo", "Placebo", "Placebo", "Placebo~
## $ Subj   <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, ~
## $ Gender <chr> "F", "M", "F", NA, "F", "M", "F", "F", "F", "M", "F", "F", "M",~
## $ SBP    <dbl> 138, 124, 150, 136, NA, 132, 130, 146, 134, 138, 144, 130, 134,~
## $ DBP    <dbl> 86, 82, 72, 84, NA, 84, 84, 88, 82, 88, 84, 88, 80, 90, NA, 88,~
# Import / transform external files for exercises in subsequent chapters

# Chapter 5: Distribution Practice 5-3
blood_pressure <- read_excel("Blood_Pressure.xlsx")
glimpse(blood_pressure)
## Rows: 60
## Columns: 5
## $ Drug   <chr> "Placebo", "Placebo", "Placebo", "Placebo", "Placebo", "Placebo~
## $ Subj   <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, ~
## $ Gender <chr> "F", "M", "F", NA, "F", "M", "F", "F", "F", "M", "F", "F", "M",~
## $ SBP    <dbl> 138, 124, 150, 136, NA, 132, 130, 146, 134, 138, 144, 130, 134,~
## $ DBP    <dbl> 86, 82, 72, 84, NA, 84, 84, 88, 82, 88, 84, 88, 80, 90, NA, 88,~
# Chapter 6: One-Sample Tests - Perch 
perch <- read_excel("Perch.xlsx")
glimpse(perch)
## Rows: 56
## Columns: 3
## $ Weight <dbl> 5.9, 32.0, 40.0, 51.5, 70.0, 100.0, 78.0, 80.0, 85.0, 85.0, 110~
## $ Height <dbl> 2.1120, 3.5280, 3.8240, 4.5924, 4.5880, 5.2224, 5.1992, 5.6358,~
## $ Width  <dbl> 1.4080, 1.9992, 2.4320, 2.6316, 2.9415, 3.3216, 3.1234, 3.0502,~
# Paired t Test - Yoga 
yoga <- read_excel("Yoga.xlsx")
glimpse(yoga)
## Rows: 9
## Columns: 3
## $ Subj   <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9
## $ Before <dbl> 78, 68, 76, 58, 83, 80, 69, 77, 77
## $ After  <dbl> 74, 68, 70, 57, 73, 77, 61, 76, 72
# Chapter 8: One-way ANOVA with test for Tukey multiple comparisons 8.6
lvef <- as.character("
  55 58 62 48 57 57 80 40 55 52
  57 65 55 78 57 84 72 80 78 81
  60 60 65 67 48 62 64 70 57 40
") %>% 
  read_table(col_names = F, na = c("", "NA")) %>% 
  tibble::rownames_to_column() %>%
  pivot_longer(-rowname) %>%
  mutate(
    Group = case_when(
      rowname == "1" ~ "Placebo"
      , rowname == "2" ~ "Calcium"
      , rowname == "3" ~ "Lasix"
      , TRUE ~ rowname
      )
    , Subj = str_remove_all(name,"X")
    ) %>%
  rename(LVEF = value) %>%
  select(Group, Subj, LVEF)
glimpse(lvef)
## Rows: 30
## Columns: 3
## $ Group <chr> "Placebo", "Placebo", "Placebo", "Placebo", "Placebo", "Placebo"~
## $ Subj  <chr> "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "1", "2", "3"~
## $ LVEF  <dbl> 55, 58, 62, 48, 57, 57, 80, 40, 55, 52, 57, 65, 55, 78, 57, 84, ~
# Chapter 9: create 25 pct sample w/o replacement for Two-Way Anova
# The SASHELP library contains the Bweight dataset containing birth weights for 50,000 babies, along with several variables believed to be related to birth weight, such as race (coded as black or not black), mother's smoking status (smoking or non-smoking), and marital status.
# Weight (in grams) is the Dependent variable
# Black (0 = not black, 1=black)
# MomSmoke (0=no, 1=yes)
# Married (0=no, 1=yes)
set.seed(13579)
Birth_Wt_Sample <- bweight %>%
  slice_sample(n = as.numeric(count(bweight)*.25), replace = FALSE)
summary(Birth_Wt_Sample) 
##      Weight         Black           Married            Boy        
##  Min.   : 240   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:3062   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :3402   Median :0.0000   Median :1.0000   Median :1.0000  
##  Mean   :3368   Mean   :0.1655   Mean   :0.7129   Mean   :0.5151  
##  3rd Qu.:3714   3rd Qu.:0.0000   3rd Qu.:1.0000   3rd Qu.:1.0000  
##  Max.   :5970   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
##      MomAge           MomSmoke        CigsPerDay       MomWtGain       
##  Min.   :-9.0000   Min.   :0.0000   Min.   : 0.000   Min.   :-30.0000  
##  1st Qu.:-4.0000   1st Qu.:0.0000   1st Qu.: 0.000   1st Qu.: -8.0000  
##  Median : 0.0000   Median :0.0000   Median : 0.000   Median :  0.0000  
##  Mean   : 0.4449   Mean   :0.1308   Mean   : 1.482   Mean   :  0.7021  
##  3rd Qu.: 5.0000   3rd Qu.:0.0000   3rd Qu.: 0.000   3rd Qu.:  9.0000  
##  Max.   :18.0000   Max.   :1.0000   Max.   :40.000   Max.   : 68.0000  
##      Visit         MomEdLevel   
##  Min.   :0.000   Min.   :0.000  
##  1st Qu.:3.000   1st Qu.:0.000  
##  Median :3.000   Median :1.000  
##  Mean   :2.701   Mean   :1.218  
##  3rd Qu.:3.000   3rd Qu.:2.000  
##  Max.   :3.000   Max.   :3.000
# writexl::write_xlsx(Birth_Wt_Sample, "Birth_Wt_Sample_R.xlsx")
set.seed(123456)
# results of this R sample extract snippet does not match the equivalent SAS proc surveyselect with same parameters and random seed, so re-do extract using LOJ to sas extract export.
Birth_Wt_Sample_SAS <- read_excel("Birth_Wt_Sample.xlsx")
summary(Birth_Wt_Sample_SAS) 
##      Weight         Black           Married            Boy        
##  Min.   : 322   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:3062   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :3402   Median :0.0000   Median :1.0000   Median :1.0000  
##  Mean   :3373   Mean   :0.1578   Mean   :0.7095   Mean   :0.5106  
##  3rd Qu.:3714   3rd Qu.:0.0000   3rd Qu.:1.0000   3rd Qu.:1.0000  
##  Max.   :5970   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
##      MomAge           MomSmoke        CigsPerDay       MomWtGain       
##  Min.   :-9.0000   Min.   :0.0000   Min.   : 0.000   Min.   :-30.0000  
##  1st Qu.:-4.0000   1st Qu.:0.0000   1st Qu.: 0.000   1st Qu.: -8.0000  
##  Median : 0.0000   Median :0.0000   Median : 0.000   Median :  0.0000  
##  Mean   : 0.3814   Mean   :0.1319   Mean   : 1.479   Mean   :  0.6146  
##  3rd Qu.: 5.0000   3rd Qu.:0.0000   3rd Qu.: 0.000   3rd Qu.:  9.0000  
##  Max.   :18.0000   Max.   :1.0000   Max.   :40.000   Max.   : 68.0000  
##      Visit         MomEdLevel  
##  Min.   :0.000   Min.   :0.00  
##  1st Qu.:3.000   1st Qu.:0.00  
##  Median :3.000   Median :1.00  
##  Mean   :2.699   Mean   :1.22  
##  3rd Qu.:3.000   3rd Qu.:2.00  
##  Max.   :3.000   Max.   :3.00
# Chapter 10: Correlation - Exercise 
exercise <- read_excel("Exercise.xls")
glimpse(exercise)
## Rows: 50
## Columns: 6
## $ Subj       <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, ~
## $ Age        <dbl> 68, 64, 76, 44, 55, 57, 64, 30, 35, 49, 63, 63, 19, 51, 54,~
## $ Pushups    <dbl> 19, 36, 11, 35, 24, 14, 21, 48, 25, 9, 51, 30, 34, 23, 7, 4~
## $ Rest_Pulse <dbl> 75, 61, 74, 59, 76, 74, 69, 60, 55, 88, 55, 73, 65, 66, 59,~
## $ Max_Pulse  <dbl> 124, 107, 115, 111, 115, 121, 106, 114, 107, 137, 102, 126,~
## $ Run_Pulse  <dbl> 121, 110, 105, 108, 110, 118, 103, 110, 107, 134, 103, 125,~
# Chapter 12: Binary Logistic Regression
# Create a categorical weight variable from arbitrary median 3402 gram cutoff using non-missing weight from previously-created sample
high_low <- Birth_Wt_Sample_SAS %>%
  filter(!is.na(Weight)) %>%
  mutate(Wt_Group = case_when(Weight < 3402 ~ 1,
                              TRUE ~ 0))
glimpse(high_low)
## Rows: 12,500
## Columns: 11
## $ Weight     <dbl> 3430, 3657, 4054, 4536, 3295, 3458, 3714, 2807, 3625, 3884,~
## $ Black      <dbl> 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,~
## $ Married    <dbl> 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1,~
## $ Boy        <dbl> 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0,~
## $ MomAge     <dbl> -4, 6, -5, 3, 6, 8, 2, -5, 2, -2, -6, 6, 7, -8, -1, -9, -9,~
## $ MomSmoke   <dbl> 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1,~
## $ CigsPerDay <dbl> 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 4~
## $ MomWtGain  <dbl> -6, 15, 21, -1, -29, -18, 25, 13, 0, -10, 12, -9, 7, -7, 23~
## $ Visit      <dbl> 3, 3, 3, 3, 3, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,~
## $ MomEdLevel <dbl> 0, 0, 2, 3, 2, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 3, 2, 2, 3,~
## $ Wt_Group   <dbl> 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0,~
# Chapter 13: Prepare generated dataset Heart_Attack
Heart_Attack <- read_excel("Heart_Attack.xlsx") %>% 
  mutate(Gender_ = case_when(Gender == 'F' ~ 'Female',
                             Gender == 'M' ~ 'Male',
                             TRUE ~ Gender),
  High_Chol_ = case_when(High_Chol == 0 ~ 'No',
                         High_Chol == 1 ~ 'Yes',
                         TRUE ~ as.character(High_Chol)),
  Heart_Attack_ = case_when(Heart_Attack == 0 ~ 'No',
                            Heart_Attack == 1 ~ 'Yes',
                            TRUE ~ as.character(Heart_Attack)),
  Age_Group_ = case_when(Age_Group == 1 ~ '< 60',
                         Age_Group == 2 ~ '60-70',
                         Age_Group == 3 ~ '71+',
                         TRUE ~ as.character(Age_Group))
  )
glimpse(Heart_Attack)
## Rows: 500
## Columns: 10
## $ Gender        <chr> "F", "M", "F", "M", "F", "M", "F", "M", "F", "M", "F", "~
## $ Age           <dbl> 63, 69, 69, 59, 71, 50, 57, 75, 60, 52, 80, 54, 75, 57, ~
## $ Age_Group     <dbl> 2, 2, 2, 1, 3, 1, 1, 3, 2, 1, 3, 1, 3, 1, 2, 2, 2, 2, 1,~
## $ Chol          <dbl> 211, 249, 139, 239, 195, 193, 179, 186, 164, 237, 178, 2~
## $ High_Chol     <dbl> 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1,~
## $ Heart_Attack  <dbl> 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0,~
## $ Gender_       <chr> "Female", "Male", "Female", "Male", "Female", "Male", "F~
## $ High_Chol_    <chr> "Yes", "Yes", "No", "Yes", "No", "No", "No", "No", "No",~
## $ Heart_Attack_ <chr> "No", "No", "No", "No", "No", "No", "No", "Yes", "No", "~
## $ Age_Group_    <chr> "60-70", "60-70", "60-70", "< 60", "71+", "< 60", "< 60"~

Chapter 5: Descriptive Statistics - Univariate Analysis

Descriptive Statistics for Continuous Variables

R Code:

# summary(heart) 
# summary(heart[c('Weight','Height','Systolic','Diastolic')]) 
# describe(heart)
# Hmisc::describe(heart[c('Weight','Height','Systolic','Diastolic')],na.rm=TRUE)
psych::describe(heart[c('Weight','Height','Systolic','Diastolic')],na.rm=TRUE)
##           vars    n   mean    sd median trimmed   mad  min   max range skew
## Weight       1 5203 153.09 28.92  150.0  151.66 29.65 67.0 300.0   233 0.56
## Height       2 5203  64.81  3.58   64.5   64.74  3.71 51.5  76.5    25 0.18
## Systolic     3 5209 136.91 23.74  132.0  134.35 17.79 82.0 300.0   218 1.49
## Diastolic    4 5209  85.36 12.97   84.0   84.44 11.86 50.0 160.0   110 0.88
##           kurtosis   se
## Weight        0.52 0.40
## Height       -0.40 0.05
## Systolic      4.22 0.33
## Diastolic     1.85 0.18
cat(c("95% Confidence Intervals for Weight 2.5%,",
  "97.5%: \n"),
lsr::ciMean(heart$Weight, conf=.95, na.rm=TRUE))
## 95% Confidence Intervals for Weight 2.5%, 97.5%: 
##  152.3008 153.8726
cat(c("95% Confidence Intervals for Height 2.5%,",
  "97.5%: \n"),
lsr::ciMean(heart$Height, conf=.95, na.rm=TRUE))
## 95% Confidence Intervals for Height 2.5%, 97.5%: 
##  64.71581 64.91056
cat(c("95% Confidence Intervals for Systolic 2.5%,",
  "97.5%: \n"),
lsr::ciMean(heart$Systolic, conf=.95, na.rm=TRUE))
## 95% Confidence Intervals for Systolic 2.5%, 97.5%: 
##  136.2647 137.5544
cat(c("95% Confidence Intervals for Diastolic 2.5%,",
  "97.5%: \n"),
lsr::ciMean(heart$Diastolic, conf=.95, na.rm=TRUE))
## 95% Confidence Intervals for Diastolic 2.5%, 97.5%: 
##  85.00623 85.71099
# Visualize distribution of Weight
heart %>% 
  select(Weight) %>%
  filter(!is.na(Weight)) %>%
  ggplot(aes(x=Weight)) +
  geom_histogram(aes(y=(..count..)/sum(..count..)),
    bins=24, color="black", fill="lightgray") +
  labs(title="Descriptive Statistics for Continuous Variables",
         y="Percentage", x= "Weight") + 
  scale_x_continuous(breaks = seq(70, 290, 20)) + 
  scale_y_continuous(breaks = seq(0, .15, .025),
    labels = scales::percent) + 
  theme_minimal()

heart %>% 
  select(Weight) %>%
  filter(!is.na(Weight)) %>%
  ggplot(aes(x=Weight)) +
  geom_histogram(aes(y=..density..),
    bins=24, color="black", fill="lightgray") +
  labs(title="Descriptive Statistics for Continuous Variables",
         y="Density", x= "Weight") +
  scale_x_continuous(breaks = seq(70, 290, 20)) +  
  stat_function(fun = dnorm, args = list(
    mean=mean(heart$Weight,na.rm=TRUE),
    sd=sd(heart$Weight,na.rm=TRUE)),
    col='red', lwd=2, lty='dashed') + 
  theme_minimal()

heart %>% 
  select(Weight) %>%
  filter(!is.na(Weight)) %>%
  ggplot(aes(y=Weight, x="")) +
  stat_boxplot(geom="errorbar", width=0.15) +
  geom_boxplot(color="black", fill="lightgray") +
#  geom_point() +
  stat_summary(fun="mean", pch=13, color="red", size=1) +
  labs(title="Descriptive Statistics for Continuous Variables",
         x="", y= "Weight") + 
  scale_y_continuous(breaks = seq(70, 290, 20)) + 
  theme_minimal() +
  coord_flip()
## Warning: Removed 1 rows containing missing values (geom_segment).

# Visualize distribution of Systolic
heart %>% 
  select(Systolic) %>%
  filter(!is.na(Systolic)) %>%
  ggplot(aes(x=Systolic)) +
  geom_histogram(aes(y=(..count..)/sum(..count..)),
    bins=26, color="black", fill="lightgray") +
  labs(title="Descriptive Statistics for Continuous Variables",
         y="Percentage", x= "Systolic") + 
  scale_x_continuous(breaks = seq(84, 292, 16)) + 
  scale_y_continuous(breaks = seq(0, .15, .05),
    labels = scales::percent_format(accuracy = 1L)) + 
  theme_minimal()

heart %>% 
  select(Systolic) %>%
  filter(!is.na(Systolic)) %>%
  ggplot(aes(x=Systolic)) +
  geom_histogram(aes(y=..density..),
    bins=24, color="black", fill="lightgray") +
  labs(title="Descriptive Statistics for Continuous Variables",
         y="Density", x= "Systolic") +
  scale_x_continuous(breaks = seq(84, 292, 16)) +  
  stat_function(fun = dnorm, args = list(
    mean=mean(heart$Systolic,na.rm=TRUE),
    sd=sd(heart$Systolic,na.rm=TRUE)),
    col='red', lwd=2, lty='dashed') + 
  theme_minimal()

heart %>% 
  select(Systolic) %>%
  filter(!is.na(Systolic)) %>%
  ggplot(aes(y=Systolic, x="")) +
  stat_boxplot(geom="errorbar", width=0.15) +
  geom_boxplot(color="black", fill="lightgray") +
#  geom_point() +
  stat_summary(fun="mean", pch=13, color="red", size=1) +
  labs(title="Descriptive Statistics for Continuous Variables",
         x="", y= "Systolic") + 
  scale_y_continuous(breaks = seq(84, 292, 16)) + 
  theme_minimal() +
  coord_flip()
## Warning: Removed 1 rows containing missing values (geom_segment).

##

TO BE CONTINUED - R