Supervised Machine Learning

Author

OJALA BRIAN OLOO

Linear Regression Algorithm

#clear enviroment
rm(list = ls())
#Working directory
setwd("C:/Users/USER/Desktop/JOOUST")
# Import dataset
library(readxl)
Anxiety <- read_excel("Anxiety.xlsx")

Cleaning data set:Convert character to factor variable

Anxiety$Gender<-as.factor(Anxiety$Gender)
Anxiety$FamiliyHistry<-as.factor(Anxiety$FamiliyHistry)
Anxiety$Medication<-as.factor(Anxiety$Medication)
Anxiety$Dizziness<-as.factor(Anxiety$Dizziness)
library(dplyr)

Attaching package: 'dplyr'
The following objects are masked from 'package:stats':

    filter, lag
The following objects are masked from 'package:base':

    intersect, setdiff, setequal, union

Divide data set

set.seed(2)
ind<-sample(2,nrow(Anxiety),replace = T,prob = c(0.8,0.2))
Train_dataset<-Anxiety[ind==1,]
Test_dataset<-Anxiety[ind==2,]

Exploratory Analysis

library(corrplot)
corrplot 0.95 loaded
corr <- Anxiety %>% 
  select(AnxietyAttack,Age,SleepHrs,CaffeineIntake,HeartRate) %>% 
  replace(is.na(.), 0)
correlation = cor(corr)
corrplot(correlation, type="upper", method="color", addCoef.col = "black")

Implementing Model From Training data set

Model<-lm(AnxietyAttack~Age+Gender+FamiliyHistry+Medication+SleepHrs+CaffeineIntake+HeartRate+Dizziness,data =Train_dataset )
summary(Model)

Call:
lm(formula = AnxietyAttack ~ Age + Gender + FamiliyHistry + Medication + 
    SleepHrs + CaffeineIntake + HeartRate + Dizziness, data = Train_dataset)

Residuals:
    Min      1Q  Median      3Q     Max 
-4.8937 -2.4876 -0.2633  2.4895  4.7226 

Coefficients:
                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)       5.5556910  0.1826466  30.418   <2e-16 ***
Age              -0.0040530  0.0021767  -1.862   0.0626 .  
GenderMale        0.0453431  0.0596408   0.760   0.4471    
GenderOther       0.2289252  0.1543316   1.483   0.1380    
FamiliyHistryYes  0.0366965  0.0596894   0.615   0.5387    
MedicationYes     0.0216700  0.0732075   0.296   0.7672    
SleepHrs         -0.0113479  0.0145983  -0.777   0.4370    
CaffeineIntake    0.0001757  0.0002025   0.868   0.3856    
HeartRate         0.0005990  0.0008375   0.715   0.4745    
DizzinessYes      0.0940909  0.0638457   1.474   0.1406    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.861 on 9568 degrees of freedom
Multiple R-squared:  0.001114,  Adjusted R-squared:  0.0001746 
F-statistic: 1.186 on 9 and 9568 DF,  p-value: 0.299

Optimize model

R-squared value indicates the perfection and accuracy of the predictive values.If R-square is closer to 1.0,then the linear model is best suited. In context to our Training data set model R-square is 0.001114 which is very low,therefore the trained data set model is not accurate for predication.

On the other hand,the coefficients of the covariates are not statistically significant because there p-value is above 0.05.

Model validation

predic<-predict(Model,Test_dataset)
predic
       1        2        3        4        5        6        7        8 
5.608667 5.567660 5.546457 5.562770 5.516937 5.508822 5.674886 5.518631 
       9       10       11       12       13       14       15       16 
5.523803 5.647284 5.597838 5.476738 5.530308 5.685527 5.374573 5.495984 
      17       18       19       20       21       22       23       24 
5.560071 5.591872 5.420765 5.644663 5.610245 5.510620 5.364314 5.497779 
      25       26       27       28       29       30       31       32 
5.625910 5.420671 5.627937 5.561136 5.512245 5.445776 5.394218 5.401787 
      33       34       35       36       37       38       39       40 
5.445967 5.598570 5.498213 5.504291 5.449153 5.577370 5.671011 5.619132 
      41       42       43       44       45       46       47       48 
5.364889 5.548936 5.423444 5.418655 5.534596 5.488988 5.561701 5.408094 
      49       50       51       52       53       54       55       56 
5.633099 5.487312 5.718591 5.649456 5.572739 5.787775 5.524046 5.483049 
      57       58       59       60       61       62       63       64 
5.833325 5.544461 5.440369 5.479079 5.525832 5.599989 5.622811 5.558398 
      65       66       67       68       69       70       71       72 
5.532715 5.427332 5.466073 5.678108 5.484759 5.528338 5.543118 5.630059 
      73       74       75       76       77       78       79       80 
5.521192 5.468610 5.625953 5.625652 5.460793 5.383369 5.446189 5.445489 
      81       82       83       84       85       86       87       88 
5.369855 5.439171 5.419178 5.667864 5.494138 5.675848 5.345673 5.687815 
      89       90       91       92       93       94       95       96 
5.464021 5.350775 5.572993 5.565025 5.441024 5.512733 5.593105 5.647842 
      97       98       99      100      101      102      103      104 
5.566569 5.507648 5.465332 5.401545 5.422617 5.568675 5.514203 5.542323 
     105      106      107      108      109      110      111      112 
5.666243 5.422766 5.406366 5.482165 5.487784 5.621071 5.606741 5.570371 
     113      114      115      116      117      118      119      120 
5.551435 5.546564 5.465160 5.708958 5.619910 5.570375 5.573637 5.482173 
     121      122      123      124      125      126      127      128 
5.407691 5.472653 5.432598 5.642668 5.503309 5.511448 5.463648 5.364624 
     129      130      131      132      133      134      135      136 
5.498958 5.382536 5.467698 5.355663 5.505545 5.608299 5.473808 5.447884 
     137      138      139      140      141      142      143      144 
5.414504 5.542786 5.477722 5.512949 5.548688 5.294102 5.414236 5.519177 
     145      146      147      148      149      150      151      152 
5.587118 5.595521 5.568640 5.667606 5.463231 5.550322 5.545329 5.422551 
     153      154      155      156      157      158      159      160 
5.484655 5.585264 5.530023 5.618198 5.579033 5.658970 5.551374 5.468134 
     161      162      163      164      165      166      167      168 
5.526082 5.588311 5.541651 5.615996 5.458960 5.433535 5.535755 5.481654 
     169      170      171      172      173      174      175      176 
5.467551 5.507081 5.484571 5.587442 5.474663 5.468228 5.507692 5.642981 
     177      178      179      180      181      182      183      184 
5.556454 5.484727 5.459842 5.609093 5.392981 5.474370 5.446799 5.535891 
     185      186      187      188      189      190      191      192 
5.506831 5.518861 5.561186 5.572468 5.553001 5.608288 5.469347 5.416177 
     193      194      195      196      197      198      199      200 
5.456104 5.466009 5.406865 5.562219 5.479420 5.386632 5.452986 5.321307 
     201      202      203      204      205      206      207      208 
5.462555 5.427039 5.777664 5.369577 5.543244 5.391134 5.554747 5.493760 
     209      210      211      212      213      214      215      216 
5.644009 5.561400 5.505871 5.505759 5.524462 5.650333 5.460192 5.563588 
     217      218      219      220      221      222      223      224 
5.489397 5.456569 5.601375 5.441069 5.610550 5.421031 5.647285 5.388176 
     225      226      227      228      229      230      231      232 
5.497620 5.662622 5.580849 5.374018 5.398054 5.546818 5.375333 5.495521 
     233      234      235      236      237      238      239      240 
5.532806 5.505553 5.411864 5.586629 5.578177 5.398979 5.662542 5.575572 
     241      242      243      244      245      246      247      248 
5.473378 5.598164 5.403611 5.439699 5.441731 5.338676 5.366845 5.553137 
     249      250      251      252      253      254      255      256 
5.443864 5.585983 5.505163 5.356363 5.363934 5.577391 5.579434 5.429930 
     257      258      259      260      261      262      263      264 
5.607494 5.603273 5.484578 5.502091 5.561167 5.303735 5.522813 5.470994 
     265      266      267      268      269      270      271      272 
5.536106 5.700914 5.468317 5.536463 5.504370 5.530814 5.577852 5.668059 
     273      274      275      276      277      278      279      280 
5.501666 5.468778 5.541621 5.546462 5.470321 5.571195 5.462448 5.646525 
     281      282      283      284      285      286      287      288 
5.608290 5.450091 5.332577 5.603905 5.395602 5.461600 5.580169 5.545036 
     289      290      291      292      293      294      295      296 
5.355842 5.402938 5.497199 5.652671 5.559339 5.468491 5.532304 5.568437 
     297      298      299      300      301      302      303      304 
5.537652 5.541019 5.502366 5.437827 5.519609 5.346536 5.359069 5.392076 
     305      306      307      308      309      310      311      312 
5.441527 5.368214 5.479331 5.456029 5.454168 5.540708 5.434604 5.497633 
     313      314      315      316      317      318      319      320 
5.534285 5.550883 5.505349 5.397604 5.428093 5.574440 5.430918 5.417104 
     321      322      323      324      325      326      327      328 
5.552491 5.342495 5.380011 5.632704 5.529644 5.464982 5.285107 5.569681 
     329      330      331      332      333      334      335      336 
5.590446 5.569885 5.592989 5.475691 5.528295 5.370299 5.359700 5.568331 
     337      338      339      340      341      342      343      344 
5.511110 5.481101 5.600223 5.439261 5.542913 5.448360 5.358513 5.550042 
     345      346      347      348      349      350      351      352 
5.381535 5.620830 5.646375 5.444046 5.489315 5.441158 5.433062 5.531783 
     353      354      355      356      357      358      359      360 
5.515204 5.581898 5.471024 5.581052 5.472994 5.552724 5.487227 5.483329 
     361      362      363      364      365      366      367      368 
5.466403 5.317912 5.527091 5.352773 5.418716 5.564067 5.435127 5.483160 
     369      370      371      372      373      374      375      376 
5.392475 5.487267 5.358834 5.525920 5.526611 5.435641 5.639797 5.365775 
     377      378      379      380      381      382      383      384 
5.644335 5.520807 5.472288 5.471645 5.473445 5.441618 5.462301 5.589392 
     385      386      387      388      389      390      391      392 
5.505246 5.477869 5.647210 5.492179 5.640807 5.413308 5.610200 5.512144 
     393      394      395      396      397      398      399      400 
5.540790 5.546167 5.434235 5.475944 5.581310 5.441732 5.569173 5.460057 
     401      402      403      404      405      406      407      408 
5.555114 5.437690 5.567652 5.432829 5.512064 5.413637 5.586697 5.330667 
     409      410      411      412      413      414      415      416 
5.782127 5.655184 5.381779 5.478674 5.478216 5.734186 5.496757 5.460673 
     417      418      419      420      421      422      423      424 
5.565342 5.557095 5.556458 5.513652 5.451519 5.546423 5.604997 5.535341 
     425      426      427      428      429      430      431      432 
5.610204 5.462369 5.359868 5.428182 5.621660 5.600655 5.493158 5.704207 
     433      434      435      436      437      438      439      440 
5.465823 5.283180 5.461938 5.613586 5.445492 5.561014 5.330244 5.555329 
     441      442      443      444      445      446      447      448 
5.613256 5.592248 5.446396 5.420850 5.414230 5.421998 5.471405 5.487711 
     449      450      451      452      453      454      455      456 
5.704005 5.553372 5.398693 5.358945 5.544308 5.698700 5.483333 5.382534 
     457      458      459      460      461      462      463      464 
5.551866 5.433372 5.536288 5.546260 5.476195 5.411173 5.442173 5.492446 
     465      466      467      468      469      470      471      472 
5.353543 5.549579 5.563978 5.361965 5.573305 5.461101 5.426966 5.498020 
     473      474      475      476      477      478      479      480 
5.656327 5.447653 5.362866 5.388954 5.488685 5.545852 5.492858 5.382015 
     481      482      483      484      485      486      487      488 
5.465670 5.461713 5.467957 5.421595 5.615459 5.464954 5.421449 5.437118 
     489      490      491      492      493      494      495      496 
5.485828 5.351639 5.430033 5.361469 5.379019 5.436290 5.611388 5.388536 
     497      498      499      500      501      502      503      504 
5.500954 5.504722 5.478906 5.552935 5.563341 5.569541 5.338792 5.391059 
     505      506      507      508      509      510      511      512 
5.654733 5.622463 5.555703 5.378101 5.367360 5.650044 5.398690 5.360743 
     513      514      515      516      517      518      519      520 
5.467585 5.408297 5.541386 5.467083 5.384656 5.606600 5.450004 5.446238 
     521      522      523      524      525      526      527      528 
5.461124 5.588814 5.413080 5.505667 5.486053 5.372424 5.511890 5.526535 
     529      530      531      532      533      534      535      536 
5.538300 5.447578 5.409166 5.526491 5.430633 5.369109 5.433335 5.603903 
     537      538      539      540      541      542      543      544 
5.572155 5.523884 5.559118 5.426891 5.531628 5.417020 5.462561 5.429509 
     545      546      547      548      549      550      551      552 
5.585118 5.712634 5.481986 5.430967 5.478587 5.547790 5.431314 5.593271 
     553      554      555      556      557      558      559      560 
5.677358 5.434702 5.595788 5.529800 5.559522 5.557033 5.637159 5.479891 
     561      562      563      564      565      566      567      568 
5.446148 5.441914 5.404423 5.546929 5.551625 5.507364 5.412217 5.552551 
     569      570      571      572      573      574      575      576 
5.410011 5.409610 5.633001 5.414717 5.515397 5.309281 5.642802 5.610574 
     577      578      579      580      581      582      583      584 
5.370563 5.669118 5.626833 5.496004 5.572565 5.398851 5.457107 5.515568 
     585      586      587      588      589      590      591      592 
5.537527 5.544068 5.447965 5.560433 5.477281 5.600472 5.525655 5.483990 
     593      594      595      596      597      598      599      600 
5.516003 5.381252 5.591410 5.533952 5.570724 5.486366 5.515707 5.376056 
     601      602      603      604      605      606      607      608 
5.701828 5.425443 5.389757 5.538182 5.511976 5.429197 5.524883 5.466559 
     609      610      611      612      613      614      615      616 
5.505710 5.605507 5.426866 5.488367 5.426589 5.493231 5.440793 5.482063 
     617      618      619      620      621      622      623      624 
5.501710 5.454808 5.581223 5.421610 5.641916 5.470280 5.508393 5.510183 
     625      626      627      628      629      630      631      632 
5.631706 5.633825 5.290569 5.411847 5.542510 5.546403 5.385177 5.554033 
     633      634      635      636      637      638      639      640 
5.465647 5.563080 5.369834 5.589412 5.593070 5.400853 5.700635 5.375986 
     641      642      643      644      645      646      647      648 
5.536799 5.616702 5.462666 5.525260 5.449471 5.527075 5.840950 5.479207 
     649      650      651      652      653      654      655      656 
5.450302 5.539720 5.531600 5.475207 5.535152 5.453463 5.422270 5.465828 
     657      658      659      660      661      662      663      664 
5.564460 5.534109 5.384732 5.508543 5.360027 5.464001 5.422132 5.451196 
     665      666      667      668      669      670      671      672 
5.455238 5.376834 5.471704 5.578258 5.418060 5.520724 5.397895 5.405504 
     673      674      675      676      677      678      679      680 
5.523957 5.504885 5.354766 5.319179 5.508028 5.634172 5.346124 5.439580 
     681      682      683      684      685      686      687      688 
5.566260 5.434729 5.679168 5.398274 5.389868 5.690191 5.314628 5.474858 
     689      690      691      692      693      694      695      696 
5.434575 5.422192 5.331408 5.473123 5.431476 5.619445 5.461407 5.526440 
     697      698      699      700      701      702      703      704 
5.521629 5.572190 5.542095 5.542683 5.653962 5.499926 5.483097 5.504782 
     705      706      707      708      709      710      711      712 
5.352134 5.440416 5.387901 5.518698 5.539767 5.715572 5.424183 5.426100 
     713      714      715      716      717      718      719      720 
5.538166 5.592524 5.404432 5.519967 5.459677 5.621928 5.549270 5.599766 
     721      722      723      724      725      726      727      728 
5.459258 5.457800 5.624532 5.513532 5.377635 5.503015 5.687815 5.555997 
     729      730      731      732      733      734      735      736 
5.312091 5.699225 5.585490 5.603357 5.470418 5.348428 5.602068 5.394018 
     737      738      739      740      741      742      743      744 
5.496090 5.376476 5.371106 5.544661 5.581506 5.448460 5.467528 5.679594 
     745      746      747      748      749      750      751      752 
5.544001 5.430752 5.380344 5.540295 5.518843 5.569407 5.645654 5.497678 
     753      754      755      756      757      758      759      760 
5.596353 5.594979 5.400149 5.554979 5.376834 5.466968 5.456661 5.575777 
     761      762      763      764      765      766      767      768 
5.503163 5.295978 5.453957 5.429756 5.472539 5.546680 5.670231 5.476722 
     769      770      771      772      773      774      775      776 
5.446431 5.416093 5.554903 5.431528 5.510070 5.495201 5.480100 5.389102 
     777      778      779      780      781      782      783      784 
5.484829 5.389518 5.870446 5.464220 5.542125 5.636038 5.327508 5.642519 
     785      786      787      788      789      790      791      792 
5.787449 5.417618 5.467927 5.555267 5.492223 5.443565 5.454126 5.618103 
     793      794      795      796      797      798      799      800 
5.708573 5.347148 5.642713 5.590827 5.583819 5.852208 5.598270 5.496502 
     801      802      803      804      805      806      807      808 
5.436726 5.747849 5.412035 5.450321 5.502645 5.453220 5.397826 5.551833 
     809      810      811      812      813      814      815      816 
5.532300 5.348198 5.608438 5.472352 5.516603 5.475898 5.452556 5.588580 
     817      818      819      820      821      822      823      824 
5.445953 5.505214 5.401485 5.578966 5.693572 5.510185 5.458532 5.521363 
     825      826      827      828      829      830      831      832 
5.606827 5.426914 5.507017 5.548051 5.498577 5.459189 5.354811 5.475382 
     833      834      835      836      837      838      839      840 
5.511826 5.475099 5.517649 5.559130 5.613506 5.434006 5.456936 5.572789 
     841      842      843      844      845      846      847      848 
5.487940 5.574947 5.569484 5.396092 5.451933 5.623084 5.452040 5.492079 
     849      850      851      852      853      854      855      856 
5.680249 5.485720 5.367226 5.531261 5.467806 5.656710 5.468104 5.437095 
     857      858      859      860      861      862      863      864 
5.439025 5.595740 5.505838 5.436945 5.511333 5.535720 5.569750 5.762156 
     865      866      867      868      869      870      871      872 
5.509685 5.490642 5.523413 5.471344 5.411420 5.476334 5.383082 5.457288 
     873      874      875      876      877      878      879      880 
5.548142 5.472085 5.497299 5.362777 5.434558 5.539651 5.497198 5.438223 
     881      882      883      884      885      886      887      888 
5.496765 5.688073 5.333837 5.463551 5.902287 5.294836 5.618804 5.475611 
     889      890      891      892      893      894      895      896 
5.560708 5.598227 5.626058 5.521959 5.625717 5.530375 5.494451 5.792197 
     897      898      899      900      901      902      903      904 
5.523565 5.565598 5.417646 5.473432 5.408333 5.423789 5.536226 5.682601 
     905      906      907      908      909      910      911      912 
5.511731 5.579685 5.525271 5.550097 5.447105 5.481051 5.452688 5.521469 
     913      914      915      916      917      918      919      920 
5.585084 5.514416 5.461663 5.622411 5.507720 5.455341 5.465984 5.550447 
     921      922      923      924      925      926      927      928 
5.606632 5.471070 5.606052 5.570642 5.454889 5.430584 5.615102 5.541591 
     929      930      931      932      933      934      935      936 
5.580690 5.414620 5.312530 5.591448 5.442860 5.630052 5.448153 5.433997 
     937      938      939      940      941      942      943      944 
5.581868 5.554792 5.332985 5.373339 5.391008 5.516763 5.557812 5.624108 
     945      946      947      948      949      950      951      952 
5.465170 5.524501 5.423886 5.436611 5.596154 5.531829 5.498371 5.492924 
     953      954      955      956      957      958      959      960 
5.347177 5.504325 5.631963 5.543109 5.410188 5.546587 5.553477 5.427386 
     961      962      963      964      965      966      967      968 
5.665223 5.431121 5.457287 5.765834 5.632173 5.517704 5.590168 5.443487 
     969      970      971      972      973      974      975      976 
5.354909 5.520385 5.617380 5.501405 5.485190 5.489233 5.629588 5.484518 
     977      978      979      980      981      982      983      984 
5.396371 5.481452 5.337273 5.648209 5.375824 5.347134 5.469736 5.426028 
     985      986      987      988      989      990      991      992 
5.328871 5.455688 5.473609 5.588403 5.614803 5.511403 5.407177 5.619251 
     993      994      995      996      997      998      999     1000 
5.448738 5.508628 5.399087 5.555937 5.634087 5.510487 5.768266 5.749919 
    1001     1002     1003     1004     1005     1006     1007     1008 
5.348537 5.381246 5.449438 5.426552 5.620357 5.634718 5.295622 5.563845 
    1009     1010     1011     1012     1013     1014     1015     1016 
5.548745 5.669448 5.569720 5.633811 5.607706 5.654699 5.532569 5.500254 
    1017     1018     1019     1020     1021     1022     1023     1024 
5.469145 5.534891 5.597642 5.611159 5.823954 5.531009 5.486536 5.636311 
    1025     1026     1027     1028     1029     1030     1031     1032 
5.393809 5.474558 5.607496 5.499249 5.595855 5.572326 5.643718 5.522265 
    1033     1034     1035     1036     1037     1038     1039     1040 
5.409606 5.507035 5.608736 5.430268 5.535496 5.484588 5.538149 5.415679 
    1041     1042     1043     1044     1045     1046     1047     1048 
5.518940 5.704041 5.580791 5.653541 5.402621 5.333989 5.486816 5.460035 
    1049     1050     1051     1052     1053     1054     1055     1056 
5.534092 5.491447 5.417143 5.486992 5.725663 5.541049 5.626454 5.458756 
    1057     1058     1059     1060     1061     1062     1063     1064 
5.485872 5.587676 5.542062 5.506193 5.495568 5.419821 5.342538 5.559342 
    1065     1066     1067     1068     1069     1070     1071     1072 
5.400048 5.492764 5.715775 5.411798 5.443562 5.575182 5.403321 5.439110 
    1073     1074     1075     1076     1077     1078     1079     1080 
5.628729 5.575303 5.513984 5.444867 5.472142 5.522870 5.450822 5.525760 
    1081     1082     1083     1084     1085     1086     1087     1088 
5.644924 5.437989 5.359467 5.522881 5.726319 5.380099 5.535146 5.461663 
    1089     1090     1091     1092     1093     1094     1095     1096 
5.452952 5.481020 5.519308 5.589865 5.500359 5.639685 5.547345 5.520370 
    1097     1098     1099     1100     1101     1102     1103     1104 
5.572152 5.467393 5.398354 5.728184 5.624594 5.533000 5.561445 5.619387 
    1105     1106     1107     1108     1109     1110     1111     1112 
5.319865 5.296596 5.429408 5.513627 5.542534 5.470546 5.572507 5.550928 
    1113     1114     1115     1116     1117     1118     1119     1120 
5.590103 5.543470 5.517712 5.545206 5.444308 5.454132 5.690574 5.584527 
    1121     1122     1123     1124     1125     1126     1127     1128 
5.676603 5.435543 5.448207 5.488629 5.442223 5.382852 5.422223 5.493547 
    1129     1130     1131     1132     1133     1134     1135     1136 
5.330401 5.443034 5.713248 5.531347 5.633103 5.468422 5.647227 5.512218 
    1137     1138     1139     1140     1141     1142     1143     1144 
5.406790 5.424435 5.477026 5.675948 5.541237 5.564065 5.441092 5.529721 
    1145     1146     1147     1148     1149     1150     1151     1152 
5.416351 5.588544 5.296492 5.609741 5.443600 5.521784 5.414645 5.617000 
    1153     1154     1155     1156     1157     1158     1159     1160 
5.451909 5.445218 5.463078 5.549167 5.569640 5.328800 5.321895 5.532436 
    1161     1162     1163     1164     1165     1166     1167     1168 
5.544056 5.530876 5.345908 5.403359 5.410530 5.408845 5.613148 5.439818 
    1169     1170     1171     1172     1173     1174     1175     1176 
5.405407 5.604529 5.755539 5.477894 5.478638 5.412771 5.402970 5.455730 
    1177     1178     1179     1180     1181     1182     1183     1184 
5.490070 5.565481 5.530715 5.558035 5.818908 5.688307 5.471722 5.541132 
    1185     1186     1187     1188     1189     1190     1191     1192 
5.564270 5.555449 5.324069 5.467378 5.468080 5.301024 5.757983 5.503301 
    1193     1194     1195     1196     1197     1198     1199     1200 
5.416956 5.552832 5.508869 5.354975 5.474797 5.575304 5.535963 5.500309 
    1201     1202     1203     1204     1205     1206     1207     1208 
5.470634 5.588785 5.423901 5.646753 5.411976 5.389991 5.487602 5.560368 
    1209     1210     1211     1212     1213     1214     1215     1216 
5.464994 5.466463 5.647240 5.362712 5.665291 5.634570 5.525600 5.758197 
    1217     1218     1219     1220     1221     1222     1223     1224 
5.598454 5.425610 5.619056 5.493334 5.427669 5.639046 5.584863 5.610753 
    1225     1226     1227     1228     1229     1230     1231     1232 
5.364348 5.541008 5.533285 5.444877 5.436582 5.609036 5.467070 5.563510 
    1233     1234     1235     1236     1237     1238     1239     1240 
5.571558 5.531549 5.502316 5.380927 5.687828 5.651223 5.482727 5.453442 
    1241     1242     1243     1244     1245     1246     1247     1248 
5.473287 5.411778 5.487343 5.453317 5.448027 5.562089 5.533644 5.438440 
    1249     1250     1251     1252     1253     1254     1255     1256 
5.404232 5.388516 5.447363 5.550978 5.449183 5.449079 5.269945 5.399990 
    1257     1258     1259     1260     1261     1262     1263     1264 
5.375618 5.527386 5.488513 5.388705 5.428897 5.428773 5.524358 5.697497 
    1265     1266     1267     1268     1269     1270     1271     1272 
5.507475 5.512189 5.559281 5.590957 5.394832 5.599012 5.534732 5.470318 
    1273     1274     1275     1276     1277     1278     1279     1280 
5.354575 5.460423 5.435649 5.414497 5.587809 5.548506 5.474478 5.626160 
    1281     1282     1283     1284     1285     1286     1287     1288 
5.505376 5.418613 5.415339 5.452339 5.679625 5.584905 5.397308 5.563105 
    1289     1290     1291     1292     1293     1294     1295     1296 
5.570663 5.467038 5.543252 5.407516 5.550708 5.508749 5.335368 5.375859 
    1297     1298     1299     1300     1301     1302     1303     1304 
5.410744 5.515453 5.547918 5.428478 5.397459 5.391403 5.548654 5.498156 
    1305     1306     1307     1308     1309     1310     1311     1312 
5.710090 5.575194 5.491577 5.572553 5.476791 5.477692 5.691882 5.508767 
    1313     1314     1315     1316     1317     1318     1319     1320 
5.456612 5.369883 5.421336 5.541679 5.715607 5.440784 5.448671 5.453308 
    1321     1322     1323     1324     1325     1326     1327     1328 
5.535241 5.484039 5.449408 5.596260 5.385025 5.608728 5.564902 5.385659 
    1329     1330     1331     1332     1333     1334     1335     1336 
5.579918 5.353336 5.514858 5.705993 5.507689 5.453555 5.702102 5.564146 
    1337     1338     1339     1340     1341     1342     1343     1344 
5.480211 5.596392 5.618840 5.589323 5.343654 5.447368 5.315119 5.501148 
    1345     1346     1347     1348     1349     1350     1351     1352 
5.547039 5.343925 5.344731 5.514756 5.489349 5.593869 5.448284 5.360060 
    1353     1354     1355     1356     1357     1358     1359     1360 
5.413188 5.480259 5.472164 5.608391 5.552277 5.497092 5.539784 5.438927 
    1361     1362     1363     1364     1365     1366     1367     1368 
5.480428 5.410214 5.654844 5.547503 5.470038 5.502290 5.540956 5.552577 
    1369     1370     1371     1372     1373     1374     1375     1376 
5.392898 5.489736 5.424400 5.650539 5.648651 5.469240 5.590691 5.550404 
    1377     1378     1379     1380     1381     1382     1383     1384 
5.498742 5.412734 5.429729 5.503912 5.410788 5.528159 5.444029 5.358027 
    1385     1386     1387     1388     1389     1390     1391     1392 
5.537840 5.480377 5.698079 5.506510 5.511667 5.535605 5.421956 5.497982 
    1393     1394     1395     1396     1397     1398     1399     1400 
5.520992 5.577795 5.607782 5.568243 5.438971 5.661669 5.613487 5.539220 
    1401     1402     1403     1404     1405     1406     1407     1408 
5.498278 5.596766 5.724895 5.463742 5.464366 5.471817 5.739080 5.497269 
    1409     1410     1411     1412     1413     1414     1415     1416 
5.464075 5.552109 5.366974 5.596407 5.699051 5.581831 5.389074 5.479422 
    1417     1418     1419     1420     1421     1422     1423     1424 
5.463781 5.414297 5.596894 5.511135 5.621594 5.392527 5.621697 5.506566 
    1425     1426     1427     1428     1429     1430     1431     1432 
5.388910 5.540444 5.562726 5.390923 5.563994 5.547903 5.467259 5.359943 
    1433     1434     1435     1436     1437     1438     1439     1440 
5.452128 5.550044 5.499962 5.515962 5.388762 5.633663 5.614255 5.434332 
    1441     1442     1443     1444     1445     1446     1447     1448 
5.458321 5.569964 5.390502 5.500349 5.727496 5.430838 5.488626 5.536576 
    1449     1450     1451     1452     1453     1454     1455     1456 
5.577132 5.543326 5.447128 5.567133 5.427641 5.647441 5.431912 5.412283 
    1457     1458     1459     1460     1461     1462     1463     1464 
5.490542 5.591826 5.594911 5.596776 5.343699 5.422556 5.440707 5.644660 
    1465     1466     1467     1468     1469     1470     1471     1472 
5.631287 5.542122 5.554522 5.436615 5.457258 5.541963 5.658620 5.536323 
    1473     1474     1475     1476     1477     1478     1479     1480 
5.608339 5.396663 5.572150 5.619785 5.474669 5.356702 5.434385 5.396943 
    1481     1482     1483     1484     1485     1486     1487     1488 
5.580774 5.495771 5.509599 5.419688 5.346655 5.449880 5.501169 5.445164 
    1489     1490     1491     1492     1493     1494     1495     1496 
5.718510 5.456264 5.547815 5.347979 5.578103 5.554775 5.367940 5.574841 
    1497     1498     1499     1500     1501     1502     1503     1504 
5.431594 5.436798 5.554417 5.556509 5.558343 5.440634 5.611635 5.425981 
    1505     1506     1507     1508     1509     1510     1511     1512 
5.568694 5.553725 5.580491 5.572797 5.506475 5.519172 5.713867 5.663450 
    1513     1514     1515     1516     1517     1518     1519     1520 
5.538951 5.483047 5.500919 5.550278 5.364724 5.405486 5.679903 5.586461 
    1521     1522     1523     1524     1525     1526     1527     1528 
5.522001 5.514671 5.818541 5.508524 5.565734 5.452193 5.592979 5.509188 
    1529     1530     1531     1532     1533     1534     1535     1536 
5.556907 5.454832 5.452951 5.609840 5.438484 5.588616 5.404525 5.378793 
    1537     1538     1539     1540     1541     1542     1543     1544 
5.660127 5.343180 5.440579 5.530169 5.635101 5.507154 5.436479 5.494208 
    1545     1546     1547     1548     1549     1550     1551     1552 
5.515738 5.575756 5.451243 5.476354 5.575793 5.416690 5.451406 5.545795 
    1553     1554     1555     1556     1557     1558     1559     1560 
5.597742 5.364881 5.582190 5.578824 5.524423 5.541836 5.546566 5.598876 
    1561     1562     1563     1564     1565     1566     1567     1568 
5.537494 5.557955 5.597524 5.532359 5.389989 5.448381 5.383045 5.563957 
    1569     1570     1571     1572     1573     1574     1575     1576 
5.439054 5.546669 5.580140 5.363553 5.365470 5.681177 5.551283 5.477182 
    1577     1578     1579     1580     1581     1582     1583     1584 
5.593151 5.550113 5.325025 5.374603 5.460589 5.500091 5.362018 5.551329 
    1585     1586     1587     1588     1589     1590     1591     1592 
5.542940 5.409389 5.440507 5.519379 5.522340 5.519411 5.579994 5.408480 
    1593     1594     1595     1596     1597     1598     1599     1600 
5.501748 5.569377 5.507997 5.381969 5.595309 5.347026 5.444100 5.567478 
    1601     1602     1603     1604     1605     1606     1607     1608 
5.540813 5.556066 5.631884 5.591578 5.560948 5.387318 5.403806 5.495208 
    1609     1610     1611     1612     1613     1614     1615     1616 
5.599858 5.638171 5.517038 5.525707 5.428099 5.492359 5.488949 5.517989 
    1617     1618     1619     1620     1621     1622     1623     1624 
5.455557 5.568210 5.564818 5.516930 5.364930 5.572314 5.605014 5.536067 
    1625     1626     1627     1628     1629     1630     1631     1632 
5.485532 5.467593 5.526860 5.614731 5.385915 5.450385 5.527610 5.458988 
    1633     1634     1635     1636     1637     1638     1639     1640 
5.518833 5.600823 5.531731 5.313864 5.476549 5.565370 5.496486 5.506695 
    1641     1642     1643     1644     1645     1646     1647     1648 
5.387007 5.462806 5.500105 5.609409 5.639253 5.467141 5.526360 5.656098 
    1649     1650     1651     1652     1653     1654     1655     1656 
5.668134 5.506529 5.538242 5.407301 5.530160 5.539525 5.587524 5.316037 
    1657     1658     1659     1660     1661     1662     1663     1664 
5.357630 5.527972 5.725762 5.458905 5.538052 5.606369 5.485551 5.510654 
    1665     1666     1667     1668     1669     1670     1671     1672 
5.544568 5.465605 5.578065 5.386218 5.439525 5.524616 5.712680 5.492904 
    1673     1674     1675     1676     1677     1678     1679     1680 
5.593134 5.580662 5.438211 5.510936 5.657860 5.505334 5.449062 5.407341 
    1681     1682     1683     1684     1685     1686     1687     1688 
5.367155 5.424970 5.416020 5.556875 5.435874 5.668817 5.537292 5.358130 
    1689     1690     1691     1692     1693     1694     1695     1696 
5.488743 5.687995 5.573568 5.594152 5.516539 5.490568 5.378995 5.325208 
    1697     1698     1699     1700     1701     1702     1703     1704 
5.435984 5.439217 5.646011 5.632664 5.459576 5.566911 5.619436 5.627392 
    1705     1706     1707     1708     1709     1710     1711     1712 
5.567240 5.456696 5.474683 5.520995 5.611800 5.563671 5.769686 5.609844 
    1713     1714     1715     1716     1717     1718     1719     1720 
5.495096 5.470069 5.449632 5.524962 5.481858 5.408870 5.417617 5.619454 
    1721     1722     1723     1724     1725     1726     1727     1728 
5.568144 5.426534 5.666517 5.525878 5.581377 5.522814 5.502720 5.508701 
    1729     1730     1731     1732     1733     1734     1735     1736 
5.538617 5.506151 5.654896 5.402683 5.559841 5.381731 5.395395 5.659573 
    1737     1738     1739     1740     1741     1742     1743     1744 
5.437786 5.613566 5.345701 5.530782 5.353154 5.643482 5.517651 5.457007 
    1745     1746     1747     1748     1749     1750     1751     1752 
5.520379 5.461189 5.363218 5.368535 5.611968 5.481000 5.339177 5.519484 
    1753     1754     1755     1756     1757     1758     1759     1760 
5.602394 5.414284 5.391030 5.491720 5.513186 5.429987 5.458139 5.576388 
    1761     1762     1763     1764     1765     1766     1767     1768 
5.626753 5.526404 5.506101 5.552313 5.405522 5.503155 5.641565 5.468506 
    1769     1770     1771     1772     1773     1774     1775     1776 
5.425034 5.507264 5.560686 5.570392 5.593380 5.614100 5.475397 5.658489 
    1777     1778     1779     1780     1781     1782     1783     1784 
5.339332 5.474190 5.579446 5.562901 5.469743 5.356963 5.554594 5.483523 
    1785     1786     1787     1788     1789     1790     1791     1792 
5.492552 5.582425 5.463837 5.478232 5.848182 5.432412 5.584322 5.373892 
    1793     1794     1795     1796     1797     1798     1799     1800 
5.500186 5.694287 5.477851 5.625769 5.491819 5.554556 5.536354 5.537446 
    1801     1802     1803     1804     1805     1806     1807     1808 
5.390814 5.556841 5.628615 5.496660 5.484099 5.409361 5.608179 5.544962 
    1809     1810     1811     1812     1813     1814     1815     1816 
5.630071 5.517016 5.561880 5.461858 5.413213 5.539036 5.504100 5.418598 
    1817     1818     1819     1820     1821     1822     1823     1824 
5.403153 5.413476 5.525558 5.336028 5.534272 5.426179 5.404965 5.492088 
    1825     1826     1827     1828     1829     1830     1831     1832 
5.566054 5.370963 5.513934 5.573955 5.672869 5.396501 5.439630 5.591336 
    1833     1834     1835     1836     1837     1838     1839     1840 
5.532003 5.468988 5.380770 5.502984 5.463527 5.411831 5.493732 5.534467 
    1841     1842     1843     1844     1845     1846     1847     1848 
5.530726 5.446366 5.517352 5.632514 5.458638 5.455190 5.486947 5.504354 
    1849     1850     1851     1852     1853     1854     1855     1856 
5.544835 5.358152 5.507380 5.515664 5.366625 5.659160 5.322790 5.493538 
    1857     1858     1859     1860     1861     1862     1863     1864 
5.361708 5.406431 5.489873 5.373948 5.628273 5.544194 5.385358 5.591899 
    1865     1866     1867     1868     1869     1870     1871     1872 
5.514576 5.616978 5.450833 5.477503 5.579950 5.439104 5.883458 5.363086 
    1873     1874     1875     1876     1877     1878     1879     1880 
5.389378 5.431360 5.442830 5.541550 5.490319 5.401353 5.410767 5.487949 
    1881     1882     1883     1884     1885     1886     1887     1888 
5.486280 5.502682 5.451976 5.600853 5.300039 5.558540 5.507572 5.501227 
    1889     1890     1891     1892     1893     1894     1895     1896 
5.470106 5.710133 5.490198 5.401135 5.447024 5.402171 5.523381 5.483799 
    1897     1898     1899     1900     1901     1902     1903     1904 
5.457890 5.487586 5.487374 5.640377 5.473893 5.472819 5.449995 5.376668 
    1905     1906     1907     1908     1909     1910     1911     1912 
5.523337 5.270687 5.586838 5.547334 5.442887 5.652580 5.354217 5.329296 
    1913     1914     1915     1916     1917     1918     1919     1920 
5.351904 5.534150 5.610758 5.507621 5.487083 5.505129 5.475171 5.333495 
    1921     1922     1923     1924     1925     1926     1927     1928 
5.485343 5.556259 5.586761 5.744202 5.577504 5.449744 5.489975 5.559149 
    1929     1930     1931     1932     1933     1934     1935     1936 
5.468685 5.412251 5.455896 5.470912 5.600890 5.674600 5.586394 5.533826 
    1937     1938     1939     1940     1941     1942     1943     1944 
5.434070 5.469440 5.446207 5.468951 5.724469 5.342969 5.578684 5.451588 
    1945     1946     1947     1948     1949     1950     1951     1952 
5.516177 5.324112 5.523128 5.648062 5.556588 5.442436 5.554096 5.674939 
    1953     1954     1955     1956     1957     1958     1959     1960 
5.579211 5.469075 5.448378 5.448457 5.825683 5.481194 5.487446 5.579246 
    1961     1962     1963     1964     1965     1966     1967     1968 
5.537658 5.461970 5.507949 5.522529 5.427589 5.462919 5.595882 5.486064 
    1969     1970     1971     1972     1973     1974     1975     1976 
5.612222 5.386173 5.578178 5.459163 5.282611 5.587370 5.422495 5.426448 
    1977     1978     1979     1980     1981     1982     1983     1984 
5.433253 5.506128 5.444695 5.460399 5.599220 5.474569 5.546811 5.661007 
    1985     1986     1987     1988     1989     1990     1991     1992 
5.512127 5.436284 5.569110 5.525495 5.528601 5.561027 5.303885 5.315000 
    1993     1994     1995     1996     1997     1998     1999     2000 
5.398604 5.625033 5.595360 5.781946 5.548164 5.419101 5.410601 5.534168 
    2001     2002     2003     2004     2005     2006     2007     2008 
5.441641 5.461710 5.577042 5.376131 5.461070 5.519164 5.486712 5.605238 
    2009     2010     2011     2012     2013     2014     2015     2016 
5.484965 5.584446 5.456235 5.602059 5.529277 5.467533 5.504942 5.432292 
    2017     2018     2019     2020     2021     2022     2023     2024 
5.606888 5.412889 5.531999 5.445246 5.466062 5.511600 5.663619 5.870392 
    2025     2026     2027     2028     2029     2030     2031     2032 
5.457014 5.349670 5.509013 5.370886 5.464577 5.567535 5.450421 5.652630 
    2033     2034     2035     2036     2037     2038     2039     2040 
5.464053 5.565365 5.557237 5.610757 5.561141 5.439209 5.477637 5.498663 
    2041     2042     2043     2044     2045     2046     2047     2048 
5.598702 5.543318 5.531282 5.574988 5.614195 5.620474 5.464168 5.491257 
    2049     2050     2051     2052     2053     2054     2055     2056 
5.453425 5.464462 5.277701 5.542778 5.518756 5.516824 5.465565 5.502295 
    2057     2058     2059     2060     2061     2062     2063     2064 
5.516898 5.445648 5.634901 5.511507 5.582061 5.517978 5.474503 5.622949 
    2065     2066     2067     2068     2069     2070     2071     2072 
5.403381 5.683929 5.570928 5.671351 5.484966 5.605138 5.467015 5.688608 
    2073     2074     2075     2076     2077     2078     2079     2080 
5.511278 5.412621 5.527183 5.542387 5.429199 5.544516 5.550014 5.465273 
    2081     2082     2083     2084     2085     2086     2087     2088 
5.722954 5.482504 5.548400 5.648938 5.499152 5.484634 5.655337 5.456369 
    2089     2090     2091     2092     2093     2094     2095     2096 
5.517458 5.696089 5.454350 5.395988 5.441042 5.480456 5.404097 5.594628 
    2097     2098     2099     2100     2101     2102     2103     2104 
5.521752 5.512659 5.597345 5.614409 5.481774 5.510912 5.620052 5.455369 
    2105     2106     2107     2108     2109     2110     2111     2112 
5.454954 5.383443 5.513082 5.503968 5.527451 5.446340 5.454707 5.395450 
    2113     2114     2115     2116     2117     2118     2119     2120 
5.565521 5.454352 5.603348 5.608637 5.419325 5.408609 5.523970 5.521303 
    2121     2122     2123     2124     2125     2126     2127     2128 
5.420941 5.459756 5.621172 5.624023 5.424763 5.439903 5.449339 5.464274 
    2129     2130     2131     2132     2133     2134     2135     2136 
5.486977 5.532941 5.488787 5.376778 5.456912 5.422050 5.631854 5.511041 
    2137     2138     2139     2140     2141     2142     2143     2144 
5.579528 5.382651 5.534661 5.487936 5.432507 5.464723 5.714968 5.543644 
    2145     2146     2147     2148     2149     2150     2151     2152 
5.485006 5.601286 5.385612 5.581517 5.331152 5.374947 5.410990 5.391642 
    2153     2154     2155     2156     2157     2158     2159     2160 
5.387471 5.436707 5.440737 5.455107 5.528975 5.528113 5.611580 5.469791 
    2161     2162     2163     2164     2165     2166     2167     2168 
5.496933 5.476162 5.440763 5.552308 5.525319 5.484776 5.548098 5.423217 
    2169     2170     2171     2172     2173     2174     2175     2176 
5.770596 5.523637 5.581813 5.498792 5.641547 5.362448 5.594323 5.490349 
    2177     2178     2179     2180     2181     2182     2183     2184 
5.393152 5.531024 5.441021 5.621985 5.616921 5.365012 5.390542 5.663981 
    2185     2186     2187     2188     2189     2190     2191     2192 
5.524792 5.466177 5.461740 5.472164 5.589796 5.489217 5.485867 5.332476 
    2193     2194     2195     2196     2197     2198     2199     2200 
5.446636 5.419348 5.412750 5.516799 5.432503 5.571749 5.482136 5.512765 
    2201     2202     2203     2204     2205     2206     2207     2208 
5.559007 5.453654 5.299155 5.436959 5.514721 5.523286 5.513065 5.540293 
    2209     2210     2211     2212     2213     2214     2215     2216 
5.580261 5.478119 5.515983 5.463121 5.501953 5.492175 5.587814 5.493761 
    2217     2218     2219     2220     2221     2222     2223     2224 
5.442090 5.739490 5.518637 5.416398 5.569383 5.592653 5.501006 5.536233 
    2225     2226     2227     2228     2229     2230     2231     2232 
5.486548 5.316391 5.556408 5.378196 5.470144 5.534987 5.348167 5.375580 
    2233     2234     2235     2236     2237     2238     2239     2240 
5.634242 5.347041 5.384467 5.609153 5.589375 5.328701 5.623240 5.409990 
    2241     2242     2243     2244     2245     2246     2247     2248 
5.362631 5.524259 5.616289 5.463672 5.497015 5.480187 5.485810 5.564999 
    2249     2250     2251     2252     2253     2254     2255     2256 
5.731322 5.475308 5.600827 5.424780 5.548116 5.476117 5.621473 5.745415 
    2257     2258     2259     2260     2261     2262     2263     2264 
5.544510 5.484186 5.508154 5.356096 5.393338 5.350294 5.455646 5.497413 
    2265     2266     2267     2268     2269     2270     2271     2272 
5.487491 5.433331 5.562236 5.462207 5.470819 5.450871 5.544679 5.389508 
    2273     2274     2275     2276     2277     2278     2279     2280 
5.622780 5.505572 5.559057 5.511696 5.526960 5.489114 5.547975 5.515810 
    2281     2282     2283     2284     2285     2286     2287     2288 
5.411326 5.419000 5.537115 5.480474 5.700350 5.429732 5.421928 5.395043 
    2289     2290     2291     2292     2293     2294     2295     2296 
5.317872 5.478817 5.527418 5.649854 5.418807 5.523449 5.528893 5.447327 
    2297     2298     2299     2300     2301     2302     2303     2304 
5.621522 5.452508 5.442952 5.581458 5.392669 5.677206 5.432688 5.384225 
    2305     2306     2307     2308     2309     2310     2311     2312 
5.554761 5.512884 5.510971 5.536243 5.539730 5.373045 5.441589 5.631631 
    2313     2314     2315     2316     2317     2318     2319     2320 
5.513803 5.590377 5.495468 5.493335 5.380133 5.380825 5.469100 5.346095 
    2321     2322     2323     2324     2325     2326     2327     2328 
5.505622 5.566194 5.513876 5.530787 5.774228 5.434768 5.632202 5.585158 
    2329     2330     2331     2332     2333     2334     2335     2336 
5.452681 5.655894 5.475121 5.476012 5.591250 5.414961 5.523938 5.535144 
    2337     2338     2339     2340     2341     2342     2343     2344 
5.524789 5.698688 5.733450 5.554264 5.605514 5.701599 5.431127 5.715768 
    2345     2346     2347     2348     2349     2350     2351     2352 
5.473800 5.538669 5.431253 5.574424 5.713372 5.291478 5.584451 5.429196 
    2353     2354     2355     2356     2357     2358     2359     2360 
5.514207 5.414482 5.479018 5.547402 5.423707 5.456622 5.515348 5.360135 
    2361     2362     2363     2364     2365     2366     2367     2368 
5.403660 5.516220 5.458447 5.493064 5.643697 5.711875 5.618568 5.389432 
    2369     2370     2371     2372     2373     2374     2375     2376 
5.620659 5.334539 5.369550 5.495699 5.515808 5.477686 5.644390 5.492850 
    2377     2378     2379     2380     2381     2382     2383     2384 
5.401566 5.476895 5.539760 5.267932 5.423383 5.528186 5.578067 5.684839 
    2385     2386     2387     2388     2389     2390     2391     2392 
5.553156 5.670706 5.529446 5.585241 5.637687 5.509103 5.639729 5.440606 
    2393     2394     2395     2396     2397     2398     2399     2400 
5.538195 5.595222 5.472600 5.554063 5.491470 5.691637 5.556261 5.465062 
    2401     2402     2403     2404     2405     2406     2407     2408 
5.587564 5.535273 5.553506 5.552117 5.504837 5.494494 5.526992 5.496100 
    2409     2410     2411     2412     2413     2414     2415     2416 
5.364075 5.462573 5.618755 5.412223 5.581792 5.603194 5.435767 5.478930 
    2417     2418     2419     2420     2421     2422 
5.651334 5.452128 5.537557 5.465770 5.437129 5.424375 

Comparing values using plot

plot(Test_dataset$AnxietyAttack,type = "l",lty=1.8,col="blue")
lines(predic,type = "l",col="black")

Classification Algorithm

#Clear r environment
rm(list=ls())
#Working directory
setwd("C:/Users/USER/Desktop/JOOUST")
#Load data set
library(readxl)
birth <- read_excel("birth.xlsx")

Clean the data set

birth$smoke<-as.factor(birth$smoke)
birth$urineirritability<-as.factor(birth$urineirritability)
birth$Birth_Weight<-as.factor(birth$Birth_Weight)

Divide data set

set.seed(2)
ind<-sample(2,nrow(birth),replace = T,prob = c(0.6,0.4))
Train_dataset<-birth[ind==1,]
Test_dataset<-birth[ind==2,]

Exploratory data analysis

library(table1)

Attaching package: 'table1'
The following objects are masked from 'package:base':

    units, units<-
table1(~smoke+urineirritability+`age(Yrs)`|Birth_Weight,data=birth,Total="Overall")
low weight
(N=59)
Normal Weight
(N=130)
Overall
(N=189)
smoke
No 29 (49.2%) 86 (66.2%) 115 (60.8%)
Yes 30 (50.8%) 44 (33.8%) 74 (39.2%)
urineirritability
No 45 (76.3%) 116 (89.2%) 161 (85.2%)
Yes 14 (23.7%) 14 (10.8%) 28 (14.8%)
age(Yrs)
Mean (SD) 22.3 (4.51) 23.7 (5.58) 23.2 (5.30)
Median [Min, Max] 22.0 [14.0, 34.0] 23.0 [14.0, 45.0] 23.0 [14.0, 45.0]

Implement Model

Model1<-glm(Birth_Weight~.,data =Train_dataset,family = "binomial" )
summary(Model1)

Call:
glm(formula = Birth_Weight ~ ., family = "binomial", data = Train_dataset)

Coefficients:
                     Estimate Std. Error z value Pr(>|z|)  
(Intercept)           0.44383    1.06418   0.417   0.6766  
smokeYes             -1.07550    0.42892  -2.507   0.0122 *
urineirritabilityYes -1.00561    0.54068  -1.860   0.0629 .
`age(Yrs)`            0.04552    0.04478   1.017   0.3093  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 141.34  on 114  degrees of freedom
Residual deviance: 130.80  on 111  degrees of freedom
AIC: 138.8

Number of Fisher Scoring iterations: 4

Model prediction

pred<-predict(Model1,Train_dataset,type = "response")
pred
        1         2         3         4         5         6         7         8 
0.5752186 0.5692548 0.3359758 0.8092838 0.6656398 0.6345895 0.7873107 0.7873107 
        9        10        11        12        13        14        15        16 
0.6908171 0.5468033 0.6239698 0.5863022 0.6554325 0.7004551 0.8479366 0.6402204 
       17        18        19        20        21        22        23        24 
0.8479366 0.5354999 0.8537140 0.7716659 0.7716659 0.6132297 0.8294785 0.6450798 
       25        26        27        28        29        30        31        32 
0.7048761 0.7873107 0.8162114 0.8021583 0.7873107 0.8229425 0.8092838 0.8162114 
       33        34        35        36        37        38        39        40 
0.7873107 0.8479366 0.5863022 0.8229425 0.6554325 0.5863022 0.8092838 0.5914251 
       41        42        43        44        45        46        47        48 
0.6855892 0.6023782 0.7635456 0.5241598 0.8294785 0.5692548 0.8162114 0.8092838 
       49        50        51        52        53        54        55        56 
0.8593083 0.7948341 0.8162114 0.8162114 0.8092838 0.8021583 0.5580587 0.3777328 
       57        58        59        60        61        62        63        64 
0.5241598 0.8537140 0.8537140 0.5580587 0.5580587 0.8593083 0.8229425 0.5580587 
       65        66        67        68        69        70        71        72 
0.7948341 0.8294785 0.8092838 0.5468033 0.7635456 0.8699600 0.6656398 0.7192036 
       73        74        75        76        77        78        79        80 
0.8479366 0.7635456 0.7948341 0.8358214 0.8294785 0.8846456 0.5580587 0.9236088 
       81        82        83        84        85        86        87        88 
0.4103280 0.7142572 0.6402204 0.6189921 0.8229425 0.5803805 0.6953184 0.3159758 
       89        90        91        92        93        94        95        96 
0.7635456 0.6239698 0.6132297 0.8021583 0.5863022 0.8294785 0.7873107 0.6345895 
       97        98        99       100       101       102       103       104 
0.2966344 0.3462068 0.6609138 0.3258966 0.7948341 0.5468033 0.8021583 0.6855892 
      105       106       107       108       109       110       111       112 
0.7552282 0.5692548 0.6132297 0.8162114 0.5914251 0.5354999 0.7716659 0.7948341 
      113       114       115 
0.6554325 0.6023782 0.5803805 

Model classification

Performing model classification at 50 % the probability.

classify <- function(probability) ifelse(probability < 0.5, "Normal weight","Low weight")
Birthweight <- classify(predict(Model1, Train_dataset))

Confusion matrix

After classify at threshold of 50/50 then we compare the predicted classification against the actual classification using the table() function.

The correct predictions are on the diagonal, and the off-diagonal values are where our model predicts incorrectly.

table(Train_dataset$Birth_Weight, Birthweight)
               Birthweight
                Low weight Normal weight
  low weight            19            16
  Normal Weight         59            21

The first row where the data says that birth weight is low with the first column where the model predicts that the birth weight is also low, and the data agrees, is called the true positive. The element to the right of it, where the model says birth weight is low but the data says it is not, is called the false positives and this is Type 1 error. On the other hand, the second row where the data says that birth weight is low while on the first column where the model predict that birth weight is normal is called False negative which is a type II error. Lastly, the second row where data says that birth weight is normal while on the second column where the model also predict that birth weight is normal is the True negative. The aim is to predict birth low weight.

table(Train_dataset$Birth_Weight, Birthweight,
 dnn=c("Data", "Predictions"))
               Predictions
Data            Low weight Normal weight
  low weight            19            16
  Normal Weight         59            21

Model Accuracy

It measures how many classes it gets right out of the total, so it is the diagonal values of the confusion matrix divided by the total.

confusion_matrix <- table(Train_dataset$Birth_Weight, Birthweight,
 dnn=c("Data", "Predictions"))
(accuracy <- sum(diag(confusion_matrix))/sum(confusion_matrix))
[1] 0.3478261