0.1 Code Description

The following R script generates the regresssions from the steps dataset.

1 Clear the workspace

rm(list = ls())

1.1 Load Libraries

The script begins by loading the necessary R libraries:

library(tidyverse) # For data manipulation and visualization
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr     1.1.4     ✔ readr     2.1.5
## ✔ forcats   1.0.0     ✔ stringr   1.5.1
## ✔ ggplot2   3.5.2     ✔ tibble    3.2.1
## ✔ lubridate 1.9.4     ✔ tidyr     1.3.1
## ✔ purrr     1.0.4     
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
library(rstatix) # For statistical tests
## 
## Attaching package: 'rstatix'
## 
## The following object is masked from 'package:stats':
## 
##     filter
library(car) # For Levene's test
## Loading required package: carData
## 
## Attaching package: 'car'
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## The following object is masked from 'package:dplyr':
## 
##     recode
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## The following object is masked from 'package:purrr':
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##     some
library(haven) # For reading STATA files

1.2 Load Data

The script loads the STEPS dataset

# Load the STEPS dataset from rda file
load('/Users/jamesoguta/Documents/James Oguta/My PhD Folder-2023-2025/Trainings/KenyaCVDModel/data/steps_data.rda')
# Display the first few rows of the dataset
head(steps_data)
## # A tibble: 6 × 21
##      id   psu stratum wealth      age county   sex region   bmi   smk   htn
##   <dbl> <dbl>   <dbl> <chr>     <dbl>  <dbl> <dbl> <chr>  <dbl> <dbl> <dbl>
## 1  1001    32       1 4 Fourth     39     19     1 Coast   38.7     0     0
## 2  1003    32       1 2 Second     35     19     0 Coast   20.2     1     0
## 3  1008    32       1 3 Middle     60     19     0 Coast   18.8     0     1
## 4  1011    32       1 2 Second     18     19     0 Coast   22.9     0     0
## 5  1013    32       1 4 Fourth     51     19     1 Coast   19.1     0     1
## 6  1016    32       1 5 Richest    47     19     1 Coast   34.3     0     0
## # ℹ 10 more variables: htn_treatment <dbl>, weights <dbl>, sbp <dbl>,
## #   dbp <dbl>, tc <dbl>, dm <dbl>, dm_treatment <dbl>, female <dbl>,
## #   male <dbl>, weight <dbl>

1.3 Summarising the dataset

# Summarise the dataset
summary(steps_data)
##        id              psu            stratum         wealth         
##  Min.   :  1001   Min.   :  1.00   Min.   :1.000   Length:4500       
##  1st Qu.: 51074   1st Qu.: 51.75   1st Qu.:1.000   Class :character  
##  Median :103013   Median :103.00   Median :1.000   Mode  :character  
##  Mean   :101783   Mean   :102.00   Mean   :1.488                     
##  3rd Qu.:153026   3rd Qu.:152.00   3rd Qu.:2.000                     
##  Max.   :200123   Max.   :200.00   Max.   :2.000                     
##       age           county           sex            region         
##  Min.   :16.0   Min.   : 1.00   Min.   :0.0000   Length:4500       
##  1st Qu.:27.0   1st Qu.:12.00   1st Qu.:0.0000   Class :character  
##  Median :35.0   Median :23.00   Median :1.0000   Mode  :character  
##  Mean   :37.5   Mean   :23.43   Mean   :0.6002                     
##  3rd Qu.:46.0   3rd Qu.:35.00   3rd Qu.:1.0000                     
##  Max.   :70.0   Max.   :47.00   Max.   :1.0000                     
##       bmi               smk              htn         htn_treatment    
##  Min.   :  7.942   Min.   :0.0000   Min.   :0.0000   Min.   :0.00000  
##  1st Qu.: 20.062   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.00000  
##  Median : 22.515   Median :0.0000   Median :0.0000   Median :0.00000  
##  Mean   : 23.438   Mean   :0.1229   Mean   :0.2964   Mean   :0.02622  
##  3rd Qu.: 25.796   3rd Qu.:0.0000   3rd Qu.:1.0000   3rd Qu.:0.00000  
##  Max.   :100.000   Max.   :1.0000   Max.   :1.0000   Max.   :1.00000  
##     weights             sbp             dbp               tc        
##  Min.   :  105.8   Min.   : 71.0   Min.   : 48.00   Min.   : 2.000  
##  1st Qu.: 1130.1   1st Qu.:114.0   1st Qu.: 75.00   1st Qu.: 2.900  
##  Median : 2631.9   Median :124.0   Median : 82.00   Median : 3.550  
##  Mean   : 3839.8   Mean   :127.1   Mean   : 82.43   Mean   : 3.702  
##  3rd Qu.: 4969.9   3rd Qu.:135.0   3rd Qu.: 89.00   3rd Qu.: 4.240  
##  Max.   :55389.3   Max.   :264.0   Max.   :152.00   Max.   :10.300  
##        dm           dm_treatment          female            male       
##  Min.   :0.00000   Min.   :0.000000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.00000   1st Qu.:0.000000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :0.00000   Median :0.000000   Median :1.0000   Median :0.0000  
##  Mean   :0.03311   Mean   :0.008222   Mean   :0.6002   Mean   :0.3998  
##  3rd Qu.:0.00000   3rd Qu.:0.000000   3rd Qu.:1.0000   3rd Qu.:1.0000  
##  Max.   :1.00000   Max.   :1.000000   Max.   :1.0000   Max.   :1.0000  
##      weight         
##  Min.   :6.124e-06  
##  1st Qu.:6.540e-05  
##  Median :1.523e-04  
##  Mean   :2.222e-04  
##  3rd Qu.:2.876e-04  
##  Max.   :3.206e-03
# Check the structure of the dataset
str(steps_data)
## tibble [4,500 × 21] (S3: tbl_df/tbl/data.frame)
##  $ id           : num [1:4500] 1001 1003 1008 1011 1013 ...
##  $ psu          : num [1:4500] 32 32 32 32 32 32 32 32 32 32 ...
##  $ stratum      : num [1:4500] 1 1 1 1 1 1 1 1 1 1 ...
##  $ wealth       : chr [1:4500] "4 Fourth" "2 Second" "3 Middle" "2 Second" ...
##  $ age          : num [1:4500] 39 35 60 18 51 47 38 45 41 48 ...
##  $ county       : num [1:4500] 19 19 19 19 19 19 19 19 19 19 ...
##  $ sex          : num [1:4500] 1 0 0 0 1 1 0 0 1 0 ...
##  $ region       : chr [1:4500] "Coast" "Coast" "Coast" "Coast" ...
##  $ bmi          : num [1:4500] 38.7 20.2 18.8 22.9 19.1 ...
##  $ smk          : num [1:4500] 0 1 0 0 0 0 0 0 0 1 ...
##  $ htn          : num [1:4500] 0 0 1 0 1 0 1 0 1 0 ...
##  $ htn_treatment: num [1:4500] 0 0 0 0 0 0 0 0 0 0 ...
##  $ weights      : num [1:4500] 4027 5714 3973 9097 3578 ...
##  $ sbp          : num [1:4500] 125 132 213 114 175 115 131 137 219 115 ...
##  $ dbp          : num [1:4500] 85 81 95 69 101 84 91 85 98 73 ...
##  $ tc           : num [1:4500] 3.68 4.49 3.79 2.59 3.31 4.14 3.72 3.72 4.49 4.26 ...
##  $ dm           : num [1:4500] 0 0 0 0 0 0 0 0 0 1 ...
##  $ dm_treatment : num [1:4500] 0 0 0 0 0 0 0 0 0 1 ...
##  $ female       : num [1:4500] 1 0 0 0 1 1 0 0 1 0 ...
##  $ male         : num [1:4500] 0 1 1 1 0 0 1 1 0 1 ...
##  $ weight       : num [1:4500] 0.000233 0.000331 0.00023 0.000526 0.000207 ...
# Check the number of rows and columns
dim(steps_data)
## [1] 4500   21
# Check the column names
colnames(steps_data)
##  [1] "id"            "psu"           "stratum"       "wealth"       
##  [5] "age"           "county"        "sex"           "region"       
##  [9] "bmi"           "smk"           "htn"           "htn_treatment"
## [13] "weights"       "sbp"           "dbp"           "tc"           
## [17] "dm"            "dm_treatment"  "female"        "male"         
## [21] "weight"
# Check the number of missing values in each column
missing_values <- sapply(steps_data, function(x) sum(is.na(x)))
missing_values
##            id           psu       stratum        wealth           age 
##             0             0             0             0             0 
##        county           sex        region           bmi           smk 
##             0             0             0             0             0 
##           htn htn_treatment       weights           sbp           dbp 
##             0             0             0             0             0 
##            tc            dm  dm_treatment        female          male 
##             0             0             0             0             0 
##        weight 
##             0
# Check the number of unique values in each column
unique_values <- sapply(steps_data, function(x) length(unique(x)))
unique_values
##            id           psu       stratum        wealth           age 
##          4500           200             2             5            55 
##        county           sex        region           bmi           smk 
##            47             2             8          3861             2 
##           htn htn_treatment       weights           sbp           dbp 
##             2             2          1327           143            89 
##            tc            dm  dm_treatment        female          male 
##           410             2             2             2             2 
##        weight 
##          1327
# Check the data types of each column
data_types <- sapply(steps_data, class)
data_types
##            id           psu       stratum        wealth           age 
##     "numeric"     "numeric"     "numeric"   "character"     "numeric" 
##        county           sex        region           bmi           smk 
##     "numeric"     "numeric"   "character"     "numeric"     "numeric" 
##           htn htn_treatment       weights           sbp           dbp 
##     "numeric"     "numeric"     "numeric"     "numeric"     "numeric" 
##            tc            dm  dm_treatment        female          male 
##     "numeric"     "numeric"     "numeric"     "numeric"     "numeric" 
##        weight 
##     "numeric"
# Check the number of levels in each factor variable
factor_levels <- sapply(steps_data, function(x) if(is.factor(x)) length(levels(x)) else NA)
factor_levels
##            id           psu       stratum        wealth           age 
##            NA            NA            NA            NA            NA 
##        county           sex        region           bmi           smk 
##            NA            NA            NA            NA            NA 
##           htn htn_treatment       weights           sbp           dbp 
##            NA            NA            NA            NA            NA 
##            tc            dm  dm_treatment        female          male 
##            NA            NA            NA            NA            NA 
##        weight 
##            NA

2 Create hypertension variable

# Create a new variable for hypertension based on sbp and dbp
steps_data <- steps_data %>%
  mutate(htn = case_when(
    sbp >= 140 | dbp >= 90 ~ 1, # Hypertensive
    TRUE ~ 0 # Not hypertensive
  ))
# Check the distribution of the new variable
htn_distribution <- steps_data %>%
  group_by(htn) %>%
  summarise(count = n()) %>%
  mutate(percentage = count / sum(count) * 100)
# Print the distribution
htn_distribution
## # A tibble: 2 × 3
##     htn count percentage
##   <dbl> <int>      <dbl>
## 1     0  3205       71.2
## 2     1  1295       28.8

3 Summarising sbp by sample characteristics

# Summarise sbp by sample characteristics
# Summarise sbp for whole population
sbp_summary_all <- steps_data %>%
  summarise(
    mean = mean(sbp, na.rm = TRUE),
    sd = sd(sbp, na.rm = TRUE),
    median = median(sbp, na.rm = TRUE),
    min = min(sbp, na.rm = TRUE),
    max = max(sbp, na.rm = TRUE)
  )
# Print the summary
sbp_summary_all
## # A tibble: 1 × 5
##    mean    sd median   min   max
##   <dbl> <dbl>  <dbl> <dbl> <dbl>
## 1  127.  19.8    124    71   264

#Summarise sbp for rural population

# Summarise sbp for rural population
steps_data$residence <- steps_data$stratum
sbp_summary_rural <- steps_data %>%
  filter(residence == 1) %>%
  summarise(
    mean = mean(sbp, na.rm = TRUE),
    sd = sd(sbp, na.rm = TRUE),
    median = median(sbp, na.rm = TRUE),
    min = min(sbp, na.rm = TRUE),
    max = max(sbp, na.rm = TRUE)
  )
# Print the summary
sbp_summary_rural
## # A tibble: 1 × 5
##    mean    sd median   min   max
##   <dbl> <dbl>  <dbl> <dbl> <dbl>
## 1  127.  20.3    123    80   258

4 Summarise sbp for urban population

# Summarise sbp for urban population
sbp_summary_urban <- steps_data %>%
  filter(residence == 2) %>%
  summarise(
    mean = mean(sbp, na.rm = TRUE),
    sd = sd(sbp, na.rm = TRUE),
    median = median(sbp, na.rm = TRUE),
    min = min(sbp, na.rm = TRUE),
    max = max(sbp, na.rm = TRUE)
  )
# Print the summary
sbp_summary_urban
## # A tibble: 1 × 5
##    mean    sd median   min   max
##   <dbl> <dbl>  <dbl> <dbl> <dbl>
## 1  127.  19.1    124    71   264

5 Summarise sbp for hypertensive population

# Summarise sbp for hypertensive population
sbp_summary_hypertensive <- steps_data %>%
  filter(htn == 1) %>%
  summarise(
    mean = mean(sbp, na.rm = TRUE),
    sd = sd(sbp, na.rm = TRUE),
    median = median(sbp, na.rm = TRUE),
    min = min(sbp, na.rm = TRUE),
    max = max(sbp, na.rm = TRUE)
  )
# Print the summary
sbp_summary_hypertensive
## # A tibble: 1 × 5
##    mean    sd median   min   max
##   <dbl> <dbl>  <dbl> <dbl> <dbl>
## 1  149.  20.7    144   111   264

6 Summarise sbp for non-hypertensive population

# Summarise sbp for non-hypertensive population
sbp_summary_non_hypertensive <- steps_data %>%
  filter(htn == 0) %>%
  summarise(
    mean = mean(sbp, na.rm = TRUE),
    sd = sd(sbp, na.rm = TRUE),
    median = median(sbp, na.rm = TRUE),
    min = min(sbp, na.rm = TRUE),
    max = max(sbp, na.rm = TRUE)
  )
# Print the summary
sbp_summary_non_hypertensive
## # A tibble: 1 × 5
##    mean    sd median   min   max
##   <dbl> <dbl>  <dbl> <dbl> <dbl>
## 1  118.  10.3    119    71   139

7 Create subsets of the dataset

# Create subsets of the dataset
# Create a subset for rural population
rural_data <- steps_data %>%
  filter(residence == 1)
# Create a subset for urban population
urban_data <- steps_data %>%
  filter(residence == 2)
# Create a subset for hypertensive population
hypertensive_data <- steps_data %>%
  filter(htn == 1)
# Create a subset for patients on hypertension treatment
htn_treatment_data <- steps_data %>%
  filter(htn == 1 & htn_treatment == 1)
# Create a subset for diabetic population
diabetic_data <- steps_data %>%
  filter(dm == 1)

8 Fit a linear regression model for predicting sbp for whole population

# Fit a linear regression model for predicting sbp for whole population
lm_all <- lm(sbp~age+male+bmi+dm+smk+tc+age*smk, data = steps_data, weights = weights) # To explore other interactions +male*smk
# Print the summary of the model
summary(lm_all)
## 
## Call:
## lm(formula = sbp ~ age + male + bmi + dm + smk + tc + age * smk, 
##     data = steps_data, weights = weights)
## 
## Weighted Residuals:
##     Min      1Q  Median      3Q     Max 
## -4817.5  -516.2   -85.8   389.3  8003.9 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 87.31145    1.56443  55.810  < 2e-16 ***
## age          0.45277    0.02181  20.762  < 2e-16 ***
## male         6.97074    0.51994  13.407  < 2e-16 ***
## bmi          0.72100    0.05250  13.733  < 2e-16 ***
## dm           4.32989    1.59573   2.713 0.006685 ** 
## smk          5.07953    2.19541   2.314 0.020729 *  
## tc           0.84106    0.27800   3.025 0.002498 ** 
## age:smk     -0.20495    0.05511  -3.719 0.000203 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1009 on 4492 degrees of freedom
## Multiple R-squared:  0.1816, Adjusted R-squared:  0.1804 
## F-statistic: 142.4 on 7 and 4492 DF,  p-value: < 2.2e-16
# Print the coefficients of the model
coef(lm_all)
## (Intercept)         age        male         bmi          dm         smk 
##  87.3114488   0.4527687   6.9707359   0.7210036   4.3298852   5.0795298 
##          tc     age:smk 
##   0.8410599  -0.2049454

9 Model diagnostics

# Model diagnostics

# Print the residuals of the model
residuals(lm_all)
##             1             2             3             4             5 
## -1.098442e+01  5.640653e+00  7.481796e+01 -7.087298e+00  4.800633e+01 
##             6             7             8             9            10 
## -2.178827e+01 -6.174000e+00  2.117248e+00  8.668709e+01 -1.909687e+01 
##            11            12            13            14            15 
## -2.052493e+01 -6.980343e+00 -7.015739e+00  1.306721e+01  4.445060e+00 
##            16            17            18            19            20 
##  5.346342e+00  2.587706e+01  1.017654e+01  1.417650e+00  9.223898e+00 
##            21            22            23            24            25 
## -1.020235e+01  5.910905e+00 -4.687969e+00  2.534613e+01  9.552814e-01 
##            26            27            28            29            30 
##  3.007795e+00  3.993900e+01  1.047172e+01 -4.241587e+00 -1.983535e+01 
##            31            32            33            34            35 
##  1.832231e+01 -3.140997e+00 -2.912425e+00 -5.869362e+00 -1.307477e+01 
##            36            37            38            39            40 
## -9.128188e+00 -1.033743e+01 -2.676086e+01 -3.650899e+00 -3.990166e+00 
##            41            42            43            44            45 
## -5.820097e+00 -7.326625e+00 -7.869102e+00  1.007979e+01  2.565503e+01 
##            46            47            48            49            50 
##  5.304655e+01 -1.154288e+01  9.283995e+00 -8.518451e+00  1.033482e+01 
##            51            52            53            54            55 
##  1.228444e+01 -1.347710e+01  2.494284e+00 -9.090272e+00 -4.385697e+00 
##            56            57            58            59            60 
##  3.957559e+00  6.805075e+00  8.304833e+00 -1.001859e+01 -9.767705e-01 
##            61            62            63            64            65 
##  7.984064e+00 -8.756549e+00  1.371234e+01 -2.706442e+00  6.606767e+00 
##            66            67            68            69            70 
## -2.731027e+00 -1.134977e+01 -4.033230e+00 -1.407663e+01  1.858609e+01 
##            71            72            73            74            75 
## -4.258600e+00  1.122494e+01 -3.608129e+00 -9.259490e+00 -1.749421e+01 
##            76            77            78            79            80 
##  5.314936e+00  5.748097e+00  5.117869e+00  1.565066e+01  7.791919e+00 
##            81            82            83            84            85 
## -1.318183e+01  2.040474e+00  2.244843e-01 -1.376133e+01 -6.573052e+00 
##            86            87            88            89            90 
## -1.340076e+01 -1.135195e+01 -5.326430e+00  1.420775e+00 -8.033765e+00 
##            91            92            93            94            95 
##  1.192313e+00 -4.634824e+00  9.892169e+00  1.205722e+01  2.395208e+00 
##            96            97            98            99           100 
## -1.378170e+01  3.767810e+01  1.601148e+01  3.051354e+00  1.022974e+01 
##           101           102           103           104           105 
## -1.336771e+01  2.199645e+01  1.629779e+00 -4.862247e+00  7.869364e+00 
##           106           107           108           109           110 
##  4.099767e+01 -3.142746e+00  2.736079e+01 -2.573278e+00 -9.245924e+00 
##           111           112           113           114           115 
## -3.151380e+01  1.581243e+00 -1.810698e+01 -1.220664e+01  4.481426e-02 
##           116           117           118           119           120 
## -1.804787e+00  8.521483e-01 -6.000174e+00 -6.317750e+00 -4.679671e+00 
##           121           122           123           124           125 
##  4.708441e+00  6.428102e+00  4.217001e+00  2.349830e+01 -1.192218e+01 
##           126           127           128           129           130 
## -5.698383e+00 -1.310552e+01  3.201394e+01  5.557344e-01  1.055344e+01 
##           131           132           133           134           135 
## -1.252025e+00 -5.346829e-01 -3.433846e+01 -5.968641e+00  5.370814e+00 
##           136           137           138           139           140 
##  8.450696e+00  1.065977e+01  6.509619e+00 -1.686091e+01 -6.155912e+00 
##           141           142           143           144           145 
## -4.949911e+00 -2.846859e+00 -6.691651e+00 -1.525987e+01  1.030261e+00 
##           146           147           148           149           150 
##  1.520143e+00 -7.436963e+00 -1.864627e+01 -1.051299e+01  5.377545e+00 
##           151           152           153           154           155 
##  6.246400e+00 -1.254809e+01 -1.849623e+01 -5.242687e+00 -1.022776e+01 
##           156           157           158           159           160 
## -2.514636e+00 -1.127102e+01  2.527864e+01 -7.538657e+00 -2.841773e+01 
##           161           162           163           164           165 
##  1.117720e+01  1.845094e+01  3.963922e+00 -1.384044e+01 -1.616950e+01 
##           166           167           168           169           170 
## -1.223888e+01  1.243119e+00 -1.737718e+01 -7.033292e+00 -2.648496e-01 
##           171           172           173           174           175 
##  2.292457e+00  6.575515e-01  2.320306e-01  9.078568e+00  4.763586e+01 
##           176           177           178           179           180 
## -1.052665e+01 -3.237542e+01 -1.557032e+01 -1.729353e+01  3.881413e+01 
##           181           182           183           184           185 
## -2.858414e+00  9.080781e+00 -4.921601e-01 -1.032660e+01 -2.425455e+01 
##           186           187           188           189           190 
## -9.942763e+00  2.269477e+01 -3.895580e+00 -5.851453e+00 -1.329032e+01 
##           191           192           193           194           195 
## -9.199028e+00  2.305184e+00  1.686517e+01 -7.493838e+00 -8.679583e+00 
##           196           197           198           199           200 
## -1.221921e+01 -5.108981e+00 -4.857140e+00 -9.167415e+00  1.172012e+01 
##           201           202           203           204           205 
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##           526           527           528           529           530 
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##           561           562           563           564           565 
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##           631           632           633           634           635 
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##           711           712           713           714           715 
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##           871           872           873           874           875 
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## -7.684560e+00 -3.641642e+00  1.748592e+00  1.105198e+00 -7.716918e+00 
##           881           882           883           884           885 
##  6.914427e+00 -4.795075e+00  1.364690e+01 -2.379616e+00  2.355233e+00 
##           886           887           888           889           890 
## -1.402028e+01  8.104737e+00 -3.583810e+01  6.473186e+00  1.703857e+01 
##           891           892           893           894           895 
## -1.977018e+01  3.238396e+00  3.127287e+00 -2.742819e+00 -1.939041e+00 
##           896           897           898           899           900 
## -1.196080e+01 -1.003380e+01  1.912475e+01  1.187046e+01  1.071258e+01 
##           901           902           903           904           905 
##  1.435114e+01 -1.897961e+01 -3.478109e+00  4.927701e+01  7.980795e+00 
##           906           907           908           909           910 
##  7.577951e+00 -9.446489e-01 -9.059822e+00 -1.646081e+01  7.773650e+00 
##           911           912           913           914           915 
## -6.706779e+00 -7.817245e+00 -9.381287e+00 -1.438581e+01  4.198956e+00 
##           916           917           918           919           920 
##  1.587037e+01 -2.904594e+00 -9.831113e+00 -5.310168e-01  2.270150e+01 
##           921           922           923           924           925 
##  8.740353e-01  7.210893e+00 -1.354305e+01 -2.917626e+01 -4.432210e+00 
##           926           927           928           929           930 
## -1.402763e+01 -8.561959e+00  9.722661e+00 -3.003059e+01  1.555646e+00 
##           931           932           933           934           935 
##  9.761866e+00  6.826063e+00  5.609735e+00 -4.768650e+00 -2.321894e+00 
##           936           937           938           939           940 
## -2.022365e+01  6.352072e+01  2.860844e-01  1.122210e+01 -1.617763e+01 
##           941           942           943           944           945 
##  1.124684e-01 -7.692412e+00  2.425672e+01  5.621320e+01  3.211806e+00 
##           946           947           948           949           950 
##  1.391749e+01 -4.779756e+00 -1.089357e+01 -6.349041e+00  1.519297e+01 
##           951           952           953           954           955 
##  2.891025e+01  1.606688e+00 -1.210227e+00 -1.222936e+01 -9.419888e+00 
##           956           957           958           959           960 
##  3.759615e-01  1.292344e+01  1.419174e+01  1.827565e+00 -6.866772e+00 
##           961           962           963           964           965 
## -1.071906e+01 -1.395390e+01 -2.415628e+01  1.648430e+00  5.025114e+01 
##           966           967           968           969           970 
##  1.477047e+01 -4.052352e+00  1.459732e+01 -2.680027e+01 -6.847813e+00 
##           971           972           973           974           975 
## -1.870018e+01  1.916443e+00 -4.614113e+00  8.992858e+00 -2.381796e+01 
##           976           977           978           979           980 
## -1.656135e+01  1.970122e+01  1.568415e+01 -1.649958e+01  4.269598e+01 
##           981           982           983           984           985 
##  7.495035e+00  6.054273e+01  9.505080e+01 -1.796751e+01  3.902049e+01 
##           986           987           988           989           990 
## -2.860869e+00 -1.618815e+01 -1.549718e+01 -1.322993e+01  1.256745e+01 
##           991           992           993           994           995 
## -1.581544e+01  6.440499e+00 -2.177334e+01 -5.940149e+00  9.862112e+00 
##           996           997           998           999          1000 
## -8.816099e+00  3.201609e+01  1.883511e+00  5.339938e+01  4.728586e+01 
##          1001          1002          1003          1004          1005 
##  1.829527e-01 -2.793031e+00 -1.544477e+00 -1.571034e+01 -3.100368e+01 
##          1006          1007          1008          1009          1010 
## -2.786359e+01 -2.111851e+01 -4.729827e+00  2.970296e+01  2.537604e+00 
##          1011          1012          1013          1014          1015 
## -7.585321e+00  2.378538e+01 -1.227032e+01  1.010582e+01 -1.585172e+01 
##          1016          1017          1018          1019          1020 
## -1.968933e+01 -9.179542e+00  3.219150e+00  1.260668e+01 -1.135658e+01 
##          1021          1022          1023          1024          1025 
##  8.960247e+01  1.581289e+01 -1.798847e+01 -1.371004e+01 -2.810468e+01 
##          1026          1027          1028          1029          1030 
##  5.241178e-01 -6.775426e+00 -1.335769e+01 -1.287299e+01  1.982208e+01 
##          1031          1032          1033          1034          1035 
##  8.559916e+00  2.513243e+01  8.251511e+00  4.299356e+01 -1.401351e+01 
##          1036          1037          1038          1039          1040 
## -1.953898e+01 -1.321109e+01 -1.964937e+00  8.954513e+00  6.600943e+00 
##          1041          1042          1043          1044          1045 
##  1.042812e+01 -1.206888e+01 -1.218788e+01 -2.303564e+01 -3.314942e+00 
##          1046          1047          1048          1049          1050 
##  6.813720e+00 -1.468778e+01  7.093794e+01 -1.483868e+01 -2.334636e+01 
##          1051          1052          1053          1054          1055 
##  1.364006e+01 -3.407645e+01  9.364695e+00  5.397024e+00  1.761552e+01 
##          1056          1057          1058          1059          1060 
##  1.838294e+00  3.571689e+00 -4.698284e+00 -9.834774e+00 -9.722183e+00 
##          1061          1062          1063          1064          1065 
##  9.137633e+00  1.072161e+01 -1.310613e+01  1.929254e+01 -1.838274e+01 
##          1066          1067          1068          1069          1070 
## -1.493946e+01 -2.890389e+01 -8.365826e+00 -4.730211e+00 -4.497324e-01 
##          1071          1072          1073          1074          1075 
## -1.165229e+01 -4.893540e+00 -5.117992e+01 -3.499672e+01  1.585964e-01 
##          1076          1077          1078          1079          1080 
## -6.188241e+00 -1.441520e+00 -4.017446e+00 -4.283827e+01  4.650622e+01 
##          1081          1082          1083          1084          1085 
##  8.287238e+00  1.106108e+01 -1.628585e+01 -6.318195e+00  1.123468e+01 
##          1086          1087          1088          1089          1090 
##  4.763186e+00 -7.535085e-01 -1.373097e+01 -1.046552e+01 -2.688056e+00 
##          1091          1092          1093          1094          1095 
##  3.557508e+00 -1.936158e+01  1.623200e+01 -1.349831e+01 -6.663433e+00 
##          1096          1097          1098          1099          1100 
##  1.242977e-01  1.956665e+00  1.153716e+01 -7.197753e+00 -7.867614e+00 
##          1101          1102          1103          1104          1105 
## -1.156465e+01  1.235732e+01  1.022753e+01  1.519094e+00 -9.714723e+00 
##          1106          1107          1108          1109          1110 
## -4.407128e+00  2.484403e+00  3.371686e+00 -1.043696e+01 -8.862409e+00 
##          1111          1112          1113          1114          1115 
##  8.426097e+00  3.610707e+00  1.664836e+00 -1.913331e+00 -4.601869e+00 
##          1116          1117          1118          1119          1120 
## -1.512923e+01  8.020482e+00 -8.359928e+00 -1.708150e+01 -2.582793e+01 
##          1121          1122          1123          1124          1125 
## -1.484277e+01  3.537685e+00  7.375666e-01  7.844005e+00  9.768110e+00 
##          1126          1127          1128          1129          1130 
## -1.336817e+01 -1.415875e+01  1.295492e+00 -1.628450e+01  1.298423e+00 
##          1131          1132          1133          1134          1135 
## -1.285889e+01 -3.739559e+01 -1.726767e+01 -1.918899e+00 -6.316290e+00 
##          1136          1137          1138          1139          1140 
## -1.442152e+01  4.017112e+00  1.617485e+01 -3.484260e+00 -1.378103e+00 
##          1141          1142          1143          1144          1145 
##  1.154977e+01 -3.510510e+00 -3.905893e+00  1.394760e+01  2.585886e+01 
##          1146          1147          1148          1149          1150 
##  5.988588e+00 -9.476065e+00 -3.385334e+00  2.662352e+01 -2.793385e+00 
##          1151          1152          1153          1154          1155 
## -5.511293e+00  1.032808e+01  3.007667e+01  1.343816e+01  1.029191e+00 
##          1156          1157          1158          1159          1160 
##  4.772263e-01  1.377577e+01  4.008727e+00 -1.122977e+01 -7.910529e+00 
##          1161          1162          1163          1164          1165 
## -1.783075e+01  1.755629e+00 -3.162811e+01 -5.615361e+00 -1.040969e+01 
##          1166          1167          1168          1169          1170 
## -2.572941e+00 -7.240940e-01 -1.666279e+01  5.050018e+00 -1.470905e+00 
##          1171          1172          1173          1174          1175 
## -6.053052e+00  7.220099e+00 -1.316704e+01 -1.124662e+00 -4.068210e+00 
##          1176          1177          1178          1179          1180 
## -9.310763e+00 -1.709460e+01  2.919674e+01 -1.873601e+01  5.070797e+01 
##          1181          1182          1183          1184          1185 
##  5.791236e+00 -6.952387e+00  3.964541e+01 -8.089713e+00  4.174875e-01 
##          1186          1187          1188          1189          1190 
##  2.191803e+01 -9.403905e+00 -2.042565e+01 -1.693714e+01 -1.999886e+00 
##          1191          1192          1193          1194          1195 
##  3.749428e+01 -5.612669e+00 -1.592797e+01  4.498315e+01  7.961026e+00 
##          1196          1197          1198          1199          1200 
## -6.706779e+00  1.522874e+01 -3.580783e+00  5.052120e+00  1.218264e+01 
##          1201          1202          1203          1204          1205 
##  1.467400e+01  2.840223e+00 -2.345579e+01  4.913392e+00 -2.973837e+01 
##          1206          1207          1208          1209          1210 
## -1.961173e+01 -1.214000e+01 -1.670087e+01  2.852918e+01 -4.178636e+00 
##          1211          1212          1213          1214          1215 
## -1.819544e+01  4.127355e+00  6.079201e+00  4.688413e+00 -1.094606e+01 
##          1216          1217          1218          1219          1220 
## -7.884435e+00 -3.733761e+00 -1.491927e+01  6.769398e+00 -1.773135e+00 
##          1221          1222          1223          1224          1225 
##  1.650875e+00 -1.456684e+01 -8.938951e+00 -5.274004e+00 -5.131376e+00 
##          1226          1227          1228          1229          1230 
##  6.211073e+00  8.601065e+00 -1.078220e+01  9.733659e+00 -4.822827e+00 
##          1231          1232          1233          1234          1235 
## -7.018280e+00  8.245290e+00 -4.806433e+00 -7.635161e+00  1.483859e+01 
##          1236          1237          1238          1239          1240 
## -2.209109e+01 -1.503749e+01 -1.692242e+01 -8.821003e+00 -1.199888e+01 
##          1241          1242          1243          1244          1245 
##  1.549739e+01  1.758934e+01  3.141146e+01 -1.419132e+01 -1.260848e+01 
##          1246          1247          1248          1249          1250 
## -4.288214e+00  1.454828e+01 -1.748426e+01 -9.516769e+00 -3.195949e+00 
##          1251          1252          1253          1254          1255 
## -8.213512e+00  2.282817e+01 -8.708963e+00 -8.930546e+00  3.449925e+01 
##          1256          1257          1258          1259          1260 
## -2.991593e+00 -6.064840e-01  2.404754e+00 -8.618052e+00  5.628871e+01 
##          1261          1262          1263          1264          1265 
## -8.229572e+00 -1.689232e+00  8.591748e+00 -5.906525e+00  1.294823e+01 
##          1266          1267          1268          1269          1270 
##  4.958238e-01  6.345512e+00 -1.593426e+01 -2.828518e+01 -3.329549e+00 
##          1271          1272          1273          1274          1275 
##  1.758494e+00 -7.419308e+00 -1.540203e+01 -1.673756e+01  6.359482e+00 
##          1276          1277          1278          1279          1280 
## -1.407562e+01  9.369469e-01  1.364767e+01  3.939798e+00  3.281168e+01 
##          1281          1282          1283          1284          1285 
## -4.560873e+00 -2.151494e+01  1.309881e+01  2.778016e+00  1.631809e+01 
##          1286          1287          1288          1289          1290 
## -7.074834e-01 -1.004566e+01  6.935113e+00 -3.269294e+00  4.217846e+00 
##          1291          1292          1293          1294          1295 
## -1.068497e+01  1.147848e+01 -7.341239e+00  2.573924e-01  5.050569e+00 
##          1296          1297          1298          1299          1300 
## -2.252806e+01 -3.522491e+00 -6.818478e+00  3.106628e+00  5.708311e+00 
##          1301          1302          1303          1304          1305 
##  4.304253e+00 -5.688968e+00  4.460110e+00 -6.180599e+00 -3.303864e-01 
##          1306          1307          1308          1309          1310 
## -5.951813e+00 -1.404938e+01 -9.274369e+00 -3.498376e+00  1.688053e+00 
##          1311          1312          1313          1314          1315 
##  1.888739e+01 -1.227866e+01 -4.039558e+00 -1.231093e+01 -2.201171e+01 
##          1316          1317          1318          1319          1320 
## -8.460632e+00  8.094992e+00 -1.568779e+01  5.613400e+00  1.492300e+01 
##          1321          1322          1323          1324          1325 
## -1.129913e+01 -1.814147e+01 -8.295408e+00 -1.506192e+01 -1.273010e+01 
##          1326          1327          1328          1329          1330 
##  4.295733e-01 -3.962600e+01 -7.979514e+00 -3.514595e+00 -2.521728e+01 
##          1331          1332          1333          1334          1335 
## -1.998084e+00  2.266051e+01  3.856129e+00  7.471375e-01 -3.579191e-01 
##          1336          1337          1338          1339          1340 
##  6.983451e+00 -1.064880e+01 -1.249446e+01 -4.263162e-02 -3.460746e-01 
##          1341          1342          1343          1344          1345 
## -8.470648e+00 -2.370991e+00 -3.903656e+00 -3.537397e+00 -3.140707e+01 
##          1346          1347          1348          1349          1350 
## -1.598420e+01 -7.437449e-02  2.113042e+01 -1.529227e+01 -3.327298e+01 
##          1351          1352          1353          1354          1355 
##  2.470730e+01 -3.366596e+01 -1.555807e+01 -1.093161e+01 -1.228889e+01 
##          1356          1357          1358          1359          1360 
##  1.052334e+01 -9.078709e+00 -1.945129e+01  8.801803e+00 -8.091331e+00 
##          1361          1362          1363          1364          1365 
## -7.146079e+00  4.389502e+00 -1.097633e+01 -8.905767e+00 -1.396049e+01 
##          1366          1367          1368          1369          1370 
##  6.793336e+01  2.311945e+01 -2.785325e+01 -4.489623e+00 -1.660048e+01 
##          1371          1372          1373          1374          1375 
##  2.794250e+01 -7.305523e+00 -3.497036e+00 -4.663415e+00  9.014365e+00 
##          1376          1377          1378          1379          1380 
## -2.102044e+01 -2.027609e+01 -2.389683e+01  4.487372e+01  1.244936e+01 
##          1381          1382          1383          1384          1385 
## -1.099486e+01  5.176575e+00 -2.335430e+01  1.262751e+01 -3.692247e+00 
##          1386          1387          1388          1389          1390 
##  7.767516e-01  1.126750e+00 -4.187197e+00 -6.687547e+00 -7.069975e+00 
##          1391          1392          1393          1394          1395 
## -1.649085e+01 -1.741573e+00 -3.329748e+00  6.596672e+00  3.159965e+00 
##          1396          1397          1398          1399          1400 
## -1.476739e+01 -1.554988e+01  9.031063e+00 -1.307841e+01  3.707130e+00 
##          1401          1402          1403          1404          1405 
## -4.497159e+00 -2.930475e+01 -1.841870e+01  2.184326e+00 -1.103688e+01 
##          1406          1407          1408          1409          1410 
##  9.868958e+00  9.365743e+00  9.334299e+00 -2.277327e+01 -3.115368e+01 
##          1411          1412          1413          1414          1415 
## -1.457292e+01  2.351019e+00 -8.377736e+00 -1.067495e+00 -4.252527e+01 
##          1416          1417          1418          1419          1420 
## -2.315936e+01 -1.673767e+01 -2.965174e+01  1.063172e+01 -1.339876e+01 
##          1421          1422          1423          1424          1425 
##  3.007662e+01 -2.027019e+01  1.382133e-01 -2.646733e+01 -1.197309e+01 
##          1426          1427          1428          1429          1430 
## -1.976750e+01  1.478427e+01  5.643263e+00 -1.028792e+01 -3.080011e+00 
##          1431          1432          1433          1434          1435 
##  3.205387e+00 -2.711664e+01  3.493364e+00  1.243595e+01 -3.049284e+00 
##          1436          1437          1438          1439          1440 
## -1.531982e+01 -1.617693e+01 -1.721965e+01 -3.008292e-01 -1.015446e+01 
##          1441          1442          1443          1444          1445 
## -2.859847e+01 -2.128365e+01  1.645662e+00 -3.060714e+01 -1.576207e+01 
##          1446          1447          1448          1449          1450 
##  1.502902e+00 -2.537344e+01 -9.811073e+00 -1.676877e+01 -5.896478e+00 
##          1451          1452          1453          1454          1455 
##  9.610689e+00  1.279423e+01  4.672175e+00  4.426093e+01  2.705524e+00 
##          1456          1457          1458          1459          1460 
## -2.657107e+01 -2.668243e+01  5.910238e+01 -1.254058e+01 -1.812537e+01 
##          1461          1462          1463          1464          1465 
## -8.229635e+00 -1.590748e+01 -7.252630e-02  1.516999e+01  2.321865e+00 
##          1466          1467          1468          1469          1470 
## -5.951667e+00 -1.543186e+01 -9.143050e+00  3.825516e+00 -1.287715e+01 
##          1471          1472          1473          1474          1475 
## -2.757032e+01 -1.228136e+01 -1.012979e+01  3.320648e+01 -2.964687e+00 
##          1476          1477          1478          1479          1480 
## -1.764139e+01  1.177984e+01 -7.199094e+00 -1.787190e+01  4.909887e+00 
##          1481          1482          1483          1484          1485 
##  9.504860e+00  3.395976e+00 -8.935016e+00 -8.361893e+00 -4.562230e+00 
##          1486          1487          1488          1489          1490 
## -6.427081e+00 -4.494381e+00  9.300038e-01 -6.693926e-01 -1.651476e+01 
##          1491          1492          1493          1494          1495 
## -8.950471e+00  1.519509e+01  1.394470e+01  4.929667e+00 -5.157425e+00 
##          1496          1497          1498          1499          1500 
##  2.762510e+01  1.929747e+00  7.412695e+01  5.077105e+00 -6.192825e+00 
##          1501          1502          1503          1504          1505 
## -1.411273e+01 -1.899846e+01  5.811528e+00 -2.127925e+01  1.766728e+01 
##          1506          1507          1508          1509          1510 
## -1.373987e+01  5.558954e+00 -1.618505e+01  3.136843e+00  1.638665e+00 
##          1511          1512          1513          1514          1515 
##  4.136268e+00 -1.419587e+00 -1.916990e+01 -4.274580e+00  7.216915e+00 
##          1516          1517          1518          1519          1520 
## -8.356815e+00 -8.504212e+00 -1.366922e+01 -5.464863e+00 -3.238130e-01 
##          1521          1522          1523          1524          1525 
## -1.056890e+01 -4.860974e-01 -1.408329e+01  1.635334e+01 -2.698622e+00 
##          1526          1527          1528          1529          1530 
##  1.979664e+01 -4.537460e+00 -1.152019e+01 -1.393547e+01  1.530717e+00 
##          1531          1532          1533          1534          1535 
## -1.654389e+01  2.521566e+01  1.350352e+01 -8.970622e+00 -2.518732e+01 
##          1536          1537          1538          1539          1540 
## -4.270106e+00 -2.745920e+01 -7.546574e+00  1.507625e+01 -3.760020e-01 
##          1541          1542          1543          1544          1545 
## -6.308076e+00  4.260367e+00 -6.662447e+00 -7.503142e+00  7.096983e+00 
##          1546          1547          1548          1549          1550 
##  4.680694e+00 -3.903763e+00  1.601757e+01 -2.037066e+00 -7.459141e+00 
##          1551          1552          1553          1554          1555 
## -6.268437e+00 -6.552592e+00 -2.076111e+01  4.118460e+01  2.289747e+01 
##          1556          1557          1558          1559          1560 
## -2.012647e+01  1.712459e+00  1.522251e+01 -1.069454e+01 -5.748175e+00 
##          1561          1562          1563          1564          1565 
## -1.100768e+01 -9.977919e+00 -1.885787e+00  1.171358e+01  1.849762e+01 
##          1566          1567          1568          1569          1570 
## -1.084364e+00  7.354902e+00  6.983770e+00  2.544724e-01  7.696627e+00 
##          1571          1572          1573          1574          1575 
## -5.612238e+00  4.217917e+01  6.224036e+01  1.471103e+01  1.729772e+01 
##          1576          1577          1578          1579          1580 
##  5.071499e+00  1.494474e+01  1.827106e+01  2.663073e+01 -6.404067e-02 
##          1581          1582          1583          1584          1585 
##  2.128427e+01  2.790028e+01 -1.962448e+01 -8.300159e+00  3.429397e+01 
##          1586          1587          1588          1589          1590 
##  5.802190e-01 -3.657622e+00  1.798413e+01  2.616920e+01  2.963406e+00 
##          1591          1592          1593          1594          1595 
## -1.267256e+01 -1.911124e+01 -7.344433e+00  2.417923e+01 -5.209309e-01 
##          1596          1597          1598          1599          1600 
##  2.566518e+01 -1.282987e+01 -8.671552e+00  1.082113e+01  1.356063e+00 
##          1601          1602          1603          1604          1605 
## -1.127742e+01  1.528657e+00 -7.378340e+00 -2.092406e+00 -6.388100e-01 
##          1606          1607          1608          1609          1610 
## -2.222323e+01  2.483936e+01 -2.222715e+01  4.808162e+01  6.594754e+00 
##          1611          1612          1613          1614          1615 
## -1.651402e+01 -3.515274e+01 -8.581256e+00 -2.656212e+00 -4.460646e+00 
##          1616          1617          1618          1619          1620 
##  7.302091e+00 -1.948966e+01  5.228095e-01 -1.005847e-01 -3.127098e+00 
##          1621          1622          1623          1624          1625 
##  6.436824e+00  7.952545e+01  6.689323e+00  1.470137e+01  1.475861e+01 
##          1626          1627          1628          1629          1630 
## -1.940965e+01  7.832534e+00 -7.107843e+00  4.925555e+00 -1.766656e+01 
##          1631          1632          1633          1634          1635 
##  1.784088e+01 -6.262487e+00 -1.412650e+01  4.007299e+00  5.746466e-01 
##          1636          1637          1638          1639          1640 
##  6.893510e+00  2.464508e+00 -3.525468e+00  4.596665e+00 -8.450077e+00 
##          1641          1642          1643          1644          1645 
##  2.356667e+00 -7.156942e-01 -1.789592e+01 -4.799351e+00 -4.983762e-01 
##          1646          1647          1648          1649          1650 
## -4.043147e+00  1.345273e+01 -1.158609e+01 -1.278503e+01 -1.112647e+01 
##          1651          1652          1653          1654          1655 
##  1.221173e+01 -1.702051e-01  7.486670e-01  8.362281e+01 -9.627364e-01 
##          1656          1657          1658          1659          1660 
##  1.200380e+01 -2.511914e+00 -7.612064e+00  6.240426e+00 -2.821890e+01 
##          1661          1662          1663          1664          1665 
## -9.840410e+00 -1.910627e+01 -7.431465e+00 -1.084190e+01 -4.051430e+00 
##          1666          1667          1668          1669          1670 
##  2.774883e+01 -2.014347e+01 -1.524580e+01 -3.881223e+00  1.841421e+01 
##          1671          1672          1673          1674          1675 
##  1.382413e+01  7.254978e+00 -1.587867e+01 -7.533945e+00  1.403517e+01 
##          1676          1677          1678          1679          1680 
## -1.278501e+01  1.093981e+01  3.375232e+00  3.641155e+01  7.424936e+00 
##          1681          1682          1683          1684          1685 
## -1.653085e+00 -3.280504e+01  2.013214e+01  1.461465e+01 -1.712505e+01 
##          1686          1687          1688          1689          1690 
## -5.520207e+00 -1.292730e+01 -1.471294e+01  3.505274e+01  4.545740e+01 
##          1691          1692          1693          1694          1695 
##  2.256966e+00 -1.372299e+01 -3.992783e+00 -2.159827e+01  7.333422e+00 
##          1696          1697          1698          1699          1700 
## -1.183552e+01 -7.756581e+00  1.064196e+01  9.662009e+01  2.444811e+01 
##          1701          1702          1703          1704          1705 
##  2.571406e+01 -4.498733e+00 -1.837354e+00  7.029609e+00  2.388678e+00 
##          1706          1707          1708          1709          1710 
##  2.957332e+01 -4.209525e-01  2.590925e+01  2.393378e+01 -2.147695e+01 
##          1711          1712          1713          1714          1715 
## -2.579036e+00  2.031325e+01  1.931625e+01 -3.004567e+01 -3.796470e+00 
##          1716          1717          1718          1719          1720 
## -3.849740e+00 -1.302172e+00  9.754434e+00 -9.260538e+00 -1.092426e+00 
##          1721          1722          1723          1724          1725 
##  8.032411e-03 -7.935512e+00 -6.153514e+00 -1.537249e+01  4.007166e+01 
##          1726          1727          1728          1729          1730 
##  3.015037e+01  1.690905e-01 -3.540043e+00  2.789218e+01  1.477096e+01 
##          1731          1732          1733          1734          1735 
##  2.225298e+01  1.319467e+01  1.380951e+01  8.744293e+00  2.663632e+01 
##          1736          1737          1738          1739          1740 
##  1.318991e+00 -4.997885e+00 -7.903397e-01  1.485148e+01  2.294448e+00 
##          1741          1742          1743          1744          1745 
## -3.700745e+00 -9.152013e+00 -4.315352e+00  1.113216e+01 -5.838393e+00 
##          1746          1747          1748          1749          1750 
##  6.253973e+00 -3.644142e+00  2.217447e+01  5.582228e+00  2.008588e+01 
##          1751          1752          1753          1754          1755 
##  7.799010e+00  4.271484e+00  4.366563e+01 -3.278593e+00 -7.722649e+00 
##          1756          1757          1758          1759          1760 
## -9.859409e-01 -4.916388e+00  3.036843e+00  7.179215e+00  1.062006e+01 
##          1761          1762          1763          1764          1765 
## -1.017701e+01 -1.489154e+01 -1.767972e+00 -1.154954e+01 -1.398482e+01 
##          1766          1767          1768          1769          1770 
##  5.205422e-01  3.414538e+01  1.475082e+00  5.752067e+00  1.564886e+00 
##          1771          1772          1773          1774          1775 
## -3.523444e+00 -2.013072e+01 -4.648092e+00 -7.159547e+00 -8.877512e+00 
##          1776          1777          1778          1779          1780 
##  5.930582e+00 -3.243907e+01 -1.317314e+01  4.184039e+00 -2.921952e+00 
##          1781          1782          1783          1784          1785 
##  1.730094e+01 -5.727167e+00 -9.639709e+00 -1.043348e+01 -7.558841e+00 
##          1786          1787          1788          1789          1790 
##  2.487288e+01  2.612944e+01 -3.375208e+00  4.536376e+00  6.902962e+00 
##          1791          1792          1793          1794          1795 
##  6.685992e+00 -1.067490e+01  5.838139e+00 -1.321415e+00 -7.981861e+00 
##          1796          1797          1798          1799          1800 
## -3.812140e+00  4.255172e+00 -2.979371e+01 -3.909544e+00  1.814412e+01 
##          1801          1802          1803          1804          1805 
##  4.073022e+00 -1.014958e+01  2.527261e+00  3.260489e+01  1.306118e+01 
##          1806          1807          1808          1809          1810 
##  1.793670e+01 -6.134367e+00 -2.167303e+01 -1.635382e+01 -3.305643e+00 
##          1811          1812          1813          1814          1815 
## -1.422284e+01 -1.172653e+01 -8.067350e+00 -3.269985e+01 -2.697196e+01 
##          1816          1817          1818          1819          1820 
##  9.851243e+00 -1.717611e+01 -9.417768e+00  6.352430e+00  1.231297e+01 
##          1821          1822          1823          1824          1825 
##  2.819722e+01 -1.359972e+01 -6.396564e+00  4.306804e+00 -6.317466e+00 
##          1826          1827          1828          1829          1830 
## -2.078017e+01 -4.828068e+00  8.312608e+00  1.919534e+00  1.056055e+00 
##          1831          1832          1833          1834          1835 
##  8.270420e-01 -1.317051e+01 -2.289235e+00 -1.107342e+01  1.003603e+01 
##          1836          1837          1838          1839          1840 
## -2.301780e+01 -3.179625e+01 -1.529026e+01 -7.211521e+00 -2.763013e+01 
##          1841          1842          1843          1844          1845 
##  4.776415e+01  6.275711e-01 -1.050365e+01  3.004079e+00 -1.491539e+01 
##          1846          1847          1848          1849          1850 
##  3.237630e+00  2.498192e+01 -5.463540e+00 -1.368099e+01  4.712435e+00 
##          1851          1852          1853          1854          1855 
## -5.993499e+00  1.255008e+02 -1.497159e+01 -4.389453e+00 -2.126360e+01 
##          1856          1857          1858          1859          1860 
## -2.272320e+01  1.687799e+00 -1.926941e+01 -1.387704e+00 -8.989905e+00 
##          1861          1862          1863          1864          1865 
## -1.790003e+01 -1.207874e+01  1.302320e+01 -1.228045e+01 -6.631927e+00 
##          1866          1867          1868          1869          1870 
##  6.489225e+00  1.595293e+00 -1.933947e+01 -9.300958e+00 -1.785565e+01 
##          1871          1872          1873          1874          1875 
## -1.667339e+01 -2.645157e+01 -7.837491e+00  4.688188e+00  2.114723e+00 
##          1876          1877          1878          1879          1880 
## -1.012091e+01 -2.309471e+01  9.757785e+00 -9.205325e+00 -1.667055e+01 
##          1881          1882          1883          1884          1885 
##  1.090917e+01 -3.510368e+00  1.129052e+01  1.367701e+01 -1.160473e+00 
##          1886          1887          1888          1889          1890 
##  7.214427e+00 -6.019912e+00 -9.228146e+00  1.079897e+01 -3.529306e-01 
##          1891          1892          1893          1894          1895 
## -1.000802e+01 -2.269203e+01 -1.135564e+01 -3.736538e+00  6.292951e+00 
##          1896          1897          1898          1899          1900 
##  9.676166e+00 -8.045307e-01 -4.320111e+00  5.451032e+00 -7.471105e-01 
##          1901          1902          1903          1904          1905 
##  5.100371e+00 -1.250427e+01 -3.736951e+00 -1.730845e+01  6.128190e+01 
##          1906          1907          1908          1909          1910 
##  8.620481e+00  5.193379e+00  8.250036e-01 -1.535412e+01 -6.129321e+00 
##          1911          1912          1913          1914          1915 
##  5.541029e+00 -4.560181e+00 -1.564603e+01  7.711374e+00 -7.737640e+00 
##          1916          1917          1918          1919          1920 
## -6.125069e+00 -4.039534e+00 -4.832832e+00  2.453836e+00 -4.368106e+00 
##          1921          1922          1923          1924          1925 
## -4.237208e+00 -2.506089e+01 -1.670337e+01 -9.761690e+00 -2.605756e+01 
##          1926          1927          1928          1929          1930 
##  1.972158e+01  7.122334e+00  1.805646e+01 -1.767407e+01 -7.063007e+00 
##          1931          1932          1933          1934          1935 
##  3.736462e+01 -7.113123e+00 -1.107830e+01  1.822343e+00 -1.285086e+01 
##          1936          1937          1938          1939          1940 
##  3.680766e+01 -1.570067e+01 -1.258181e+01  3.386924e+01 -9.107070e+00 
##          1941          1942          1943          1944          1945 
## -8.151458e-01  1.435150e+01  4.261927e+00 -1.096327e+01 -1.251729e+00 
##          1946          1947          1948          1949          1950 
##  3.464989e+00  3.232566e+00  1.028303e+01 -1.545867e+01  2.271782e+01 
##          1951          1952          1953          1954          1955 
##  1.672544e+01  3.000146e+00 -3.155571e+00  9.701858e+00  4.576642e+00 
##          1956          1957          1958          1959          1960 
##  2.358189e+00  5.314642e+00  9.451527e+00  9.587712e+00 -5.546237e+00 
##          1961          1962          1963          1964          1965 
## -3.399645e+00 -4.581492e+00 -1.521860e+01 -3.006242e+00  1.616264e+00 
##          1966          1967          1968          1969          1970 
## -2.052653e+01  6.122492e+01 -2.912540e+01  1.155837e+01 -1.645078e+00 
##          1971          1972          1973          1974          1975 
## -7.979558e+00  1.047783e+01  7.284467e+00 -1.612568e+00 -5.960972e+00 
##          1976          1977          1978          1979          1980 
## -7.641665e+00 -1.634323e+01  1.969845e+01 -8.449260e+00 -5.126237e+00 
##          1981          1982          1983          1984          1985 
##  8.298084e+00  1.684745e+01  5.579315e-01 -6.148813e+00  1.978844e+01 
##          1986          1987          1988          1989          1990 
## -1.898715e+01  1.898942e+00 -8.182129e+00 -1.918273e+01 -2.069128e+00 
##          1991          1992          1993          1994          1995 
## -1.002384e+01 -8.533314e-01 -1.661099e+01 -1.029254e+01  4.062432e+00 
##          1996          1997          1998          1999          2000 
## -2.043694e+01 -5.651166e-01  2.177928e+01 -6.247959e+00  1.951975e+00 
##          2001          2002          2003          2004          2005 
## -3.477402e+00  1.223994e+00  7.981496e+00  1.237067e+01  4.625178e+00 
##          2006          2007          2008          2009          2010 
## -1.039282e+01  2.947027e+01 -8.965996e+00  1.807022e+01  1.545790e+01 
##          2011          2012          2013          2014          2015 
##  3.309756e+01 -9.323501e+00  1.479462e+00  2.439068e+01  3.067611e-01 
##          2016          2017          2018          2019          2020 
## -9.659412e+00 -1.998730e+00  1.038677e+01 -1.613303e+00  7.873457e-01 
##          2021          2022          2023          2024          2025 
## -1.797738e+01  5.482219e+00  6.728782e+00  3.442473e-01  2.872234e+00 
##          2026          2027          2028          2029          2030 
##  1.622082e+01  5.573545e+01 -3.208003e+00 -1.450189e+01 -1.732201e+01 
##          2031          2032          2033          2034          2035 
##  5.498100e+00  4.667360e+01  3.852467e+00 -7.994020e+00 -2.872299e+00 
##          2036          2037          2038          2039          2040 
## -1.059726e+01  1.377987e+01 -1.583662e+01 -1.234416e+01 -1.551008e+01 
##          2041          2042          2043          2044          2045 
## -4.072543e+00  1.140703e+01 -1.278210e+01 -4.091641e+01 -1.829489e+01 
##          2046          2047          2048          2049          2050 
## -1.238523e+01 -2.594408e-01  2.748133e+00  3.433338e+00 -5.110320e+00 
##          2051          2052          2053          2054          2055 
##  4.915751e+00  1.209187e+01  2.129960e+01  3.162543e+00 -2.950707e+00 
##          2056          2057          2058          2059          2060 
##  1.872925e+01  1.654460e+00 -7.065955e+00 -5.342583e+00 -2.199042e+01 
##          2061          2062          2063          2064          2065 
## -1.256382e+01 -8.652019e-01  1.637649e+00  9.786571e-01 -1.793330e+00 
##          2066          2067          2068          2069          2070 
##  1.407260e+01  1.673212e+01  1.487388e+01 -1.367874e+01  1.388675e+01 
##          2071          2072          2073          2074          2075 
##  1.773756e+01 -5.027349e-01  9.588889e+00  2.681627e+01 -3.073785e+01 
##          2076          2077          2078          2079          2080 
##  9.558028e+00  5.792192e+01 -1.479095e+01  2.267954e+01  9.326153e-01 
##          2081          2082          2083          2084          2085 
## -1.744400e+01  5.978558e+00 -3.543769e+00  2.451803e+00  2.938613e+00 
##          2086          2087          2088          2089          2090 
## -1.252662e+01  7.877266e+00 -1.252191e+01 -3.075206e+01 -2.358047e+01 
##          2091          2092          2093          2094          2095 
##  2.887329e+00  5.469042e+00 -1.071153e+01 -7.932444e+00  9.107702e-01 
##          2096          2097          2098          2099          2100 
##  1.950717e+01 -1.865873e+00 -1.951151e+01 -3.389669e+01 -6.096091e+00 
##          2101          2102          2103          2104          2105 
## -2.644345e+01  1.878993e-01 -1.212650e+01 -6.965082e+00  1.565162e+01 
##          2106          2107          2108          2109          2110 
##  5.220975e+01  1.599522e+01  8.708376e+00  9.561980e+00 -1.366159e+01 
##          2111          2112          2113          2114          2115 
## -6.973886e-01 -1.180251e+01  8.491223e+00  1.882220e+01  1.015065e+01 
##          2116          2117          2118          2119          2120 
##  1.485321e+01  4.651644e+01  1.376385e+00  5.102679e+00 -1.010024e+01 
##          2121          2122          2123          2124          2125 
## -1.062566e+01 -7.636458e+00 -5.298702e+00  6.115360e+00 -4.150227e+00 
##          2126          2127          2128          2129          2130 
##  1.715523e+00  4.048918e+00 -3.151234e+01 -6.407290e+00  6.776048e+00 
##          2131          2132          2133          2134          2135 
##  2.100979e+01 -2.189947e+01  2.349826e+00 -9.159336e+00 -2.373784e+01 
##          2136          2137          2138          2139          2140 
## -1.832875e+01 -3.247832e+01  6.368859e+01 -3.168254e+00 -3.551040e+00 
##          2141          2142          2143          2144          2145 
## -3.142460e+01 -3.504112e+01  1.741062e+01 -5.763365e+00 -1.738871e+01 
##          2146          2147          2148          2149          2150 
##  3.478983e+01 -3.141605e+01  7.278087e+00 -2.240663e+01 -7.364622e-01 
##          2151          2152          2153          2154          2155 
## -1.539151e+01 -1.874398e+01  1.138011e+01  3.319042e+01  9.405767e+00 
##          2156          2157          2158          2159          2160 
## -1.084753e+01 -1.739548e+01 -4.978116e+00  1.454654e+01 -1.528893e+01 
##          2161          2162          2163          2164          2165 
## -1.588233e+01  9.956863e+00 -1.031759e+01  1.270962e+01  1.550065e+01 
##          2166          2167          2168          2169          2170 
## -1.440825e+01  1.683269e+01 -8.889499e+00 -2.022386e+01 -7.091808e+00 
##          2171          2172          2173          2174          2175 
## -3.048627e-01  5.083954e+00  2.474770e-01 -9.934938e+00 -8.170256e+00 
##          2176          2177          2178          2179          2180 
## -3.893280e+00 -7.771250e+00 -1.689208e+00 -2.136176e+01  3.157261e+01 
##          2181          2182          2183          2184          2185 
## -8.065085e+00  7.602834e+00 -1.208159e+01 -1.446830e+01  9.718921e+00 
##          2186          2187          2188          2189          2190 
## -8.384108e+00  2.811473e+01 -1.194655e+01  1.759996e+01 -1.150257e+01 
##          2191          2192          2193          2194          2195 
## -2.185555e+00 -9.958218e+00 -9.938494e+00 -5.134921e+00  1.296465e+01 
##          2196          2197          2198          2199          2200 
## -4.979848e+00 -2.250641e+00 -3.774429e+00 -9.664612e+00  1.943476e+00 
##          2201          2202          2203          2204          2205 
##  4.059558e+00  5.307075e-01 -6.891858e+00 -5.972803e+00  4.624440e+00 
##          2206          2207          2208          2209          2210 
##  6.908444e+00 -1.953008e+01 -1.689013e+01  2.447478e+00 -9.478379e+00 
##          2211          2212          2213          2214          2215 
##  2.424327e+01  1.668200e+01 -6.191011e+00  1.336598e+01 -1.628823e+01 
##          2216          2217          2218          2219          2220 
##  7.705780e+00  2.848859e+00 -3.078416e+00 -3.392237e+00 -3.170184e+00 
##          2221          2222          2223          2224          2225 
## -7.908974e+00  2.040704e+01 -1.352836e+01 -2.285041e+00 -3.362080e+00 
##          2226          2227          2228          2229          2230 
## -2.237819e+00 -3.804568e+00 -1.330249e+01  1.258058e+01  1.197184e+01 
##          2231          2232          2233          2234          2235 
##  1.077094e+00 -1.870419e+01  2.513353e+00 -2.041006e+00 -6.688799e-01 
##          2236          2237          2238          2239          2240 
##  4.840394e+00 -2.985078e+00 -2.632307e+00 -5.543272e+00  3.496857e+00 
##          2241          2242          2243          2244          2245 
## -1.614719e+01  8.085633e-02 -1.715524e+01 -3.128391e+00  1.377803e+00 
##          2246          2247          2248          2249          2250 
##  5.464815e+00  2.804664e+01 -1.189950e+01  2.101478e+00  4.509673e+00 
##          2251          2252          2253          2254          2255 
## -1.454861e+01 -3.333709e+01  1.025325e+01  9.107488e+00  3.754128e+00 
##          2256          2257          2258          2259          2260 
## -1.654268e+01 -1.470291e+01 -7.337423e+00 -2.424359e+01 -2.908899e+00 
##          2261          2262          2263          2264          2265 
## -6.861643e+00 -9.176842e+00  1.498038e+01  8.507158e+00 -4.890246e+00 
##          2266          2267          2268          2269          2270 
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##          2271          2272          2273          2274          2275 
## -1.068041e+01 -3.908971e+00 -1.913951e+01  1.730689e+00 -4.240759e-01 
##          2276          2277          2278          2279          2280 
##  3.744799e+01 -6.501806e+00  1.958725e+00  6.856409e+01  6.239820e+01 
##          2281          2282          2283          2284          2285 
##  2.677737e+01  7.838591e+00  2.128771e+01 -1.966496e+01 -5.432553e+00 
##          2286          2287          2288          2289          2290 
## -7.075027e+00  1.961919e+01 -5.986344e+00  3.345229e+00  1.478356e+01 
##          2291          2292          2293          2294          2295 
## -1.458028e+01 -1.102030e+01  1.204474e+01 -8.616653e+00 -2.844813e+01 
##          2296          2297          2298          2299          2300 
## -3.556549e+00 -3.712989e+00  1.332852e+01 -2.076794e+01 -9.121867e+00 
##          2301          2302          2303          2304          2305 
##  1.108041e+01  6.440013e+00 -4.559697e-01 -1.085223e+01 -4.180214e+01 
##          2306          2307          2308          2309          2310 
## -3.407017e+01 -1.424087e+01  1.914238e+00  5.851457e+00  3.135656e+00 
##          2311          2312          2313          2314          2315 
##  7.591411e+01 -1.273050e+01 -5.492680e+00  3.929190e+00  1.131162e+02 
##          2316          2317          2318          2319          2320 
## -1.524217e+01  1.621333e+01 -1.247919e+01  6.114082e+00 -2.027352e+01 
##          2321          2322          2323          2324          2325 
## -1.126452e+01 -1.311389e+01 -1.138153e+01  1.304287e+01  1.676318e+01 
##          2326          2327          2328          2329          2330 
##  4.073927e+01 -2.916714e+01  3.741126e+00 -3.306645e+00 -6.113352e+00 
##          2331          2332          2333          2334          2335 
##  4.567080e+00  1.918143e+01 -1.819559e+01 -1.160620e+01 -1.435542e+01 
##          2336          2337          2338          2339          2340 
##  1.457067e+01 -1.167785e+00 -1.987386e+00 -8.320066e+00 -1.522878e+01 
##          2341          2342          2343          2344          2345 
## -3.491098e+00 -1.096129e+01  5.805853e+00 -1.136265e+01  2.751934e+00 
##          2346          2347          2348          2349          2350 
##  7.830490e+00 -5.299100e+00 -1.445896e+01 -2.221191e+00  2.816144e+00 
##          2351          2352          2353          2354          2355 
## -1.590167e+00 -1.504010e+01 -1.649463e+01  7.532458e+00  2.908022e+00 
##          2356          2357          2358          2359          2360 
## -1.253989e+00  3.930374e+00 -4.028608e+00  1.074140e+01 -1.705345e+01 
##          2361          2362          2363          2364          2365 
##  1.217318e+01 -1.216075e+01 -1.370162e+01 -3.601012e+00  1.109379e+01 
##          2366          2367          2368          2369          2370 
## -4.854701e+00  3.608866e+00 -1.662722e+01  8.398889e+00 -2.555593e+00 
##          2371          2372          2373          2374          2375 
## -1.477694e+01  9.158341e+00  2.036315e+01  9.265064e+00  1.495866e+01 
##          2376          2377          2378          2379          2380 
## -8.830048e+00  5.111840e+01  1.798183e+00  1.053628e+01 -1.288478e+01 
##          2381          2382          2383          2384          2385 
##  9.346980e+00 -2.182757e+01 -1.210417e+01 -2.415499e+00 -1.480066e+01 
##          2386          2387          2388          2389          2390 
##  3.132862e+01  6.183750e+00 -3.422979e+01 -1.870498e+01 -1.613514e+01 
##          2391          2392          2393          2394          2395 
##  2.178360e+00  8.436832e+00 -3.708961e+00 -1.551500e+01  4.514637e+01 
##          2396          2397          2398          2399          2400 
## -3.376707e+00  1.901521e+00  9.254468e+00  2.104014e+01 -5.831816e+00 
##          2401          2402          2403          2404          2405 
##  3.451524e+00  5.521493e+01 -2.230036e+01  1.025578e+01  2.865399e+00 
##          2406          2407          2408          2409          2410 
## -1.075279e+01 -6.630737e+00  2.666740e+01 -1.785957e+01 -8.139862e+00 
##          2411          2412          2413          2414          2415 
##  5.465343e+01 -1.299557e+01 -6.436021e+00  1.859269e+01 -6.389420e+00 
##          2416          2417          2418          2419          2420 
##  1.456634e+01 -6.452413e+00 -2.530891e+01  4.975196e+01  9.145982e+00 
##          2421          2422          2423          2424          2425 
##  5.371460e-01  1.126358e+01 -1.666996e+01  2.227755e+01 -1.359105e+00 
##          2426          2427          2428          2429          2430 
##  2.963071e+01 -1.451300e+01 -2.253941e+01 -9.662616e+00  1.082992e+01 
##          2431          2432          2433          2434          2435 
##  1.438131e+01  2.995420e+01 -4.376658e+00  2.318648e+01  3.610419e+01 
##          2436          2437          2438          2439          2440 
## -5.393081e+00  1.999319e+01  4.904287e+00 -2.641775e+00  3.013615e+01 
##          2441          2442          2443          2444          2445 
##  3.888168e+00  1.953929e+01  4.750508e+01  7.501635e+01  3.406102e+01 
##          2446          2447          2448          2449          2450 
##  2.070237e+00  6.332660e+01 -6.886047e+00 -2.467592e+01 -5.334629e+00 
##          2451          2452          2453          2454          2455 
##  2.948679e+01 -7.173392e+00  9.890473e-01 -9.667456e-01  8.779897e+00 
##          2456          2457          2458          2459          2460 
## -1.384632e+00 -3.678734e+00 -1.244336e+00 -3.239339e+01 -8.399040e+00 
##          2461          2462          2463          2464          2465 
## -5.825965e+00 -2.728701e+00 -1.845188e-01 -9.684909e+00  2.047528e+01 
##          2466          2467          2468          2469          2470 
##  2.923735e+01 -1.125801e+01  4.256638e+00 -8.994218e+00  1.363714e+01 
##          2471          2472          2473          2474          2475 
## -8.337128e+00  1.656918e+01  2.779536e+01 -1.804605e+01  1.252052e+01 
##          2476          2477          2478          2479          2480 
## -2.434275e+00  2.036791e+01  3.390791e+00 -8.937907e+00  1.739596e+00 
##          2481          2482          2483          2484          2485 
##  3.703952e-01  1.806295e+00  4.787722e+00  1.124796e+01 -1.970086e+01 
##          2486          2487          2488          2489          2490 
##  9.230049e+00 -1.130633e+01  4.144875e+01  1.085260e+01  8.401461e+00 
##          2491          2492          2493          2494          2495 
## -1.453744e+01  4.825595e+01  4.552232e+01 -8.035164e+00  1.683789e+01 
##          2496          2497          2498          2499          2500 
## -6.660490e+00  6.287585e+00 -7.634183e+00  1.407530e+00  2.682528e+00 
##          2501          2502          2503          2504          2505 
## -2.027329e+01 -1.707406e+01 -5.631040e+00  8.496592e+01 -3.057123e+00 
##          2506          2507          2508          2509          2510 
##  3.046087e+01 -4.877251e-02  1.535277e+01  3.823471e+00  2.288108e+01 
##          2511          2512          2513          2514          2515 
##  2.747809e+01  7.952138e+00 -8.860394e+00  2.945104e+01  9.633971e+01 
##          2516          2517          2518          2519          2520 
##  2.937660e+01  1.450734e+00  8.547940e+00 -3.313065e+01  4.726580e+01 
##          2521          2522          2523          2524          2525 
## -1.167398e+01 -1.763393e+01  1.658373e-01  9.228645e+00 -1.377681e+01 
##          2526          2527          2528          2529          2530 
## -1.605015e+01  5.919448e+00  9.804577e+01 -2.282062e+01 -1.916063e+01 
##          2531          2532          2533          2534          2535 
##  6.816094e+01 -6.470808e+00 -2.264175e+00  6.071916e+00 -1.931835e+00 
##          2536          2537          2538          2539          2540 
##  1.553123e+01  1.406907e+00  6.149951e+00  1.390748e+01 -5.494426e-01 
##          2541          2542          2543          2544          2545 
## -1.013274e+01 -2.221630e+01 -2.698292e+01  3.948212e+00  2.294827e+01 
##          2546          2547          2548          2549          2550 
##  1.410134e+00  5.188960e+00 -4.231557e+00  9.549756e+00  5.138557e+01 
##          2551          2552          2553          2554          2555 
##  3.673218e-01  5.714377e+00  1.856326e+01 -5.010012e+00  1.867696e+00 
##          2556          2557          2558          2559          2560 
##  8.995208e+00 -8.434001e+00  1.460815e+01  7.545470e+00  1.588877e+01 
##          2561          2562          2563          2564          2565 
## -2.762688e-01  5.330942e+01  1.938826e+01  3.602492e+01 -7.986863e+00 
##          2566          2567          2568          2569          2570 
## -9.145990e-01 -2.279149e+01  7.763232e+00  1.113305e+01 -2.579002e+00 
##          2571          2572          2573          2574          2575 
## -1.500086e+01  1.869800e+01  7.904059e+00 -7.981174e+00 -8.254805e+00 
##          2576          2577          2578          2579          2580 
##  8.645270e-02  6.770844e+00  2.300412e+01 -5.879492e+00 -1.512203e+01 
##          2581          2582          2583          2584          2585 
##  4.315780e+00  4.294190e-01 -2.555401e+00  2.580265e+01  1.985074e+01 
##          2586          2587          2588          2589          2590 
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##          2591          2592          2593          2594          2595 
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##          2596          2597          2598          2599          2600 
## -1.303219e+01 -5.355995e-01 -6.356686e+00 -4.845186e+00  2.554186e-01 
##          2601          2602          2603          2604          2605 
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##          2606          2607          2608          2609          2610 
## -8.910006e+00 -3.873750e+00  3.949342e+00  1.846183e+01 -9.991144e-01 
##          2611          2612          2613          2614          2615 
##  4.207955e+00  4.303223e+00 -1.213302e+01  4.269251e+00 -4.512298e+00 
##          2616          2617          2618          2619          2620 
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##          2621          2622          2623          2624          2625 
## -3.075301e+01 -5.169268e+00  9.623299e-01 -1.809518e+00  2.938196e+01 
##          2626          2627          2628          2629          2630 
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##          2631          2632          2633          2634          2635 
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##          2636          2637          2638          2639          2640 
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##          2641          2642          2643          2644          2645 
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##          2646          2647          2648          2649          2650 
## -1.058742e+01 -1.560877e+01 -8.378989e+00  1.342054e+01  6.467505e+00 
##          2651          2652          2653          2654          2655 
## -2.661797e+00  1.572869e+01  1.402544e+01 -1.395222e+01  8.362299e-01 
##          2656          2657          2658          2659          2660 
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##          2661          2662          2663          2664          2665 
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##          2666          2667          2668          2669          2670 
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##          2671          2672          2673          2674          2675 
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##          2676          2677          2678          2679          2680 
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##          2681          2682          2683          2684          2685 
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##          2691          2692          2693          2694          2695 
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##          2696          2697          2698          2699          2700 
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##          2701          2702          2703          2704          2705 
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##          2706          2707          2708          2709          2710 
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##          2711          2712          2713          2714          2715 
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##          2716          2717          2718          2719          2720 
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##          2721          2722          2723          2724          2725 
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##          2726          2727          2728          2729          2730 
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##          2731          2732          2733          2734          2735 
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##          2736          2737          2738          2739          2740 
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##          2741          2742          2743          2744          2745 
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##          2746          2747          2748          2749          2750 
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##          2751          2752          2753          2754          2755 
## -3.081352e+01 -3.567766e+00 -3.783294e+01  9.164199e+00  5.989099e+00 
##          2756          2757          2758          2759          2760 
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##          2761          2762          2763          2764          2765 
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##          2766          2767          2768          2769          2770 
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##          2771          2772          2773          2774          2775 
## -9.907900e+00  1.388427e-01 -9.579613e+00 -1.077656e+01 -1.507562e+00 
##          2776          2777          2778          2779          2780 
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##          2781          2782          2783          2784          2785 
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##          2786          2787          2788          2789          2790 
## -1.069607e+01  1.356315e+01 -1.171952e+01 -2.305303e-01  2.250425e+00 
##          2791          2792          2793          2794          2795 
## -7.050819e+00  1.038335e+01 -1.176636e+01 -1.163437e+01  1.681009e+01 
##          2796          2797          2798          2799          2800 
##  1.164302e+00 -1.239978e+00 -4.922177e+00  1.047569e+00 -1.776471e+01 
##          2801          2802          2803          2804          2805 
## -2.648718e+01 -1.636646e+00  1.376322e+00 -1.700618e+01 -5.391077e+00 
##          2806          2807          2808          2809          2810 
## -6.679836e+00 -1.655919e+01  8.575686e+00  2.801535e+01  1.140439e+01 
##          2811          2812          2813          2814          2815 
## -1.374691e+00  6.931447e-01 -2.665893e+01 -1.199614e+01 -2.086042e+01 
##          2816          2817          2818          2819          2820 
##  3.125613e+01  5.888673e+01 -6.705840e+00  5.470719e+00 -2.220643e+01 
##          2821          2822          2823          2824          2825 
## -1.547239e+00 -8.952154e+00 -3.226881e+01 -1.507703e+01 -1.353578e+01 
##          2826          2827          2828          2829          2830 
## -6.020669e+00  2.673890e+00  3.082893e+00 -1.268124e+01 -1.166136e+01 
##          2831          2832          2833          2834          2835 
## -1.640335e+01 -1.342988e+01  3.565016e+00 -5.963127e+00  2.363053e+01 
##          2836          2837          2838          2839          2840 
##  1.274569e+01 -2.207869e+00 -9.847796e+00 -1.105333e+01 -2.001908e+01 
##          2841          2842          2843          2844          2845 
##  1.246658e+00 -8.533267e+00  1.135694e+01  1.618050e+00  9.402747e+00 
##          2846          2847          2848          2849          2850 
## -1.102646e+01  9.760498e-02 -2.043441e+01  2.642580e+00 -3.067361e+01 
##          2851          2852          2853          2854          2855 
## -1.119617e+01 -1.324830e+00  8.175474e+00  3.298784e+00  8.602720e+00 
##          2856          2857          2858          2859          2860 
## -4.045331e+00  8.075310e+00  1.001764e+01  2.380262e+01  1.420325e+01 
##          2861          2862          2863          2864          2865 
## -5.037889e+00 -4.519990e+00 -6.528102e-01 -1.679699e+00  3.469557e+00 
##          2866          2867          2868          2869          2870 
##  1.465985e+01 -1.272588e+01 -2.219034e+00 -1.880484e+01 -7.103244e+00 
##          2871          2872          2873          2874          2875 
## -9.603267e+00  2.480547e+01 -1.158645e+01  3.323851e+01 -7.672567e-01 
##          2876          2877          2878          2879          2880 
##  1.537488e+01 -1.231572e+01 -1.451887e+01  7.397521e+00 -1.040569e+01 
##          2881          2882          2883          2884          2885 
## -3.117078e+01 -7.834549e+00 -5.846400e+00 -8.969189e+00  3.365392e+01 
##          2886          2887          2888          2889          2890 
## -3.925483e+00 -1.733478e+00 -8.998345e+00 -2.269237e+01 -9.157696e+00 
##          2891          2892          2893          2894          2895 
## -7.941015e+00 -1.147751e+01  5.358303e-01 -1.931247e+01  1.329633e+01 
##          2896          2897          2898          2899          2900 
##  1.085913e+01 -1.455620e+01 -2.656616e+01 -2.472059e+00 -1.126840e+01 
##          2901          2902          2903          2904          2905 
##  6.367108e+01 -1.608578e+01  4.489302e+00  1.541110e+01  8.666137e+00 
##          2906          2907          2908          2909          2910 
## -9.292161e+00 -1.679408e+01 -1.140704e+01 -9.722435e+00  5.468439e+00 
##          2911          2912          2913          2914          2915 
## -1.036253e+01 -9.895553e+00 -2.488202e+01  1.630110e+00 -1.606640e+01 
##          2916          2917          2918          2919          2920 
## -1.328030e+01  9.535156e+00 -1.620806e+01  1.525002e+00 -8.875989e+00 
##          2921          2922          2923          2924          2925 
##  9.689833e-01 -3.516563e+01 -2.845433e-01 -2.035030e+00 -1.070112e+01 
##          2926          2927          2928          2929          2930 
##  8.677370e-01 -1.512405e+01 -1.604463e+01 -2.450680e+00 -6.340403e+00 
##          2931          2932          2933          2934          2935 
## -7.112242e+00  8.829793e+00 -7.353132e+00  8.923729e+00  2.087539e-01 
##          2936          2937          2938          2939          2940 
##  6.863682e+00 -3.215852e+01 -1.043891e+01 -1.888605e+01 -1.318712e+01 
##          2941          2942          2943          2944          2945 
## -1.116389e+00  5.307425e+00 -1.525260e+01 -1.727068e+01 -4.605218e+00 
##          2946          2947          2948          2949          2950 
## -1.873890e+01 -9.622767e+00  1.517361e+00  2.572029e-01 -1.383318e+01 
##          2951          2952          2953          2954          2955 
## -1.430934e+01  3.646616e+00 -6.749141e+00  2.048601e+01 -3.928272e+00 
##          2956          2957          2958          2959          2960 
##  1.956844e+01 -9.612430e+00  3.909965e+00  8.635245e+00 -6.621281e+00 
##          2961          2962          2963          2964          2965 
##  5.362069e+00 -6.931573e-02 -5.351939e+00  5.567875e+00  1.659412e+01 
##          2966          2967          2968          2969          2970 
## -2.835346e+00  4.250503e+00  4.889990e+01  9.651768e-01 -1.745976e+01 
##          2971          2972          2973          2974          2975 
##  6.272419e+00  2.691674e+01 -1.553421e+01  2.029897e+01 -1.648050e+00 
##          2976          2977          2978          2979          2980 
##  3.824338e-01 -8.844515e+00 -9.172382e+00  3.234483e+00  1.087729e+01 
##          2981          2982          2983          2984          2985 
##  8.494550e+00 -4.265545e+00  1.669096e+01 -1.299925e+01 -7.986515e+00 
##          2986          2987          2988          2989          2990 
##  3.104572e+01 -1.567731e+01 -4.056771e+00 -1.385991e+01 -6.245931e-01 
##          2991          2992          2993          2994          2995 
## -4.750870e+00 -1.310518e+01  2.215087e+01  1.408892e+01  1.308854e+01 
##          2996          2997          2998          2999          3000 
##  5.330478e+00  8.357094e+00  9.218836e+00  4.553448e+00  1.466652e+01 
##          3001          3002          3003          3004          3005 
##  3.442983e+01  9.139734e+00  4.180307e+00 -1.272870e+01 -1.272601e+01 
##          3006          3007          3008          3009          3010 
## -1.509005e+01 -7.838342e+00 -2.150381e+01  8.928590e-01 -1.815849e+01 
##          3011          3012          3013          3014          3015 
##  1.590717e+01 -1.210715e+01 -9.111887e+00  3.344057e+00 -4.009873e+00 
##          3016          3017          3018          3019          3020 
## -1.888115e-01  2.757260e+01  1.782195e+00  1.931719e+01  1.981195e+01 
##          3021          3022          3023          3024          3025 
##  1.112067e+01 -2.938003e+00 -1.718022e+01 -1.088615e+01 -1.576306e+01 
##          3026          3027          3028          3029          3030 
##  8.731506e+00 -1.897640e+01 -9.524633e+00 -2.092526e+01  7.105432e+00 
##          3031          3032          3033          3034          3035 
## -1.552604e-01 -4.811048e+00 -1.327937e+01  1.448550e+01 -2.511561e+01 
##          3036          3037          3038          3039          3040 
## -1.521469e+01 -9.423391e+00  6.300022e+00 -1.981635e+01 -1.075186e+01 
##          3041          3042          3043          3044          3045 
## -3.674037e-01 -2.943287e+00  1.288957e+01 -9.139647e+00 -1.856696e+01 
##          3046          3047          3048          3049          3050 
## -1.897959e+00 -7.390867e+00  2.803821e+01 -8.704998e+00 -2.107443e+01 
##          3051          3052          3053          3054          3055 
## -9.277126e+00 -4.337154e+00  2.941925e+00 -1.122145e+01  1.852932e+01 
##          3056          3057          3058          3059          3060 
## -2.805048e+00 -3.477731e+01 -2.445111e+00  1.627113e+01 -5.594448e+00 
##          3061          3062          3063          3064          3065 
##  2.104915e+01 -1.449998e+01 -1.374310e+01 -4.468307e+00 -5.819229e+00 
##          3066          3067          3068          3069          3070 
## -1.032998e+01 -2.926932e+00  9.117597e-01 -7.173852e+00  1.155808e+00 
##          3071          3072          3073          3074          3075 
##  1.220647e+01  5.613742e+00  1.241506e+01  7.167260e-01 -5.596055e+01 
##          3076          3077          3078          3079          3080 
##  3.591736e+00 -3.875454e+00 -2.857847e+01  6.601111e+00  6.702892e+01 
##          3081          3082          3083          3084          3085 
## -6.706779e+00 -1.836433e+00 -1.209685e+01  1.015078e+01  1.430364e+01 
##          3086          3087          3088          3089          3090 
##  1.135716e+01 -1.288468e+01 -3.182545e+01  2.033414e+01 -6.659078e+00 
##          3091          3092          3093          3094          3095 
##  1.910203e+01 -9.271154e+00 -1.088468e+01  2.369055e+01  5.221543e+00 
##          3096          3097          3098          3099          3100 
##  9.020114e+00  1.413905e+01  1.125306e+01 -6.387120e+00  3.673188e+00 
##          3101          3102          3103          3104          3105 
## -3.642806e+00  1.053947e+01  1.616119e+00 -2.197839e+01  7.697971e+00 
##          3106          3107          3108          3109          3110 
## -4.305090e+00  9.594579e+00  3.381119e+01  1.655639e+01 -1.594409e+01 
##          3111          3112          3113          3114          3115 
##  2.211309e+01  2.911558e+00  6.283670e+00 -4.891320e+00 -2.509935e+00 
##          3116          3117          3118          3119          3120 
##  2.448429e+00  3.447247e+00  1.973991e+01 -2.697252e+01 -4.731416e+00 
##          3121          3122          3123          3124          3125 
##  1.697023e+01 -6.380169e+00  5.918777e+00  1.451708e+01  1.229635e+01 
##          3126          3127          3128          3129          3130 
## -1.244570e+01 -6.112038e-01  4.136268e+01  4.898465e+01  4.755088e+00 
##          3131          3132          3133          3134          3135 
## -9.560748e+00  2.354914e+01  1.009745e+01 -7.532045e+00  1.128783e+01 
##          3136          3137          3138          3139          3140 
##  2.286397e+01 -1.732228e+00  2.744301e+01  2.250842e+01 -1.650253e+01 
##          3141          3142          3143          3144          3145 
##  3.776645e+00  5.547082e-01  1.422628e+01 -6.338827e+00 -1.294560e+01 
##          3146          3147          3148          3149          3150 
##  2.393501e+01 -1.150415e+00 -2.689909e+01  2.459657e+01  5.997005e+00 
##          3151          3152          3153          3154          3155 
## -3.860257e+00  1.636017e+01 -1.870951e+01  2.077829e+00  6.319489e+00 
##          3156          3157          3158          3159          3160 
##  4.465450e+01 -1.834250e+01 -1.114093e+00 -1.353840e+00 -5.883611e+00 
##          3161          3162          3163          3164          3165 
## -2.675939e+00 -7.019973e+00  2.269831e+01 -7.871985e-01  1.064706e+00 
##          3166          3167          3168          3169          3170 
##  1.307045e+00  1.377584e+01  2.059267e+01 -3.925900e-01 -1.371845e+01 
##          3171          3172          3173          3174          3175 
## -3.397280e+00 -8.597081e+00 -9.426158e+00  2.663330e+00  2.074934e+00 
##          3176          3177          3178          3179          3180 
##  8.266120e+00  3.492560e+00 -1.709344e+01  1.953311e+01 -1.208738e+01 
##          3181          3182          3183          3184          3185 
##  3.845948e+00 -3.593507e+01 -8.640144e+00 -1.297525e+01 -1.801555e+01 
##          3186          3187          3188          3189          3190 
## -1.417767e+01  8.956808e+00 -6.275780e+00 -9.883501e+00  1.965809e+00 
##          3191          3192          3193          3194          3195 
## -2.004774e+01 -1.723809e+01 -2.972562e+00 -5.561442e+00  4.827899e+01 
##          3196          3197          3198          3199          3200 
## -1.403634e+01  1.702547e+00  4.825532e+00  2.288514e+00 -1.354822e+01 
##          3201          3202          3203          3204          3205 
## -1.539215e+01 -1.124817e+01 -1.878269e+01 -1.449758e+01  3.050028e+01 
##          3206          3207          3208          3209          3210 
##  1.529317e+01 -2.712030e+00  2.273642e-01  2.907620e+01 -6.734580e+00 
##          3211          3212          3213          3214          3215 
##  2.355522e+00 -3.271989e+00  1.594797e+01 -4.109334e+00  4.491243e+01 
##          3216          3217          3218          3219          3220 
## -1.169501e+01 -2.039437e+01  3.502126e+00  4.885726e+00 -4.407849e-01 
##          3221          3222          3223          3224          3225 
##  1.142050e+02 -2.198585e+01 -6.987465e+00  1.473489e+00  1.436962e+01 
##          3226          3227          3228          3229          3230 
## -1.628778e+01 -1.950111e+01 -1.522947e+00 -1.535944e+01  3.937822e+01 
##          3231          3232          3233          3234          3235 
##  5.278918e+00  8.521812e+00  1.959657e+01  4.225995e+01 -1.817367e+00 
##          3236          3237          3238          3239          3240 
## -8.134841e-01  2.317627e+01 -5.722308e+00 -4.898095e+00 -1.673498e+00 
##          3241          3242          3243          3244          3245 
##  4.083210e+01 -1.144333e+01 -1.117883e+01 -8.170554e-01  5.186878e+01 
##          3246          3247          3248          3249          3250 
## -6.275473e+00  1.385680e+01 -1.375271e+01  9.886632e+00 -7.356254e+00 
##          3251          3252          3253          3254          3255 
##  1.341764e-01 -6.273638e+00  1.233824e-01  5.070696e+01  1.856711e+01 
##          3256          3257          3258          3259          3260 
##  9.847054e+00  2.303563e+01  2.270286e+01 -3.170919e+00  4.538847e+01 
##          3261          3262          3263          3264          3265 
## -4.606614e+00 -5.693894e+00 -1.584605e+00 -2.111437e+00  3.159357e-02 
##          3266          3267          3268          3269          3270 
##  5.697314e+00 -1.530429e+01  5.892868e+00 -1.195666e+01  7.182007e+00 
##          3271          3272          3273          3274          3275 
##  6.348121e+00  4.908412e+00 -1.123447e+01  4.732281e+00 -1.824658e+01 
##          3276          3277          3278          3279          3280 
##  2.622899e+01 -2.734490e+00 -4.771931e+00 -3.286466e+00  3.730991e+01 
##          3281          3282          3283          3284          3285 
##  1.090857e+01  4.731624e+00 -1.454509e+01  2.349670e+01 -1.900375e+01 
##          3286          3287          3288          3289          3290 
## -6.171363e+00 -1.741074e+01  3.468116e+01  6.896159e+00 -3.170127e+00 
##          3291          3292          3293          3294          3295 
## -2.646607e+01 -9.219516e+00  5.737630e+00 -1.131156e+01 -1.693578e+01 
##          3296          3297          3298          3299          3300 
## -1.093259e+01  2.770538e+00 -2.723890e+00  5.815002e+00  3.321991e+01 
##          3301          3302          3303          3304          3305 
##  8.863250e+00  1.614655e+01 -1.886844e+00 -2.249042e+01  2.305897e+00 
##          3306          3307          3308          3309          3310 
## -4.717594e+00 -1.565917e+01  3.942835e+00  2.442063e+01  1.583010e+00 
##          3311          3312          3313          3314          3315 
##  8.317634e+00  4.578522e+00  2.765912e+01 -2.320454e+01 -5.737798e+00 
##          3316          3317          3318          3319          3320 
## -4.263730e+00 -1.472653e+01  4.327468e+00  2.085695e+01  4.844110e+01 
##          3321          3322          3323          3324          3325 
## -4.869604e+00  1.293981e+01  7.352731e+00 -1.933646e+01  2.111021e+01 
##          3326          3327          3328          3329          3330 
## -4.374648e+00 -1.170275e+01 -3.214733e+01 -1.686793e+01 -3.738223e+00 
##          3331          3332          3333          3334          3335 
## -1.374064e+01 -8.180606e+00 -2.570349e+00  1.522628e+01 -4.525728e-01 
##          3336          3337          3338          3339          3340 
##  2.249916e+01 -1.505855e+01 -4.446625e-01 -1.078302e+00 -4.932287e+00 
##          3341          3342          3343          3344          3345 
## -8.337156e+00  7.584533e+00 -3.638217e+00 -1.613427e+01 -8.598815e+00 
##          3346          3347          3348          3349          3350 
##  1.202711e+01 -3.152988e+01 -4.802664e+01  1.418016e+01 -1.015536e+01 
##          3351          3352          3353          3354          3355 
##  2.393590e+01  1.165231e+01  1.622890e+00 -5.596351e+00 -1.644643e+01 
##          3356          3357          3358          3359          3360 
##  3.404314e+00  2.130113e+00 -1.343022e+01 -1.228407e+01 -6.550031e+00 
##          3361          3362          3363          3364          3365 
##  1.177246e+01  8.283063e+00 -1.293286e+01 -1.533915e+01  1.698211e+01 
##          3366          3367          3368          3369          3370 
##  4.010310e+00  7.544156e+00  1.185840e+00 -9.073793e+00 -8.837083e+00 
##          3371          3372          3373          3374          3375 
##  4.040431e+01  1.180409e+01  1.967505e+01  2.345640e+01  2.566467e+01 
##          3376          3377          3378          3379          3380 
##  2.121569e+00 -8.971761e+00 -4.639476e+00 -9.411919e-01 -1.088902e+01 
##          3381          3382          3383          3384          3385 
##  1.054501e+00 -3.787143e+00 -1.041797e+01 -4.276579e+00  1.046323e-02 
##          3386          3387          3388          3389          3390 
## -1.614765e+01  9.905933e-01  1.647193e+01 -5.188654e+00 -1.550090e+01 
##          3391          3392          3393          3394          3395 
##  5.066594e+00 -9.766279e+00 -1.093780e+01  9.691345e+00 -1.243662e+01 
##          3396          3397          3398          3399          3400 
##  1.544901e+01  5.516079e+00 -9.623647e+00 -1.657611e+01 -1.545997e+00 
##          3401          3402          3403          3404          3405 
##  1.451509e+01  9.649063e+00  5.519254e+00 -1.254808e+01  3.015205e+00 
##          3406          3407          3408          3409          3410 
## -5.588203e+00  4.898827e+00 -4.029570e+00 -4.771099e+00  2.240185e+01 
##          3411          3412          3413          3414          3415 
##  5.348137e+01 -4.682615e+00 -1.767364e+01 -1.785127e+01 -1.506142e+01 
##          3416          3417          3418          3419          3420 
## -4.857881e-01  2.793547e+01 -1.986443e+01  1.494876e+01  1.666127e+01 
##          3421          3422          3423          3424          3425 
##  5.551324e+00  2.639573e-01  6.517287e+01  1.361534e-01 -9.876965e+00 
##          3426          3427          3428          3429          3430 
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##  4.445788e+00 -3.050843e+01  9.995772e+00 -4.471445e-01  7.247587e+00 
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## -4.672851e+00 -1.795215e+01 -1.784772e+01 -3.758910e-01  1.060118e-01 
##          3471          3472          3473          3474          3475 
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##          3476          3477          3478          3479          3480 
## -1.279523e+01  3.278476e+00 -9.509813e+00  1.075276e-01 -1.221981e+01 
##          3481          3482          3483          3484          3485 
## -8.646638e+00 -9.574116e+00 -5.082633e+00 -9.358128e+00 -5.348557e+00 
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## -4.167742e+00 -3.549762e+00  4.282901e-02 -3.708973e+00 -3.486889e+01 
##          3511          3512          3513          3514          3515 
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##          3516          3517          3518          3519          3520 
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## -8.860668e+00 -1.449697e+01  1.977340e+01  2.359622e+01 -9.671450e+00 
##          3531          3532          3533          3534          3535 
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##          3536          3537          3538          3539          3540 
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##          3541          3542          3543          3544          3545 
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##          3551          3552          3553          3554          3555 
## -2.306126e+01 -1.202486e+01  1.845408e+01  4.301783e-01 -1.596590e+01 
##          3556          3557          3558          3559          3560 
## -7.622100e+00 -1.920331e-01  3.287037e+00 -5.801241e+00 -1.767136e+01 
##          3561          3562          3563          3564          3565 
##  1.280358e+01  4.275602e+00  3.656679e+01 -3.060933e-01  2.880061e+01 
##          3566          3567          3568          3569          3570 
##  4.946052e+01  6.906671e+00 -1.633993e+00  1.519266e+01  2.726989e+00 
##          3571          3572          3573          3574          3575 
##  5.000166e+00 -4.097816e+01 -7.998992e-01  1.275364e+01 -1.399609e+01 
##          3576          3577          3578          3579          3580 
## -5.385898e+00  2.518812e+01  5.859409e+00 -1.756100e+01 -1.472013e+01 
##          3581          3582          3583          3584          3585 
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##          3591          3592          3593          3594          3595 
## -2.252419e+01  6.504665e-01 -5.554762e+00  3.118001e+01  6.509022e+00 
##          3596          3597          3598          3599          3600 
##  2.894225e-02  2.999134e+01 -1.712646e+01 -1.839669e+01  1.575301e+01 
##          3601          3602          3603          3604          3605 
##  2.517424e+01 -3.038975e+00  5.340414e+00  3.168766e+00 -2.552348e+00 
##          3606          3607          3608          3609          3610 
##  8.570090e+00 -2.333191e+01 -2.815793e+01 -2.765111e+01  2.086478e+01 
##          3611          3612          3613          3614          3615 
## -4.067400e+01 -3.208521e+01 -2.495178e+01 -2.103151e+01 -6.113893e+00 
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## -2.279613e+00  8.545836e+00 -5.646663e+00 -1.761922e+01  2.624015e+01 
##          3621          3622          3623          3624          3625 
##  5.851026e+00  4.409720e-01  1.143181e+00 -7.726865e+00  3.548889e+00 
##          3626          3627          3628          3629          3630 
## -2.414585e+00  4.851876e+00 -1.250244e+00  3.747530e+01  4.015841e+00 
##          3631          3632          3633          3634          3635 
##  1.358691e+01  7.687192e+00  2.068233e+00 -8.826041e-01 -1.385854e+00 
##          3636          3637          3638          3639          3640 
##  4.884622e+01  4.601211e+01  1.408710e+01  7.917804e+00  1.455678e+01 
##          3641          3642          3643          3644          3645 
## -5.746010e+00  1.285104e+01  1.452561e+01 -1.658618e+00 -6.131189e+00 
##          3646          3647          3648          3649          3650 
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##          3651          3652          3653          3654          3655 
##  2.994357e-03 -1.420859e+01 -1.679551e+00 -3.688955e+00  9.111664e+00 
##          3656          3657          3658          3659          3660 
##  2.998511e+01 -1.847756e+01  9.882001e+00 -9.301926e+00  2.525382e+01 
##          3661          3662          3663          3664          3665 
## -6.956527e+00 -6.898159e+00 -2.312407e+01 -3.199532e+00  5.973437e+00 
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##          3671          3672          3673          3674          3675 
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##          3681          3682          3683          3684          3685 
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##          3686          3687          3688          3689          3690 
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##          3691          3692          3693          3694          3695 
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##          3706          3707          3708          3709          3710 
## -8.615251e+00 -1.738542e+01  1.267783e+01 -1.504054e+01 -2.127832e+01 
##          3711          3712          3713          3714          3715 
## -2.920173e+01  1.072930e+01  4.841213e+01  1.006195e-01 -1.622672e+01 
##          3716          3717          3718          3719          3720 
## -2.118804e+01 -1.780934e+01 -3.001460e+00  1.112603e+01 -1.138654e+01 
##          3721          3722          3723          3724          3725 
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##          3726          3727          3728          3729          3730 
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##          3731          3732          3733          3734          3735 
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##          3751          3752          3753          3754          3755 
## -1.307461e+01  6.590892e+00 -1.223234e+00  3.020438e+01  2.012663e+00 
##          3756          3757          3758          3759          3760 
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##          3761          3762          3763          3764          3765 
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##          3771          3772          3773          3774          3775 
## -7.011053e-01 -2.228465e+00 -1.482132e+00  1.236301e+01  2.610103e+01 
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##          3786          3787          3788          3789          3790 
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##          3791          3792          3793          3794          3795 
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##          3811          3812          3813          3814          3815 
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##          3831          3832          3833          3834          3835 
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##          4011          4012          4013          4014          4015 
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##          4016          4017          4018          4019          4020 
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##          4021          4022          4023          4024          4025 
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##          4026          4027          4028          4029          4030 
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##          4031          4032          4033          4034          4035 
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##          4041          4042          4043          4044          4045 
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##          4056          4057          4058          4059          4060 
##  6.056771e+00  4.436604e+00 -2.369695e+00 -2.315609e+01 -3.363155e+00 
##          4061          4062          4063          4064          4065 
## -1.572174e+01 -1.986865e+01 -5.104703e+00 -3.682903e+01 -2.218997e+00 
##          4066          4067          4068          4069          4070 
## -5.986095e+00 -2.472707e+01 -8.391502e-01 -1.110198e+01 -1.042891e+01 
##          4071          4072          4073          4074          4075 
##  2.573124e+01 -1.692736e+00  9.569531e+00 -1.481386e+01 -3.865625e+00 
##          4076          4077          4078          4079          4080 
## -1.372103e+01  2.770731e+01 -2.452921e+01 -1.194520e+00 -2.203712e+01 
##          4081          4082          4083          4084          4085 
## -4.661362e-01 -2.589291e+01  9.784165e+00  2.023669e+01 -6.518542e-01 
##          4086          4087          4088          4089          4090 
## -6.041284e+00 -2.892584e+00 -1.443334e+01 -6.892122e+00 -1.022784e+01 
##          4091          4092          4093          4094          4095 
## -1.418464e+01 -1.363504e+01 -1.973316e+01 -2.021518e+01 -1.255840e+01 
##          4096          4097          4098          4099          4100 
##  9.887538e+00 -1.479364e+01 -1.372536e+01 -3.778788e+00 -1.342883e+01 
##          4101          4102          4103          4104          4105 
## -5.945938e+00 -6.648819e+00  1.954313e+00  1.737158e+01 -1.013970e+01 
##          4106          4107          4108          4109          4110 
## -2.316275e+01 -1.292224e+01  3.067107e+01 -3.056257e+01 -1.596233e+01 
##          4111          4112          4113          4114          4115 
## -2.400511e+00 -1.636641e+01 -8.683533e+00 -1.518345e+01 -2.974127e+01 
##          4116          4117          4118          4119          4120 
## -1.242958e+01 -1.091250e+01  2.655101e+00 -3.305590e+01  2.406921e+01 
##          4121          4122          4123          4124          4125 
## -7.420784e+00  3.197315e+01 -2.444158e+01 -7.587465e+00 -8.254365e+00 
##          4126          4127          4128          4129          4130 
##  1.893071e-02 -2.163666e+01 -2.189602e+01 -2.595666e+01 -5.380461e+01 
##          4131          4132          4133          4134          4135 
##  1.404721e+01 -1.222019e+01 -2.775192e-02 -6.756234e+00 -1.335385e+01 
##          4136          4137          4138          4139          4140 
##  1.081668e+01 -1.017420e+01 -4.442767e+00  3.182794e+01  1.425912e+01 
##          4141          4142          4143          4144          4145 
## -7.802316e+00  1.826484e+01  5.687368e+00  1.622264e+00 -6.735773e+00 
##          4146          4147          4148          4149          4150 
## -2.221161e+01 -1.163168e+01 -1.356168e+01  9.886858e+00 -2.450502e+01 
##          4151          4152          4153          4154          4155 
## -1.034804e+01  1.265194e+01  8.906051e-01  4.805121e-01 -9.044914e+00 
##          4156          4157          4158          4159          4160 
## -1.848267e+01 -1.640265e+01 -1.234312e+01 -4.882167e+00 -6.464344e+00 
##          4161          4162          4163          4164          4165 
## -1.653379e+01  9.702379e+00 -9.484267e-01  2.148492e+01 -1.208577e+01 
##          4166          4167          4168          4169          4170 
## -2.237865e+00 -9.307855e+00  2.904876e+00 -2.025508e+01  4.376157e+00 
##          4171          4172          4173          4174          4175 
##  6.057670e+01 -1.560473e+01 -9.318073e+00  1.404530e+01  2.418931e+00 
##          4176          4177          4178          4179          4180 
## -7.252604e+00 -1.747008e+01 -1.084699e+01 -5.960790e+00  3.226768e-02 
##          4181          4182          4183          4184          4185 
##  8.857315e+00  1.265586e+00  1.297783e+01  2.265624e+01  1.090398e+01 
##          4186          4187          4188          4189          4190 
## -5.182935e+00  1.301662e+00  2.178113e+01 -1.019775e+01  6.333904e+00 
##          4191          4192          4193          4194          4195 
## -7.053891e+00 -1.376445e+01  1.350735e+01 -4.557643e+00 -1.169965e+01 
##          4196          4197          4198          4199          4200 
## -6.886794e-01 -1.073943e+01 -1.355689e+01 -9.708519e-01 -1.218881e+01 
##          4201          4202          4203          4204          4205 
## -1.128404e+01 -1.784366e+01 -1.232238e+01 -1.245935e+01 -9.241551e-01 
##          4206          4207          4208          4209          4210 
##  1.152431e+01 -2.266813e+01 -5.462176e+00 -7.566858e+00 -3.572088e+00 
##          4211          4212          4213          4214          4215 
## -1.266007e+00 -1.492057e+01 -3.204749e+01 -1.163607e+01 -2.377270e+01 
##          4216          4217          4218          4219          4220 
##  3.081773e+01  1.107305e+01 -3.614637e+01  4.982878e+01  5.173180e+01 
##          4221          4222          4223          4224          4225 
## -8.513329e+00  4.999815e+01 -2.789241e+01 -2.077738e+00 -2.827609e+01 
##          4226          4227          4228          4229          4230 
##  1.696295e+01 -2.318011e+01 -7.577533e+00 -1.009560e+01  1.701163e+01 
##          4231          4232          4233          4234          4235 
## -1.741254e+01 -1.108004e+01 -2.737371e+01 -2.317442e+01 -2.306677e+00 
##          4236          4237          4238          4239          4240 
## -1.081627e+01 -1.633485e+01 -9.149112e+00  8.521547e+00 -9.365801e+00 
##          4241          4242          4243          4244          4245 
## -3.636889e+00  1.260714e+01 -5.924245e+00 -2.963975e-01  3.300811e+00 
##          4246          4247          4248          4249          4250 
## -3.538543e-01 -7.256055e+00 -1.941984e+01 -1.153707e+01 -8.945516e+00 
##          4251          4252          4253          4254          4255 
## -5.218375e+00  4.442027e+00 -5.904215e+00 -2.004286e+01 -5.083224e+00 
##          4256          4257          4258          4259          4260 
## -7.139673e+00 -1.008925e+01 -5.241642e-01  6.487916e-01 -5.806864e+00 
##          4261          4262          4263          4264          4265 
## -4.748558e-01 -2.763705e+01 -6.722765e+00 -1.918801e+01  1.894279e+00 
##          4266          4267          4268          4269          4270 
## -2.143617e+01  1.887674e+01 -5.007393e+00 -5.086340e+00 -1.685877e+01 
##          4271          4272          4273          4274          4275 
## -2.180964e+01 -1.261877e+01 -6.404575e+00  1.360690e+01 -1.475652e+01 
##          4276          4277          4278          4279          4280 
##  7.684068e-02  2.570076e+01 -5.704462e+00  2.272507e+01  1.362850e+01 
##          4281          4282          4283          4284          4285 
## -6.422083e+00  6.451180e+00  9.869149e+00  1.748440e+01 -1.695212e+01 
##          4286          4287          4288          4289          4290 
##  4.444784e+00 -3.276795e+01 -3.063061e+01  1.132037e+01 -1.577274e+01 
##          4291          4292          4293          4294          4295 
##  2.062718e+00 -8.037786e+00 -7.804770e+00  2.826862e+00  6.701242e+01 
##          4296          4297          4298          4299          4300 
## -2.255712e+00  3.893656e-01  2.918396e+00  4.053703e+01  5.468348e+00 
##          4301          4302          4303          4304          4305 
## -2.000389e+01  1.159252e+01  2.200694e+01 -6.694932e+00  1.052446e+01 
##          4306          4307          4308          4309          4310 
##  1.228106e+01  7.935238e+00 -2.088622e+01  5.661821e+00  1.561602e+01 
##          4311          4312          4313          4314          4315 
##  4.468834e+00  2.607768e+00 -5.400871e+00  2.408172e+01  1.543444e+00 
##          4316          4317          4318          4319          4320 
## -5.608157e+00 -2.137645e+00  1.415376e+01 -3.788989e+00 -3.050966e+01 
##          4321          4322          4323          4324          4325 
##  6.689834e+00 -5.246969e+00  3.497305e+01 -6.110450e+00 -1.575223e+01 
##          4326          4327          4328          4329          4330 
## -6.536179e+00  1.848853e+01 -1.141342e+01  2.112730e+01  1.895827e+00 
##          4331          4332          4333          4334          4335 
## -1.140113e+01 -4.136467e+00 -8.207455e+00  7.973946e+01  1.753201e+01 
##          4336          4337          4338          4339          4340 
##  1.319019e+01 -2.165103e+00 -2.903787e+01  1.073053e+01 -2.288302e+01 
##          4341          4342          4343          4344          4345 
## -2.366530e+00  1.713934e+01  6.282985e+01 -2.237351e+01  8.056548e+00 
##          4346          4347          4348          4349          4350 
## -7.829028e+00  2.242594e+01  5.323123e+00 -1.627219e+00 -1.355041e+01 
##          4351          4352          4353          4354          4355 
##  7.552884e-01  1.594749e+01  4.829733e+01  1.561570e+01 -1.642833e+01 
##          4356          4357          4358          4359          4360 
## -5.316683e+00 -1.978505e+00  1.082909e+01  2.646492e+00 -1.520081e+01 
##          4361          4362          4363          4364          4365 
##  1.399097e+01 -1.082231e+01 -3.828863e+00  4.611310e+00  2.828329e+01 
##          4366          4367          4368          4369          4370 
## -9.961687e+00 -1.285134e+01 -3.772926e+00  1.806313e+01  3.099046e+01 
##          4371          4372          4373          4374          4375 
## -5.117319e+00 -2.693055e+00  9.561959e+00 -1.332475e+01 -9.121739e+00 
##          4376          4377          4378          4379          4380 
## -4.863932e-01  7.019039e+00  1.838186e+01 -1.604083e+00 -1.436671e+01 
##          4381          4382          4383          4384          4385 
## -3.066206e+00  1.765367e+00  9.092079e+00  3.208898e+01 -1.632894e+01 
##          4386          4387          4388          4389          4390 
##  9.811366e-01 -5.877753e+00 -1.139199e+01 -1.262529e+01 -1.010767e+01 
##          4391          4392          4393          4394          4395 
##  1.854208e-01  1.257893e+00  3.211715e+00 -5.964164e+00 -6.067788e+00 
##          4396          4397          4398          4399          4400 
## -3.091017e+00  4.212635e+01 -3.823348e+00 -6.711221e+00 -1.904876e+01 
##          4401          4402          4403          4404          4405 
##  3.244953e+00 -2.128795e+00  2.026651e+01 -8.997262e+00 -2.249422e+01 
##          4406          4407          4408          4409          4410 
##  6.819684e+00  9.652894e+00 -1.008829e+01 -1.539792e+00 -1.981094e+00 
##          4411          4412          4413          4414          4415 
##  2.166961e+00  5.606950e+00  7.201347e+00 -1.504492e+01 -1.538155e+01 
##          4416          4417          4418          4419          4420 
##  3.032132e+00  2.403531e+01 -1.436713e+01 -9.482721e+00 -5.049666e+00 
##          4421          4422          4423          4424          4425 
## -9.639012e+00 -6.781659e+00 -9.349649e+00 -4.224412e-01  7.138113e+00 
##          4426          4427          4428          4429          4430 
## -3.983747e+00 -8.851806e+00 -2.741862e+00 -9.824491e+00 -4.168541e+00 
##          4431          4432          4433          4434          4435 
##  1.487326e+01 -1.637020e+01 -1.305524e+01 -2.746922e+00 -8.391336e+00 
##          4436          4437          4438          4439          4440 
## -1.436889e+00 -6.828783e+00  2.152339e+01 -2.487917e+01  1.202503e+01 
##          4441          4442          4443          4444          4445 
## -2.677514e+01 -1.078411e+00  1.097255e+01  3.406117e+00  4.609139e+01 
##          4446          4447          4448          4449          4450 
##  2.593293e+01  1.312933e+01 -1.028509e+01 -3.838597e+00 -5.228902e+00 
##          4451          4452          4453          4454          4455 
##  2.051456e+00 -1.898897e+01  5.805906e+01  6.230644e+01  6.232884e+00 
##          4456          4457          4458          4459          4460 
##  2.660444e+01 -6.623735e+00  7.961026e+00  1.300735e+01 -3.932811e+00 
##          4461          4462          4463          4464          4465 
## -1.390838e+01 -8.419738e+00  2.266729e+01 -5.739886e+00 -1.359543e+01 
##          4466          4467          4468          4469          4470 
##  2.927065e+00  7.176313e+00  1.657646e+01 -1.072950e+01 -1.584488e+01 
##          4471          4472          4473          4474          4475 
## -7.907687e+00 -3.434002e+00  1.946895e+01 -4.287145e+00 -8.460509e+00 
##          4476          4477          4478          4479          4480 
## -1.464011e+01 -2.363741e+00  1.309441e+01  7.293184e+00  9.207416e+00 
##          4481          4482          4483          4484          4485 
## -6.512823e+00  3.822777e+01  7.029884e+00 -7.276138e+00  1.270384e+00 
##          4486          4487          4488          4489          4490 
## -7.208558e+00 -4.018624e+00 -2.710936e+01 -2.595588e+00  1.937642e+01 
##          4491          4492          4493          4494          4495 
## -1.737268e+01 -1.784103e+00  1.996587e+00 -2.432299e+01 -6.280341e+00 
##          4496          4497          4498          4499          4500 
##  4.195487e+01 -2.634146e+00 -1.847050e+01 -6.238803e+00  6.795472e+00
# Print the fitted values of the model
sbp_fitted <- fitted(lm_all)
sbp_non_fitted <- steps_data$sbp - sbp_fitted
# Print the ANOVA table of the model
anova(lm_all)
## Analysis of Variance Table
## 
## Response: sbp
##             Df     Sum Sq   Mean Sq  F value    Pr(>F)    
## age          1  626266738 626266738 614.6690 < 2.2e-16 ***
## male         1   94504398  94504398  92.7543 < 2.2e-16 ***
## bmi          1  251147796 251147796 246.4968 < 2.2e-16 ***
## dm           1    9041807   9041807   8.8744 0.0029075 ** 
## smk          1   10998727  10998727  10.7950 0.0010255 ** 
## tc           1    9827428   9827428   9.6454 0.0019101 ** 
## age:smk      1   14088913  14088913  13.8280 0.0002028 ***
## Residuals 4492 4576756225   1018868                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Print the diagnostic plots of the model
par(mfrow=c(2,2))
plot(lm_all)

# Fit a linear regression model for predicting sbp for rural population

# Fit a linear regression model for predicting sbp for rural population
lm_rural <-lm(sbp~age+male+bmi+dm+smk+tc+age*smk, data = rural_data, weights = weights)
# Print the summary of the model
summary(lm_rural)
## 
## Call:
## lm(formula = sbp ~ age + male + bmi + dm + smk + tc + age * smk, 
##     data = rural_data, weights = weights)
## 
## Weighted Residuals:
##     Min      1Q  Median      3Q     Max 
## -4848.1  -709.8  -151.4   496.9  7870.2 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 85.02322    2.36155  36.003  < 2e-16 ***
## age          0.45533    0.03118  14.605  < 2e-16 ***
## male         5.92356    0.77284   7.665 2.63e-14 ***
## bmi          0.81672    0.08109  10.072  < 2e-16 ***
## dm           4.44458    2.47405   1.796  0.07255 .  
## smk          5.89525    3.27735   1.799  0.07218 .  
## tc           1.08162    0.41845   2.585  0.00980 ** 
## age:smk     -0.23990    0.07824  -3.066  0.00219 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1173 on 2298 degrees of freedom
## Multiple R-squared:  0.1727, Adjusted R-squared:  0.1702 
## F-statistic: 68.53 on 7 and 2298 DF,  p-value: < 2.2e-16
# Print the coefficients of the model
coef(lm_rural)
## (Intercept)         age        male         bmi          dm         smk 
##  85.0232248   0.4553255   5.9235650   0.8167202   4.4445841   5.8952451 
##          tc     age:smk 
##   1.0816162  -0.2399029

10 Model diagnostics

# Model diagnostics
# Print the residuals of the model
residuals(lm_rural)
##             1             2             3             4             5 
## -13.387656255   6.283014588  75.289932408  -6.608354470  47.534957204 
##             6             7             8             9            10 
## -23.897111898  -6.825292832   2.172981546  84.781959086 -18.143036070 
##            11            12            13            14            15 
## -21.758179391  -7.839248323  -8.678583272  12.266040118   3.408643999 
##            16            17            18            19            20 
##   5.940610278  24.454163962  10.976867750   0.571150654  10.048979872 
##            21            22            23            24            25 
## -11.264143513   3.999273936  -4.451794868  24.123189001   0.541808323 
##            26            27            28            29            30 
##   1.533307237  40.199810813  10.166733399  -4.037710332 -20.848187907 
##            31            32            33            34            35 
##  16.798955079  -2.571736243  -2.210685351  -6.354095153 -13.599322878 
##            36            37            38            39            40 
##  -7.881633405  -9.865950056 -26.095111647  -4.119739950  -3.745651445 
##            41            42            43            44            45 
##  -5.261242137  -7.018400999  -9.536521718  10.360902062  24.631555900 
##            46            47            48            49            50 
##  52.890266289 -11.922612450   9.777452322  -7.892675143  10.149376427 
##            51            52            53            54            55 
##  12.865141743 -13.840335109   1.621396886  -9.459584059  -4.529251267 
##            56            57            58            59            60 
##   3.660641905   6.481453469   7.843922284 -10.241574993   0.997482994 
##            61            62            63            64            65 
##   7.544295244  -7.201187186  13.112577111  -3.849440009   7.016204302 
##            66            67            68            69            70 
##  -1.518093964 -11.687336747  -5.424052219 -14.495076646  18.362631417 
##            71            72            73            74            75 
##  -3.746292753   9.907647943  -2.952722418  -9.169009268 -17.894731081 
##            76            77            78            79            80 
##   4.105442359   7.521727594   6.122392534  16.665791419   6.906997338 
##            81            82            83            84            85 
## -13.005031889   1.174593899   1.428100180 -14.100576276  -6.775056185 
##            86            87            88            89            90 
## -14.097251346 -12.181240159  -5.136603741   0.952225032  -8.977209219 
##            91            92            93            94            95 
##   1.521307709  -3.830303431   8.467764160  12.498511006   3.394020805 
##            96            97            98            99           100 
## -14.110471320  36.472364032  15.973609611   3.872463256   9.898324159 
##           101           102           103           104           105 
## -12.998823645  20.228239953   1.267086801  -5.302208838   7.512718021 
##           106           107           108           109           110 
##  41.628467572  -3.827462804  27.665354987  -3.106053348  -8.982400988 
##           111           112           113           114           115 
## -31.068532845   1.407568641 -17.461889876 -13.188204800  -0.825708552 
##           116           117           118           119           120 
##  -1.023015368   1.407434072  -6.184381239  -6.254066539  -4.088363289 
##           121           122           123           124           125 
##   5.900627159   5.448526487   3.870294875  23.843142131 -13.219173592 
##           126           127           128           129           130 
##  -6.786900457 -12.114941064  30.302546462   1.385552371  10.111051693 
##           131           132           133           134           135 
##  -0.863001660  -1.253336349 -35.130310018  -6.530752778   6.435775769 
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##   7.436422968  11.352993305   7.329667647 -18.109757824  -5.416105595 
##           141           142           143           144           145 
##  -5.040201139  -1.504902531  -7.558047796 -16.072941649   1.424953919 
##           146           147           148           149           150 
##   1.239320448  -8.393798527 -20.084952191 -10.905322336   4.746430560 
##           151           152           153           154           155 
##   5.201517225 -11.795843875 -19.528071957  -6.213172163  -9.327808746 
##           156           157           158           159           160 
##  -1.759038898 -10.655279505  26.016506415  -7.997232240 -28.148925295 
##           161           162           163           164           165 
##   9.746163962  16.570669693   3.848328922 -15.442163475 -17.489672786 
##           166           167           168           169           170 
## -13.352009305   0.403370414 -17.191154088  -7.466355647  -1.393043714 
##           171           172           173           174           175 
##   1.484191330   0.067032997  -0.618324844   8.036477686  46.742956565 
##           176           177           178           179           180 
## -10.100913060 -32.865679734 -16.149711553 -18.026645141  37.822017991 
##           181           182           183           184           185 
##  -3.414082081   7.931049978   0.097041762 -10.990766888 -22.995081273 
##           186           187           188           189           190 
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##  -8.583976620   2.213486249  16.719617032  -7.970386958  -9.764280996 
##           196           197           198           199           200 
## -11.708704081  -4.915546928  -4.989337505  -9.993143053  11.105703849 
##           201           202           203           204           205 
##   2.079775590   7.486566345  -3.193117928  14.765032743  -2.027392644 
##           206           207           208           209           210 
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##           211           212           213           214           215 
## -22.237868242  19.961705031  -3.712781528 -13.955250104 -25.348908986 
##           216           217           218           219           220 
## -37.837057618 -15.105607093 -32.633829853 -47.278903847   4.141339555 
##           221           222           223           224           225 
##   2.408032262 -13.017965482  37.862076220 -26.378198679 -20.103254681 
##           226           227           228           229           230 
## -19.463231213  -3.937515433 -12.232471708  -3.051029334 -42.086794397 
##           231           232           233           234           235 
##   7.387573482 -28.775900423 -14.355668377  -4.756736701  22.682354682 
##           236           237           238           239           240 
##  26.222657950 -35.196785735 -15.045616243 -21.792541214 -11.510008737 
##           241           242           243           244           245 
##   5.242990718 -11.499017411 -26.299757080  -1.146177008  17.502952210 
##           246           247           248           249           250 
## -12.458533906 -25.028339692   3.268849654 -18.013237501   1.849168693 
##           251           252           253           254           255 
## -38.668179028  14.348120737  48.557084841 -26.917298345   2.783376897 
##           256           257           258           259           260 
##  -3.890211273 -24.088032574 -14.945765448  -1.894591540 -18.682747808 
##           261           262           263           264           265 
## -16.618611983 -22.715953518 -11.529027616 -13.081395577 -17.406987800 
##           266           267           268           269           270 
## -24.624365334 -15.276651839 -17.155900042  -7.459193638  -4.565786727 
##           271           272           273           274           275 
## -21.790489239 -13.379174649  -2.982207613 -12.414806945  74.871389013 
##           276           277           278           279           280 
##  -1.987674841 -11.613255271  -8.551871532  -3.743658862  -4.607362058 
##           281           282           283           284           285 
## -10.699416274  -1.464690770  -3.259783005   4.174983378 -13.959835156 
##           286           287           288           289           290 
##   4.949022875  -8.313079583  -6.334774208  -8.336525909  -7.774905636 
##           291           292           293           294           295 
##  24.385936050 -17.244839765   3.981693574  -4.863454870   2.799446998 
##           296           297           298           299           300 
##   1.455097498   4.457091314 -22.512084018 -24.033436495 -28.187535894 
##           301           302           303           304           305 
##  -7.356662125  -8.295017747  -4.039252407 -12.992323371  -1.422802857 
##           306           307           308           309           310 
##  12.170460442  24.787709713 -28.134510566 -13.825840296 -23.389585800 
##           311           312           313           314           315 
## -15.089655319 -14.949961245 -11.557722497   0.375398665  -0.838342340 
##           316           317           318           319           320 
##   0.056444041 -10.456109836  -1.819366408 -33.439856451  10.644210008 
##           321           322           323           324           325 
##  -5.982573180  -3.885004606  -2.847309341  10.655772206  40.201466821 
##           326           327           328           329           330 
##  26.879447990   2.289075031   9.992863369   4.589823088  19.591093653 
##           331           332           333           334           335 
##  -9.396175451 -32.250450617  23.900743760  11.463797119 -30.386605785 
##           336           337           338           339           340 
## -16.078519644  -4.452989506  -9.773243722 -14.238175678 -17.668374509 
##           341           342           343           344           345 
##  -8.226110332  16.224941167 -18.959627498  -0.256850103   4.965464681 
##           346           347           348           349           350 
##   0.287378822  18.329435151  -6.178478272  -1.151640678  13.841191028 
##           351           352           353           354           355 
## -37.262891896 -26.163459535   1.821685187  50.346694330 -19.313910287 
##           356           357           358           359           360 
##  52.583742833 -25.630912757  -2.654386996   7.087260862 -13.624664420 
##           361           362           363           364           365 
##   1.207064785   9.730075415  -2.037541102   8.171379477   6.596967673 
##           366           367           368           369           370 
##   9.361346995   9.641371839  27.242663545 -12.020618313  -2.044332638 
##           371           372           373           374           375 
##  -3.415173382  28.700684029  -4.870538089   4.097329017 -10.504892343 
##           376           377           378           379           380 
## -20.377355838  -8.633727794  -3.663710407 -11.168491715  -6.959556306 
##           381           382           383           384           385 
##  -8.957005363  68.664008825  -0.785348907   3.002801522  58.886728799 
##           386           387           388           389           390 
## -17.229084951  -7.941915171   4.003818337 -13.867315308 -14.279749294 
##           391           392           393           394           395 
##   0.901556690  -0.197029526  -0.763720973 -11.349935647  14.103366702 
##           396           397           398           399           400 
##   6.488749738   7.301464016 -10.144659346   3.386715816  -0.721280112 
##           401           402           403           404           405 
##  -9.913754298  -8.129142348 -34.006701335  19.455052393   6.766809080 
##           406           407           408           409           410 
##  -0.435618245 -10.021485245 -12.921047228 -10.719137489  -3.251284158 
##           411           412           413           414           415 
##  -2.066683981  19.659181502   6.902238457  10.811825768  19.130781254 
##           416           417           418           419           420 
##  23.951072307 -16.519612505  -5.009332084  10.458192642   6.104122926 
##           421           422           423           424           425 
##  27.051125415 -21.432204440 -19.578694362 -17.654396551  -8.454798084 
##           426           427           428           429           430 
##  -7.659079040 -15.440571227  34.507142876  -7.087111418  -5.390090275 
##           431           432           433           434           435 
## -22.161858058  11.552158011   0.393212303 -13.236133669   0.802528313 
##           436           437           438           439           440 
## -12.716932183  -6.368021446 -14.767437256  -4.801268907   3.131415887 
##           441           442           443           444           445 
## -14.249931645 -30.809982131  24.394981934  58.639156069 -17.097993262 
##           446           447           448           449           450 
##  -7.079419817   4.021559200 -10.065988052  16.492160851 -13.358909662 
##           451           452           453           454           455 
##   0.545615361   4.250803670   0.802952467  -6.712184021  -6.505666252 
##           456           457           458           459           460 
##  -8.129185923 -23.158945405  17.540958539  -4.171723049   3.112082972 
##           461           462           463           464           465 
## -13.486811309   1.267262467   3.308021407  25.279706836   5.224262703 
##           466           467           468           469           470 
##   2.014718095 -17.627030398   8.788016964   5.681260191 -19.373568024 
##           471           472           473           474           475 
##  12.996874592   8.779835130   9.396699003 -11.910614092  -6.289595060 
##           476           477           478           479           480 
## -15.238472968 -22.267229425  17.405524311  15.813700308  -4.339493570 
##           481           482           483           484           485 
##  39.098669665   3.972387032  -1.283159029 -10.418022095  25.066741065 
##           486           487           488           489           490 
##  25.004246654 -11.061381945 -29.544514114   5.261960304 -10.115876020 
##           491           492           493           494           495 
##  -2.417259415  25.778703307   1.776186959 -24.125653160  10.472232735 
##           496           497           498           499           500 
##  11.719373744  -4.093158894   5.453714948  -6.085318843  24.707300069 
##           501           502           503           504           505 
##  -1.428269176 -10.378314275  16.304891091   9.158540714 -19.210709702 
##           506           507           508           509           510 
##   4.404408302 -12.375401436  -8.883340993  57.059944135  -3.197264156 
##           511           512           513           514           515 
## -10.724080598  -8.916587672   4.057351763  69.061530691  -3.500177921 
##           516           517           518           519           520 
##  23.692096523  -7.978553469  -8.352237068  21.579809578 -29.906454266 
##           521           522           523           524           525 
##  20.053423882   6.338894864  25.303581542   5.889814376  14.417150486 
##           526           527           528           529           530 
##   8.732642441  -7.795587715 -19.213686632  11.287135191 -13.829514996 
##           531           532           533           534           535 
##  12.888655557  23.040482998   4.599663881 -12.336728912  -7.441492072 
##           536           537           538           539           540 
##  21.696611820  -4.134064250  -6.660446612 -20.605698598 -17.180558640 
##           541           542           543           544           545 
## -12.161270535   3.224013296  12.321817078  25.945955918 -28.813449454 
##           546           547           548           549           550 
##   6.249527287  21.529300664 -22.814536844  19.308027178  15.615883876 
##           551           552           553           554           555 
##  18.401061947 -13.796643607  -3.200640087   3.021627040 -16.931421563 
##           556           557           558           559           560 
##  11.058658670 -11.757799900   4.927574979  -3.823023399 120.429916267 
##           561           562           563           564           565 
## -11.017795624  -6.675032757  22.031653251   2.583828400 -24.779603197 
##           566           567           568           569           570 
##  37.646362480  55.454951352   6.290146976  42.863829624  24.372757692 
##           571           572           573           574           575 
##  22.473218386  -4.096400794 -11.152202846  50.406310869  -7.404559892 
##           576           577           578           579           580 
##  59.953723758  -4.662000036 -18.259137006  19.272901723  11.898853116 
##           581           582           583           584           585 
##   7.335342078 -19.612408265  -9.956573694  42.579254763 -19.422695216 
##           586           587           588           589           590 
##  15.420437512  57.627795626 -13.958093012   9.470701301 -15.423449250 
##           591           592           593           594           595 
##   5.126918299  -4.806679647  -3.564641241 -31.691245708 -13.303135140 
##           596           597           598           599           600 
##   3.311222315  24.993729826  41.055111957  17.151067891  -3.188482115 
##           601           602           603           604           605 
## -27.999298379  22.893521121   4.615086029 -25.481534585  -3.818483740 
##           606           607           608           609           610 
##  31.557672756 -17.942203948  41.653653819 -10.367586790  11.128485717 
##           611           612           613           614           615 
##  -7.062586132 -21.012606335 -16.680498685 -37.480884826   6.324788838 
##           616           617           618           619           620 
## -19.302435968  -2.180153307  33.405278559   4.353781243  30.019392667 
##           621           622           623           624           625 
##  21.382212179  -3.351868484  -1.687806196   4.490956420 -20.044250280 
##           626           627           628           629           630 
##  -4.029378521  10.891936705 -22.417549659  17.048293337 -17.019428060 
##           631           632           633           634           635 
##  -0.048911608   7.143869712  11.176541622 -23.395860239  61.225061707 
##           636           637           638           639           640 
## -15.878788320   7.848385371  -0.731156315 -10.352101915   5.600516110 
##           641           642           643           644           645 
## -19.406821941 -15.922092408 -22.797634503   5.560265489 -19.172482682 
##           646           647           648           649           650 
##  -9.988608632  11.851488596 -18.383423084 -29.573359465 -15.100289506 
##           651           652           653           654           655 
## -21.185393092 -17.110655690  -8.349573278 -13.508443016   6.355101296 
##           656           657           658           659           660 
##  25.693267385  -0.606080982   2.680471945  -6.069754348  -4.991965353 
##           661           662           663           664           665 
## -13.611948704  17.883262081   3.594511429 -41.427003761  15.139149420 
##           666           667           668           669           670 
## -28.167976972 -25.326939430  -4.882728115   9.769912031  -5.882901880 
##           671           672           673           674           675 
## -11.318078091 -10.811656838  -5.210643111 -18.318310412 -15.464506371 
##           676           677           678           679           680 
## -17.630444559 -13.195070264  15.026429760 -15.501880563   0.678599663 
##           681           682           683           684           685 
## -17.708238616 -22.871586662 -33.621771506 -21.745983354   4.553719774 
##           686           687           688           689           690 
##   9.261859157 -33.285660444 -16.103901721  16.001175484  -7.765436393 
##           691           692           693           694           695 
##   1.011963831  24.557934874 -10.742842039  17.313707964   9.356439860 
##           696           697           698           699           700 
##  30.627410839 -12.185769986  -2.100929144  12.426508488  -4.276203678 
##           701           702           703           704           705 
##  25.667357712 -20.850940554   8.194509903 -10.652486470   1.143341959 
##           706           707           708           709           710 
##   0.901199560 -18.190429364 -18.181370038  20.482136356   7.813242935 
##           711           712           713           714           715 
## -14.924757774   4.040123328   6.732429843   1.188425915  -9.652241789 
##           716           717           718           719           720 
##   8.697177423  -2.694000245  13.209286797 -18.112067873  -4.343307650 
##           721           722           723           724           725 
##   1.289668955  10.968396294  -9.230421470 -18.705145333  -4.121882808 
##           726           727           728           729           730 
##  14.280705137  13.195029883  -0.435699281   6.071260221  11.967567497 
##           731           732           733           734           735 
##  19.836373174  -4.392394047   2.225973945 -11.812625826  -2.460933268 
##           736           737           738           739           740 
## -28.983773909 -26.976074224  -4.614742778  -1.105398684   3.708826202 
##           741           742           743           744           745 
##  14.369443970   5.071869424  -6.947022850 -15.448220522   8.973062054 
##           746           747           748           749           750 
##   0.735744427 -26.719127432  -4.213241152  -3.890975069  -4.149017128 
##           751           752           753           754           755 
##  -0.190998393   4.818387184  -3.526944238 -16.900120927   8.685453053 
##           756           757           758           759           760 
## -11.473154319 -17.752670008  -2.557937772 -27.140942651 -10.287802387 
##           761           762           763           764           765 
##  -2.543865538 -29.984636563  18.051286305   3.180087509  -8.810701459 
##           766           767           768           769           770 
## -21.396012960  -7.904394610 -27.869866942 -12.664409953 -17.859749179 
##           771           772           773           774           775 
##   8.014171165   2.004397963 -15.057244088  -2.783057976 -17.902986081 
##           776           777           778           779           780 
## -18.956957816  -7.669507245  -7.480037275 -10.874692439  35.276971093 
##           781           782           783           784           785 
## -11.693127090  19.506713417   2.705277570   1.652269749  -4.197672758 
##           786           787           788           789           790 
##  12.829850094  17.114019988   4.756798743  -5.707329771  -5.879307397 
##           791           792           793           794           795 
## -17.414136611 -16.715043915 -33.008789997   5.397164232 -20.139362692 
##           796           797           798           799           800 
##   6.959440087  -8.485916898 -14.573795346  -1.233887608 -16.145546662 
##           801           802           803           804           805 
##  -0.881528938 -26.852944032   9.774457732 -24.232348998  -0.178716720 
##           806           807           808           809           810 
##  -3.211324778 -15.640006335  -5.863586691 -18.021289731 -16.738382245 
##           811           812           813           814           815 
##  -4.886197374  -2.665764480 -13.279619185  55.508630222  12.585609778 
##           816           817           818           819           820 
##  -8.677644730  -3.797613675 -17.661390485   7.595400131  12.356150546 
##           821           822           823           824           825 
## -14.873540878 -14.424585241 -12.704204059  -6.911647493  -3.652038704 
##           826           827           828           829           830 
##  56.558180569 -18.804993824 -15.060297773  11.953173796  19.840661194 
##           831           832           833           834           835 
##  20.889464419   3.914774716  -9.187334460 -10.282179838   7.351893013 
##           836           837           838           839           840 
##   9.253392578 -12.425568825 -12.283329901   3.772795866   9.740240826 
##           841           842           843           844           845 
## -10.609159579   0.062864746  -3.873637459  -4.489692510  17.375838022 
##           846           847           848           849           850 
##  16.368395014 -13.589742787  -7.046351362 -20.504603065  -9.441812014 
##           851           852           853           854           855 
##  -3.734326242  28.446819292 -16.921143992 -16.777541718  -0.010830574 
##           856           857           858           859           860 
##   6.200722705   9.662131259   8.341447817  25.363499084 -17.240105124 
##           861           862           863           864           865 
##   1.977613812  19.757956008   9.224094596 -15.966789754   7.698181412 
##           866           867           868           869           870 
##  49.923569237   2.749827166  10.151551196  -6.447499925   2.501117243 
##           871           872           873           874           875 
##  -9.726251749  12.685350674  41.761867933  16.683463007  19.588425052 
##           876           877           878           879           880 
##  -9.141962988  -2.789688884   2.263760902  -0.574887091  -7.144320587 
##           881           882           883           884           885 
##   5.799392318  -4.157648934  12.369848101  -3.014049143   1.460270785 
##           886           887           888           889           890 
## -15.269235064   8.016702153 -37.764260298   6.651047299  16.307037407 
##           891           892           893           894           895 
## -19.708458464   2.791263716   2.091555401  -3.686407090  -2.742058814 
##           896           897           898           899           900 
## -12.847829257 -10.224696213  17.537229372  11.037887845  10.404530164 
##           901           902           903           904           905 
##  13.723330065 -17.001032060  -3.827350945  49.756056191   6.412248140 
##           906           907           908           909           910 
##   5.510955257  -1.995338748  -8.775067193 -18.643902225   7.089344585 
##           911           912           913           914           915 
##  -6.477604682  -8.239113371  -9.825591046 -15.605486020   3.305742404 
##           916           917           918           919           920 
##  16.355715683  -2.946424547 -10.775332474  -1.432651089  21.610257854 
##           921           922           923           924           925 
##   1.534261964   7.618910614 -14.517089425 -33.656018530  -4.326584714 
##           926           927           928           929           930 
## -16.003639742  -9.316465790  10.079237060 -29.140568499   0.138316229 
##           931           932           933           934           935 
##   8.649654470   4.866627424   6.410124653  -5.763626514  -2.836424465 
##           936           937           938           939           940 
## -19.925149602  64.166799988  -1.011276941  11.316259653 -16.723393455 
##           941           942           943           944           945 
##  -0.737737923  -8.490934740  23.731994595  55.672258182   2.244954421 
##           946           947           948           949           950 
##  13.627801656  -6.488633999 -12.368472219  -8.328983472  15.787937268 
##           951           952           953           954           955 
##  29.123116131   0.851830374  -1.806793681 -12.196261399  -9.980312158 
##           956           957           958           959           960 
##   0.363338803  11.791992085  13.033151323   0.222605689  -7.927386373 
##           961           962           963           964           965 
## -10.221948685 -14.192389992 -24.207807792   0.657549309  48.636555795 
##           966           967           968           969           970 
##  12.402256085  -4.586877600  15.207040177 -26.707304592  -6.144820994 
##           971           972           973           974           975 
## -18.111482198   1.164806488  -4.408961409   8.624823140 -24.464838716 
##           976           977           978           979           980 
## -17.230742783  18.271362017  15.493019638 -17.373261830  41.265852412 
##           981           982           983           984           985 
##   7.878536416  59.132081020  94.472128482 -18.789939242  38.413601048 
##           986           987           988           989           990 
##  -2.435435493 -17.235732469 -15.229078995 -12.532782572  11.642258660 
##           991           992           993           994           995 
## -17.339835140   5.889142420 -20.544919356  -6.670141825  10.715640519 
##           996           997           998           999          1000 
##  -9.907710725  33.342855500   3.136383194  53.105021595  47.743131515 
##          1001          1002          1003          1004          1005 
##  -1.235347838  -1.284152920  -1.785428123 -16.193221665 -32.737221842 
##          1006          1007          1008          1009          1010 
## -27.522128229 -20.979720947  -4.516610196  29.006280195   2.826401779 
##          1011          1012          1013          1014          1015 
##  -8.587856523  24.225995470 -13.062329244  10.589384967 -17.342365063 
##          1016          1017          1018          1019          1020 
## -18.564520617  -8.606220320   2.326269870  11.809091438 -12.294384621 
##          1021          1022          1023          1024          1025 
##  87.639692712  16.256801495 -19.112102624 -14.862265860 -27.782683178 
##          1026          1027          1028          1029          1030 
##  -0.470032548  -6.157633947 -14.374111980 -15.042185596  18.853308559 
##          1031          1032          1033          1034          1035 
##   9.287840214  26.835468602   7.655680713  44.319485396 -14.812824537 
##          1036          1037          1038          1039          1040 
## -20.441292662 -11.930797516  -1.345472223  10.667434729   7.981655505 
##          1041          1042          1043          1044          1045 
##   9.489603483 -11.806271318 -13.196201334 -23.011392031  -4.721802924 
##          1046          1047          1048          1049          1050 
##   4.867897187 -15.389693501  69.473292170 -15.692788950 -23.992714271 
##          1051          1052          1053          1054          1055 
##  12.576788329 -35.162804277   7.972252107   5.214869516  16.631917018 
##          1056          1057          1058          1059          1060 
##   1.116473610   2.944421225  -5.333861052 -11.380427465 -10.799211810 
##          1061          1062          1063          1064          1065 
##   7.723837843  10.702810169 -12.653215782  18.417219095 -17.887821415 
##          1066          1067          1068          1069          1070 
## -14.904188000 -30.365056809  -9.471332426  -5.353745395  -1.698516181 
##          1071          1072          1073          1074          1075 
## -13.811000291  -4.815245436 -50.401916584 -36.128038100  -1.114553743 
##          1076          1077          1078          1079          1080 
##  -7.234310681  -3.289151686  -5.331396444 -44.063562502  45.258921377 
##          1081          1082          1083          1084          1085 
##   6.692518680  10.957361608 -15.929503153  -7.572473605  10.329116481 
##          1086          1087          1088          1089          1090 
##   2.330587579  -3.616374721 -10.544096685   0.259553555   1.999897463 
##          1091          1092          1093          1094          1095 
##  -1.444721272  -7.028093625  -8.358205451   3.473983081   2.646869110 
##          1096          1097          1098          1099          1100 
## -20.676515774 -16.517237336   0.306892564  -8.987544873  22.834659684 
##          1101          1102          1103          1104          1105 
##  15.299824695  -8.457091219  13.080829280 -18.328994844   6.167464435 
##          1106          1107          1108          1109          1110 
##   2.177164497  -2.395318803  -4.310972252  -3.176233979  -7.300427808 
##          1111          1112          1113          1114          1115 
##  21.063674688 -15.145005362  -1.570878027  -3.674161635  -2.720123133 
##          1116          1117          1118          1119          1120 
##  -4.779317755 -12.996202517  13.013942634  10.721598099  -0.052109381 
##          1121          1122          1123          1124          1125 
## -20.887288965   1.826373595  -2.064504258  -3.076270627   5.696179701 
##          1126          1127          1128          1129          1130 
##  -3.745925390  -2.260323706  -5.949798742   3.079747288 -16.193763722 
##          1131          1132          1133          1134          1135 
##   0.405714178 -19.021808018  -4.063912100  -0.105022693   5.702604024 
##          1136          1137          1138          1139          1140 
##  27.298441648 -11.656227170   2.468670582   3.148793009 -15.795470554 
##          1141          1142          1143          1144          1145 
## -35.479215431   9.588216896  10.584690057   4.205357245 -16.101353963 
##          1146          1147          1148          1149          1150 
## -15.637513104  -8.653373172 -25.559927630  -2.562922738  -5.753625879 
##          1151          1152          1153          1154          1155 
## -10.260825390  15.457671341   7.331645947  -4.574833864  42.211871835 
##          1156          1157          1158          1159          1160 
##  -0.439534325  -0.120473132 -12.742837738 -22.712563977  -9.859699551 
##          1161          1162          1163          1164          1165 
##  -4.915170739 -18.585224089   1.550323761  -0.180286875  37.127099844 
##          1166          1167          1168          1169          1170 
##  -7.014552431   0.068389391  68.461281897  61.971456757  26.605115076 
##          1171          1172          1173          1174          1175 
##   8.215432817  20.650451034 -18.424305770  -5.238465168  -7.072322909 
##          1176          1177          1178          1179          1180 
##  17.473835173  -6.528749539   3.333367252  13.794598452 -16.282628601 
##          1181          1182          1183          1184          1185 
## -12.476324986  11.253852983  -9.255158730 -27.877047106  -3.932531060 
##          1186          1187          1188          1189          1190 
##  -3.798125218  12.562702860 -21.004663897  -9.457529200  10.732766875 
##          1191          1192          1193          1194          1195 
##   7.615145494  -0.401393598  -9.851470320 -40.128607036 -34.411623903 
##          1196          1197          1198          1199          1200 
## -14.771385186   1.473984833   5.411142644   2.573216005  76.986341505 
##          1201          1202          1203          1204          1205 
## -12.580499101  -6.096908980   3.479922718 113.362734191 -13.361987972 
##          1206          1207          1208          1209          1210 
##  15.750521752 -12.191859629   5.782575316 -19.247152386 -12.300928413 
##          1211          1212          1213          1214          1215 
## -13.911435375 -11.420304072  11.878785669  17.377965505  41.842573314 
##          1216          1217          1218          1219          1220 
## -30.279490511   5.565801014  -2.684169638  -5.058511273   4.244606131 
##          1221          1222          1223          1224          1225 
##  18.511525118 -18.648302092 -12.027007497 -15.459607234  15.402472876 
##          1226          1227          1228          1229          1230 
##  -0.696531373  -1.436073178  -8.446273820 -13.689265713  -4.195405122 
##          1231          1232          1233          1234          1235 
## -11.584106562   4.817838310 -10.121829133   3.142020402   8.148706363 
##          1236          1237          1238          1239          1240 
##  -5.104369257 -15.691928788  -2.863850479   4.621535887  -2.924405812 
##          1241          1242          1243          1244          1245 
## -16.300529324 -17.814033077   5.934109283   2.247522831  -0.712793463 
##          1246          1247          1248          1249          1250 
##   2.934805157  -5.133327179   9.946434974 -18.127996797  12.535110115 
##          1251          1252          1253          1254          1255 
## -13.371781604 -14.166312743  -4.600124353   9.784195694  -3.110365939 
##          1256          1257          1258          1259          1260 
##   2.537871702 -16.496554822   8.827744304  -2.544626884 -15.917584976 
##          1261          1262          1263          1264          1265 
##   8.437970532  20.142692006   9.849892305  16.033265197 -11.161212900 
##          1266          1267          1268          1269          1270 
##  48.874325540   0.987278106   8.046109704 -14.193853171   8.382418299 
##          1271          1272          1273          1274          1275 
## -20.676432496 -14.177353820  -3.298498791 -14.263250090  30.158925216 
##          1276          1277          1278          1279          1280 
##   5.394875675 -35.586103843 -18.633600935 -15.895320678   2.661115972 
##          1281          1282          1283          1284          1285 
##   8.514893096  -2.529084307 -17.540564862  45.449891202  -4.030239210 
##          1286          1287          1288          1289          1290 
##   3.195405651   7.211374835  20.612305661  -6.530304758   2.014750891 
##          1291          1292          1293          1294          1295 
##  54.172073438 -23.140425690   9.799631420   4.890461747 -12.049631356 
##          1296          1297          1298          1299          1300 
##  -7.489550765  25.456599745 -19.304995732  -9.777717233  55.942300155 
##          1301          1302          1303          1304          1305 
## -12.433134997  -7.240851061  19.100231891  -4.206592670  14.209515501 
##          1306          1307          1308          1309          1310 
##  -7.866574008 -24.175226772  49.183809419   7.687381639   0.253326505 
##          1311          1312          1313          1314          1315 
##  11.860418170 -16.150002083  21.031768694  -2.260405240  29.266045369 
##          1316          1317          1318          1319          1320 
## -15.213026305 -22.977964625  -7.187400348  10.268356527  16.214485298 
##          1321          1322          1323          1324          1325 
##  28.549969842  -5.774871167  21.268067821  36.628269511  -5.191260170 
##          1326          1327          1328          1329          1330 
##  20.497279337   4.565847982  -3.919260978  31.677305326   2.763985509 
##          1331          1332          1333          1334          1335 
##  18.691168481  46.521275326  73.982979000  34.307437305   0.806716374 
##          1336          1337          1338          1339          1340 
##  62.959130659  -7.687361357 -23.245124663  -6.987965748  29.252681800 
##          1341          1342          1343          1344          1345 
##  -8.241385962   0.869111682  -2.344861214   8.110648905  -1.955136082 
##          1346          1347          1348          1349          1350 
##  -4.801820951  -1.985960029 -34.232262025  -8.783043260  -4.578000683 
##          1351          1352          1353          1354          1355 
##  -3.373668005  -0.911644492 -10.513926111  21.177708895  28.039867615 
##          1356          1357          1358          1359          1360 
##  -9.467594189   3.286146525  -9.254319176  14.320696807  -9.873649864 
##          1361          1362          1363          1364          1365 
##  17.259379378  26.767927087 -19.118616399  11.293697242  -2.325778487 
##          1366          1367          1368          1369          1370 
##  19.274524879   2.676269434  -8.158315556   1.829092012  -0.967257510 
##          1371          1372          1373          1374          1375 
##   2.511813019   5.583666770  11.089724713 -20.828367936   9.548282989 
##          1376          1377          1378          1379          1380 
## -10.582918443  40.405840903  10.537137861   9.575260952 -15.173570240 
##          1381          1382          1383          1384          1385 
##  46.981353560  44.982351030  -9.965360243  15.166860598  -5.234105844 
##          1386          1387          1388          1389          1390 
##   5.750492884  -8.344965667   0.670900325   0.965098769 -19.791158954 
##          1391          1392          1393          1394          1395 
## -17.899791383  -4.838671085  85.414440554  -2.582353833  30.588336094 
##          1396          1397          1398          1399          1400 
##  -1.252530087  16.890039379   2.402485813  22.135146552  26.672359637 
##          1401          1402          1403          1404          1405 
##   6.893705219  -9.135284573  28.632339276  95.326261670  29.426043798 
##          1406          1407          1408          1409          1410 
##   2.066591121   9.744676377 -35.160944261  48.135290924 -12.536629255 
##          1411          1412          1413          1414          1415 
## -18.751450408  -0.426339250   8.480211183 -14.979697673 -16.615434969 
##          1416          1417          1418          1419          1420 
##   5.307851531  95.913439849 -23.304743906 -18.323419937  66.364856557 
##          1421          1422          1423          1424          1425 
##  -7.068557550  -2.881443592   3.678780028  -2.741048239  14.527801036 
##          1426          1427          1428          1429          1430 
##   2.298553906   5.365192322  12.212342253  -2.433286905 -10.169870412 
##          1431          1432          1433          1434          1435 
## -22.787598373 -26.613164612   3.012813772  23.351128785   0.374237741 
##          1436          1437          1438          1439          1440 
##   4.653241528  -4.775154000   9.256401287  49.983413418  -0.299525532 
##          1441          1442          1443          1444          1445 
##   5.066813756  17.841774697  -5.542730739   2.349603412   9.697651795 
##          1446          1447          1448          1449          1450 
##  -8.489656295  13.000195622   6.517760426  13.920565366  -1.826496718 
##          1451          1452          1453          1454          1455 
##  51.593105819  17.134414019  35.533925577  -7.184592647  -2.532925626 
##          1456          1457          1458          1459          1460 
## -24.471052842   7.064646403  10.252607410  -4.380637668 -16.013057380 
##          1461          1462          1463          1464          1465 
##  18.034534216   6.681163175  -8.792348719  -7.740374322  -0.106611958 
##          1466          1467          1468          1469          1470 
##   7.283600801  23.544277102  -7.053497733 -14.421623928   3.401997199 
##          1471          1472          1473          1474          1475 
##  -0.346015598  -2.756791741  24.472186848  19.393260785 -23.616735834 
##          1476          1477          1478          1479          1480 
##  10.857398110  24.149203090 -12.343748469  -8.544305171  -3.312072266 
##          1481          1482          1483          1484          1485 
##   3.951185814   2.060915997 -14.643769418 -14.379040661 -12.003560964 
##          1486          1487          1488          1489          1490 
##  -2.332279159  -6.907164905  -4.100629609   1.608374788  15.527306955 
##          1491          1492          1493          1494          1495 
##   2.697802989  -8.738161107   6.344512040  13.551625788  -8.533023365 
##          1496          1497          1498          1499          1500 
##  -5.826441768   2.287627931  17.997217469  -2.298672416   2.614760146 
##          1501          1502          1503          1504          1505 
##   4.691147847 -10.373723683   3.854045932  -4.760492147 -22.584319440 
##          1506          1507          1508          1509          1510 
##  14.705275169  10.546526302   3.183963678 -22.088987101 -30.869079482 
##          1511          1512          1513          1514          1515 
##  -6.017946165  -1.046471420  -2.067598884  27.322020678  -6.992832507 
##          1516          1517          1518          1519          1520 
##   6.922635111  -9.208106355  36.360374444  -4.946157548  11.577241832 
##          1521          1522          1523          1524          1525 
##  -7.611690706   7.036594274  -3.741318467  -7.630541805  14.453738929 
##          1526          1527          1528          1529          1530 
##  -7.361939020 -16.160716803  -3.975254537  -3.922274330 -21.678540892 
##          1531          1532          1533          1534          1535 
##  -7.071137990  -9.398452921  22.298172710   9.686098586 -11.128579672 
##          1536          1537          1538          1539          1540 
## -16.078334652  -7.752521119  13.180036215   6.379667657  -2.472362208 
##          1541          1542          1543          1544          1545 
##  15.003103604  13.403419105 -13.149043423   1.746468188  -4.367360997 
##          1546          1547          1548          1549          1550 
##  35.255021801 -11.581187962  -0.699613414 -29.757141005  -7.644185486 
##          1551          1552          1553          1554          1555 
##  -0.871051415   5.278850595 -12.881616222  13.216701159   8.325340912 
##          1556          1557          1558          1559          1560 
##  -9.354663563 -14.821872324  12.473036218 -14.810213224  -4.278568624 
##          1561          1562          1563          1564          1565 
##  17.642712795   6.974524644  -9.154462986 -28.377572943 -16.223056589 
##          1566          1567          1568          1569          1570 
##  -1.754233498  -3.970423977 -14.822491458  10.098739355  -8.954424766 
##          1571          1572          1573          1574          1575 
##  -1.357603160  -0.004590935  -2.393082638   4.651280357   2.582156318 
##          1576          1577          1578          1579          1580 
##   0.430143544   2.269056361  77.768913373  -0.852356362   1.362296328 
##          1581          1582          1583          1584          1585 
##  10.818794691  40.143686448 -14.947024743  44.603753458  -3.836140439 
##          1586          1587          1588          1589          1590 
##   2.000761950 -18.103706910   4.086613082   5.116684383  -3.692434242 
##          1591          1592          1593          1594          1595 
##  -6.841666951 -13.840973258   6.285874100   6.017024291 -13.228202371 
##          1596          1597          1598          1599          1600 
## -10.136745049  -7.812426699  16.579031635  -2.875138566  12.068508760 
##          1601          1602          1603          1604          1605 
##   2.406062838  18.322726310   4.334231171 -12.409766713   2.291911077 
##          1606          1607          1608          1609          1610 
## -10.911989029  -9.953787595  -8.946724491 -17.318929376  15.602737190 
##          1611          1612          1613          1614          1615 
##   4.517310151  19.752329270   0.712027106   9.176701349  79.711854688 
##          1616          1617          1618          1619          1620 
##  20.608454571   4.593825499  -5.828577699  21.999595366  -2.979995419 
##          1621          1622          1623          1624          1625 
##  13.076025718 -12.266351574  -2.331638191 -10.200818863  -4.313508439 
##          1626          1627          1628          1629          1630 
## -19.159492337  -3.926807898 -25.554142812 -14.771368615  -0.447717941 
##          1631          1632          1633          1634          1635 
##  -2.204295006  17.549458794   8.143865942   8.722484205   5.379041552 
##          1636          1637          1638          1639          1640 
##   7.898578943   4.468375603  -4.362749761 -11.136124965 -30.279878041 
##          1641          1642          1643          1644          1645 
##  -3.034510983 -38.225473886   8.985648784   5.252935644  -0.117918123 
##          1646          1647          1648          1649          1650 
## -11.963743305  12.993625716 -14.644579001   2.963706956  -3.273408790 
##          1651          1652          1653          1654          1655 
##  -9.206166311  22.789793904 -13.678432560   5.587728089 -11.120922363 
##          1656          1657          1658          1659          1660 
##   7.905998515  14.801143375  -5.945679986  -8.934841138  -9.281354301 
##          1661          1662          1663          1664          1665 
##   0.024399428  -8.598999920 -11.896936977  -1.267669318  -0.316951991 
##          1666          1667          1668          1669          1670 
## -10.427275444 -16.984319027 -13.722289011 -11.475065894   1.828421138 
##          1671          1672          1673          1674          1675 
##  -2.636531364 -10.692738489  -7.780533277  -0.323582773  -9.067736024 
##          1676          1677          1678          1679          1680 
##  13.486483810 -12.471058418   0.303653933   4.115610333  -8.211147652 
##          1681          1682          1683          1684          1685 
##   9.415714427 -12.931299841 -12.267982320  15.544466176  -0.293512263 
##          1686          1687          1688          1689          1690 
##  -1.348278074  -4.296334714   0.353769376 -15.899382075 -27.280764717 
##          1691          1692          1693          1694          1695 
##  -0.568413779   1.199743132 -17.078038561  -6.561542474  -6.343887417 
##          1696          1697          1698          1699          1700 
## -18.493643653   8.521813697  27.469409236  10.488525514  -1.405642522 
##          1701          1702          1703          1704          1705 
##   1.780582894 -25.816865642 -12.760009112 -21.156064702  31.761686122 
##          1706          1707          1708          1709          1710 
##  58.217896215  -7.238696372   6.522927052 -23.014753592  -1.622105669 
##          1711          1712          1713          1714          1715 
##  -8.994957381 -32.962540831 -15.426819836 -13.419737038  -6.610486285 
##          1716          1717          1718          1719          1720 
##   3.427698586   2.633027937 -11.898791305 -12.613901483 -16.555125773 
##          1721          1722          1723          1724          1725 
## -13.243571975   4.082015138  -7.099021776  22.601983630  11.662329141 
##          1726          1727          1728          1729          1730 
##  -4.381651631 -12.079414382 -12.265569877 -21.280472339   0.841749693 
##          1731          1732          1733          1734          1735 
##  -8.833754465  10.294957994   0.607849988   9.427518849 -11.661819234 
##          1736          1737          1738          1739          1740 
##  -0.891230938 -21.283516789   1.725686104 -32.824457241 -10.867490824 
##          1741          1742          1743          1744          1745 
##  -3.146217546   7.377820413   3.321302770   7.820517862  -5.109151533 
##          1746          1747          1748          1749          1750 
##   7.530353782   8.846337184  22.605066235  15.309334963  -6.130257615 
##          1751          1752          1753          1754          1755 
##  -5.681270409  -0.132110346  -0.956340474   3.080781927  15.468182201 
##          1756          1757          1758          1759          1760 
## -12.043961400  -1.287999399 -19.359563760  -7.612153746 -10.659619274 
##          1761          1762          1763          1764          1765 
##  23.825267663 -12.674542724  31.897676931  -4.230184870  13.612854034 
##          1766          1767          1768          1769          1770 
## -13.212743499 -14.910304881   8.060515141 -11.190298300 -32.442552666 
##          1771          1772          1773          1774          1775 
##  -8.188098719  -5.404815850  -9.096624950  35.847207369  -5.003832499 
##          1776          1777          1778          1779          1780 
##  -3.162121678  -9.431754145 -24.819993885  -9.746081703  -8.429866143 
##          1781          1782          1783          1784          1785 
## -13.108568449   0.258113170 -20.082525316  12.235480938  10.659806093 
##          1786          1787          1788          1789          1790 
## -14.987369385 -26.970631380  -1.762554826 -10.589801274  62.224773886 
##          1791          1792          1793          1794          1795 
## -16.963269542   3.767170346  15.043347720   8.061053594 -10.055048618 
##          1796          1797          1798          1799          1800 
## -15.154718019 -12.283356850 -10.998685352   4.856467155 -11.038085971 
##          1801          1802          1803          1804          1805 
##  -8.814855999 -25.843931721   1.488089674 -17.117333949 -13.545286055 
##          1806          1807          1808          1809          1810 
##   9.055204567 -16.884064188   2.172631446  -9.614830826   1.952334535 
##          1811          1812          1813          1814          1815 
## -35.905805271  -0.413300260  -2.481831378 -10.055993763   0.025799784 
##          1816          1817          1818          1819          1820 
## -15.735821233 -15.271219558  -3.274949725  -5.980969787  -6.664219607 
##          1821          1822          1823          1824          1825 
##   8.195478547  -6.991885261   9.598462001  -0.081321500   6.328076633 
##          1826          1827          1828          1829          1830 
## -32.057025689  -9.915661113 -18.333516142 -12.286478378  -1.498001772 
##          1831          1832          1833          1834          1835 
##   5.808050219 -14.989747733 -16.875351761  -4.185826340 -19.017631281 
##          1836          1837          1838          1839          1840 
##  -8.984708276   2.391157926  -0.216920784 -13.138387360 -15.132743635 
##          1841          1842          1843          1844          1845 
##   3.003276253  -5.127855024  20.042261738  -4.223648170  19.396549716 
##          1846          1847          1848          1849          1850 
##  -9.883530991   4.905148401   9.000846572  -6.999480378   5.008490370 
##          1851          1852          1853          1854          1855 
##  -0.029396768  -6.044272286   5.193245050  15.168864021  -2.065922893 
##          1856          1857          1858          1859          1860 
##   4.933876324  48.154837169   1.628325881 -17.104233665   5.850004703 
##          1861          1862          1863          1864          1865 
##  26.799745360 -14.686981800  19.014153641  -0.880593659  -0.239477489 
##          1866          1867          1868          1869          1870 
## -10.262434106  -8.474533111   3.003516809  10.427936601   8.266668624 
##          1871          1872          1873          1874          1875 
##  -4.904877320  16.021975680 -13.913412060  -6.784235432  30.415352377 
##          1876          1877          1878          1879          1880 
## -15.572919984  -5.987215504 -15.148640831  -0.433953884  -4.914999698 
##          1881          1882          1883          1884          1885 
## -14.335020715  20.346744233  13.334339581  13.192308596   6.099672602 
##          1886          1887          1888          1889          1890 
##   9.320126565   8.087236110   2.964120610  15.367784774  35.132424647 
##          1891          1892          1893          1894          1895 
##   8.534332839   3.068770506 -12.735202296 -14.018351671 -14.570607903 
##          1896          1897          1898          1899          1900 
##  -6.975470929 -23.057105606   0.228448732 -17.510702639  14.814719128 
##          1901          1902          1903          1904          1905 
## -11.342788525  -9.620711797   2.859220808  -4.354749929  -1.009365230 
##          1906          1907          1908          1909          1910 
##  25.828067335   2.301895199  18.028203794  18.624579491   9.359217154 
##          1911          1912          1913          1914          1915 
##  -3.205637103 -17.018489989 -10.388998476 -15.070721612   9.421184367 
##          1916          1917          1918          1919          1920 
## -19.874017685  -9.099160024 -22.171486534   6.272275261   1.104474702 
##          1921          1922          1923          1924          1925 
##  -6.482074640 -12.396285173  13.367498396 -26.489496922 -16.065338406 
##          1926          1927          1928          1929          1930 
##  -9.209557919   6.482370153 -21.040728721 -11.616822382   0.437310091 
##          1931          1932          1933          1934          1935 
##  -4.788897803  11.676321625  -9.761119672 -19.827751568  -1.774133270 
##          1936          1937          1938          1939          1940 
## -10.968480766  26.845556496  -9.655585617 -22.643662013  -9.751568614 
##          1941          1942          1943          1944          1945 
##  -5.343719478   1.895229467 -12.347150556  18.707343801  -3.708412131 
##          1946          1947          1948          1949          1950 
## -33.906629263  -4.407206864  14.980254295  -5.286648921  22.011194427 
##          1951          1952          1953          1954          1955 
## -13.864227417 -13.435068945  -3.713585760  -7.291656989 -10.868461377 
##          1956          1957          1958          1959          1960 
##  -2.921709727   0.498337511  -8.077571891  -0.787565746  10.834027351 
##          1961          1962          1963          1964          1965 
##   5.850965069  12.800869829  -0.098714151 -64.361700888   2.709998967 
##          1966          1967          1968          1969          1970 
##  -5.070780792 -27.818728085   4.913616538  64.617798197  -6.477604682 
##          1971          1972          1973          1974          1975 
##  -3.269923908 -13.582628664  10.538736546  13.262839639  10.760296793 
##          1976          1977          1978          1979          1980 
## -12.073431986 -32.854723180  22.078591035  -5.156436263  18.828334126 
##          1981          1982          1983          1984          1985 
##  -9.589169701 -11.185118296  23.235395386   4.968297856   8.475957262 
##          1986          1987          1988          1989          1990 
##  13.441817284  10.623149052  -6.402696905   4.221256570  -4.506746319 
##          1991          1992          1993          1994          1995 
##   9.899383277   1.951278939 -20.467920433   7.387264122  -5.057399446 
##          1996          1997          1998          1999          2000 
##  10.084951390  32.990634770  16.091797873 -16.603818140  20.608307240 
##          2001          2002          2003          2004          2005 
##   2.890511711   5.759930199  -5.679175671  -3.284849354   3.006380966 
##          2006          2007          2008          2009          2010 
##   4.050815031  19.467207815 -29.370756530  -5.558046416  16.303007595 
##          2011          2012          2013          2014          2015 
##  -6.184521568   4.176953748  15.125329322  12.013140719 -13.278566177 
##          2016          2017          2018          2019          2020 
##  -1.895273008  40.092967354  47.709071717   5.331682319  -9.650344577 
##          2021          2022          2023          2024          2025 
##  22.814294206   9.562335775  -8.675933843  11.783832730  22.333058921 
##          2026          2027          2028          2029          2030 
##  -2.580682609  25.653197126  21.201102488 -15.786960891   3.372035933 
##          2031          2032          2033          2034          2035 
##  -0.050533120  13.593511606  -5.680791434 -13.646542471  23.464946157 
##          2036          2037          2038          2039          2040 
##  -0.419343698 -27.188725111  23.677360835   5.776090685  -4.591902378 
##          2041          2042          2043          2044          2045 
##  15.443896815 -20.198965702   0.763089868   6.570827936  43.458831055 
##          2046          2047          2048          2049          2050 
## -18.060378634  -1.908894554  -2.975455480  -6.363363403  -2.903284223 
##          2051          2052          2053          2054          2055 
##  -7.663710407  21.707773585  -1.330644623   1.280665852   1.639388656 
##          2056          2057          2058          2059          2060 
##  14.311818504  19.299723692 -22.880469327  -3.866672695 -16.653229474 
##          2061          2062          2063          2064          2065 
## -21.206931088  -5.834893960 -37.344505795  -1.677744260  -6.329632665 
##          2066          2067          2068          2069          2070 
## -23.784388447  -1.811996421 -10.006566765  -9.759192560  24.735411723 
##          2071          2072          2073          2074          2075 
##  -2.241295702   8.957045089 -15.199969379  -4.341441107 -14.264454632 
##          2076          2077          2078          2079          2080 
##  26.806405856 -23.912172242  -1.981056209 -21.846583804   0.024653311 
##          2081          2082          2083          2084          2085 
## -26.200546623   9.541272193  19.923192419  -0.052964926  -6.430923957 
##          2086          2087          2088          2089          2090 
##  -3.581486621 -14.640770105  -5.890850096 -10.545329468 -15.057606102 
##          2091          2092          2093          2094          2095 
## -14.856081590 -20.519633604 -21.192056978 -13.320587494   8.922823617 
##          2096          2097          2098          2099          2100 
## -14.222915820 -14.771462668  -4.319828461 -13.440561338  -4.943341203 
##          2101          2102          2103          2104          2105 
##  -6.638579042   1.555080390  15.929244959  -9.154354199 -23.542495001 
##          2106          2107          2108          2109          2110 
## -12.332415300  28.915027238 -31.348894875 -14.365033740 -11.791514064 
##          2111          2112          2113          2114          2115 
##  -6.108018578  -5.826509070 -18.664600324   9.644624819  -1.858487795 
##          2116          2117          2118          2119          2120 
##  20.509132986 -14.927288635  -1.276879170 -10.376816095   2.591938110 
##          2121          2122          2123          2124          2125 
## -21.977005346   2.104032962  60.325591629 -16.088972245 -10.128808828 
##          2126          2127          2128          2129          2130 
##  13.235268128   3.079940372  -9.034342223 -18.839777587 -11.856955967 
##          2131          2132          2133          2134          2135 
##  -6.904164969   0.080873780   7.811982164   1.680863932  10.746277309 
##          2136          2137          2138          2139          2140 
##  22.238568010  11.493966425  -5.470754918   2.040199911  21.032207810 
##          2141          2142          2143          2144          2145 
##  -9.596125752   6.227877453  -8.135388535 -14.044433221  14.265416168 
##          2146          2147          2148          2149          2150 
##  -4.407798851 -11.236560335  -1.164074279 -11.403409785 -14.086121786 
##          2151          2152          2153          2154          2155 
##  -0.569308194 -13.009365230 -10.447308103 -17.558345047 -12.422619584 
##          2156          2157          2158          2159          2160 
## -12.121952185  -1.634902383  10.699030486 -23.338178807  -6.480084391 
##          2161          2162          2163          2164          2165 
##  -7.182298013  -2.772304973  -2.054180066 -13.864217103 -31.452468389 
##          2166          2167          2168          2169          2170 
## -12.059556876 -24.874245415  30.226424488  10.589114139 -35.488853533 
##          2171          2172          2173          2174          2175 
##  48.373729720  51.172135413  -9.099923364  51.119538449 -27.289444249 
##          2176          2177          2178          2179          2180 
##  -3.100402216 -28.728977093  17.353998627 -22.726745126  -8.041164562 
##          2181          2182          2183          2184          2185 
##  -9.424609318  16.023420034 -18.280978021 -10.874114576 -27.789664060 
##          2186          2187          2188          2189          2190 
## -22.522940372  -3.127500803 -10.305237579 -30.605078561  11.742923208 
##          2191          2192          2193          2194          2195 
## -16.424360899   0.622353409  -8.700975380  -7.049341670   3.044085334 
##          2196          2197          2198          2199          2200 
##  64.791973444  -3.089525902   0.919685415   1.505886963  40.338501277 
##          2201          2202          2203          2204          2205 
##   5.743868136 -20.927231392  11.618159288  22.555942471  -7.235734116 
##          2206          2207          2208          2209          2210 
##  10.161023810  11.794246761   7.552506191 -21.398400430   6.430315356 
##          2211          2212          2213          2214          2215 
##  14.449577848   4.042675313   2.424062616  -5.005253745  22.251872451 
##          2216          2217          2218          2219          2220 
##   2.006425016  -6.205460589  -1.346824230  12.157711257  -4.199085111 
##          2221          2222          2223          2224          2225 
## -28.212199365   5.663761565  -6.896683195  35.388513841  -4.466262442 
##          2226          2227          2228          2229          2230 
## -16.412463649  -5.531120227  17.668167988 -12.687873295  21.335385517 
##          2231          2232          2233          2234          2235 
##   2.173580568 -13.090182511  -3.399172609  -9.767947923  79.520146829 
##          2236          2237          2238          2239          2240 
##  18.407747818  13.480681081  -2.863352223 -28.247136843  10.154659509 
##          2241          2242          2243          2244          2245 
## -20.552633496  -3.681419510  18.929656138  62.938580495 -23.000941882 
##          2246          2247          2248          2249          2250 
##   8.522515452  -8.988600763  20.782690925   4.448488017  -2.155557416 
##          2251          2252          2253          2254          2255 
## -12.769994059   0.277372348  16.346696750  47.599028631  14.963670357 
##          2256          2257          2258          2259          2260 
## -15.220749831  -4.488036711  -1.815709776   9.554586421 -12.542766362 
##          2261          2262          2263          2264          2265 
##  -2.170055742  -1.643476756   1.858209348   6.315400470   7.495168145 
##          2266          2267          2268          2269          2270 
## -15.006285039 -15.649416239   1.209199295  23.332948990 -14.969314994 
##          2271          2272          2273          2274          2275 
##  -8.683543864  -6.068883476 -10.552719822  -7.477377450  -9.109781080 
##          2276          2277          2278          2279          2280 
##  -1.136821265   7.091169542  -4.432370784 -10.305979585  -3.512257744 
##          2281          2282          2283          2284          2285 
## -10.801051255  -3.649919392  14.575135543 -16.013435538 -13.946753394 
##          2286          2287          2288          2289          2290 
##  -2.286304769  -7.722553715  -0.923862978  -8.051253970  21.314807669 
##          2291          2292          2293          2294          2295 
## -26.394425189  11.219263955 -26.226715716  -0.699623251  10.272390242 
##          2296          2297          2298          2299          2300 
##   2.894870709  45.640433567  25.518358476  12.528417574  -9.982116109 
##          2301          2302          2303          2304          2305 
##  -3.627378494  -5.422596914   2.606369639 -20.666503038  56.284965713 
##          2306 
##  61.316305363
# Print the fitted values of the model
fitted(lm_rural)
##        1        2        3        4        5        6        7        8 
## 138.3877 125.7170 137.7101 120.6084 127.4650 138.8971 137.8253 134.8270 
##        9       10       11       12       13       14       15       16 
## 134.2180 133.1430 123.7582 131.8392 128.6786 121.7340 120.5914 126.0594 
##       17       18       19       20       21       22       23       24 
## 123.5458 122.0231 124.4288 122.9510 120.2641 125.0007 122.4518 127.8768 
##       25       26       27       28       29       30       31       32 
## 121.4582 132.4667 138.8002 112.8333 132.0377 125.8482 127.2010 121.5717 
##       33       34       35       36       37       38       39       40 
## 122.2107 122.3541 125.5993 129.8816 129.8660 131.0951 126.1197 127.7457 
##       41       42       43       44       45       46       47       48 
## 129.2612 124.0184 139.5365 140.6391 115.3684 118.1097 116.9226 118.2225 
##       49       50       51       52       53       54       55       56 
## 128.8927 117.8506 122.1349 117.8403 123.3786 122.4596 114.5293 113.3394 
##       57       58       59       60       61       62       63       64 
## 116.5185 114.1561 118.2416 128.0025 114.4557 133.2012 118.8874 121.8494 
##       65       66       67       68       69       70       71       72 
## 120.9838 126.5181 122.6873 123.4241 137.4951 123.6374 121.7463 121.0924 
##       73       74       75       76       77       78       79       80 
## 121.9527 124.1690 131.8947 127.8946 125.4783 123.8776 120.3342 124.0930 
##       81       82       83       84       85       86       87       88 
## 131.0050 117.8254 123.5719 120.1006 115.7751 132.0973 122.1812 125.1366 
##       89       90       91       92       93       94       95       96 
## 113.0478 123.9772 125.4787 117.8303 133.5322 122.5015 116.6060 113.1105 
##       97       98       99      100      101      102      103      104 
## 120.5276 111.0264 131.1275 119.1017 123.9988 140.7718 113.7329 122.3022 
##      105      106      107      108      109      110      111      112 
## 132.4873 126.3715 123.8275 142.3346 133.1061 124.9824 136.0685 112.5924 
##      113      114      115      116      117      118      119      120 
## 130.4619 118.1882 118.8257 118.0230 125.5926 136.1844 126.2541 133.0884 
##      121      122      123      124      125      126      127      128 
## 131.0994 122.5515 117.1297 132.1569 123.2192 120.7869 123.1149 144.6975 
##      129      130      131      132      133      134      135      136 
## 117.6144 122.8889 123.8630 122.2533 151.1303 118.5308 123.5642 121.5636 
##      137      138      139      140      141      142      143      144 
## 119.6470 123.6703 121.1098 123.4161 111.0402 124.5049 118.5580 120.0729 
##      145      146      147      148      149      150      151      152 
## 132.5750 117.7607 120.3938 131.0850 113.9053 123.2536 121.7985 121.7958 
##      153      154      155      156      157      158      159      160 
## 123.5281 119.2132 122.3278 125.7590 125.6553 120.9835 115.9972 128.1489 
##      161      162      163      164      165      166      167      168 
## 136.2538 142.4293 112.1517 135.4422 125.4897 131.3520 116.5966 141.1912 
##      169      170      171      172      173      174      175      176 
## 113.4664 130.3930 115.5158 116.9330 119.6183 119.9635 118.2570 130.1009 
##      177      178      179      180      181      182      183      184 
## 117.8657 122.1497 116.0266 138.1780 118.4141 123.0690 120.9030 117.9908 
##      185      186      187      188      189      190      191      192 
## 118.9951 133.0257 129.9528 121.4059 118.7636 114.3396 124.5840 109.7865 
##      193      194      195      196      197      198      199      200 
## 116.2804 112.9704 117.7643 127.7087 129.9155 121.9893 120.9931 113.8943 
##      201      202      203      204      205      206      207      208 
## 125.9202 136.5134 117.1931 124.2350 127.0274 118.3459 112.6452 125.6871 
##      209      210      211      212      213      214      215      216 
## 119.6678 118.5265 128.2379 119.0383 116.7128 131.9553 133.3489 132.8371 
##      217      218      219      220      221      222      223      224 
## 127.1056 124.6338 133.2789 117.8587 118.5920 123.0180 118.1379 123.3782 
##      225      226      227      228      229      230      231      232 
## 122.1033 116.4632 125.9375 114.2325 125.0510 126.0868 135.6124 118.7759 
##      233      234      235      236      237      238      239      240 
## 116.3557 121.7567 128.3176 120.7773 123.1968 111.0456 126.7925 115.5100 
##      241      242      243      244      245      246      247      248 
## 123.7570 114.4990 127.2998 121.1462 133.4970 111.4585 118.0283 137.7312 
##      249      250      251      252      253      254      255      256 
## 114.0132 113.1508 129.6682 115.6519 120.4429 117.9173 127.2166 124.8902 
##      257      258      259      260      261      262      263      264 
## 118.0880 122.9458 120.8946 133.6827 118.6186 135.7160 118.5290 115.0814 
##      265      266      267      268      269      270      271      272 
## 129.4070 137.6244 111.2767 127.1559 118.4592 123.5658 127.7905 124.3792 
##      273      274      275      276      277      278      279      280 
## 121.9822 116.4148 117.1286 116.9877 131.6133 121.5519 113.7437 122.6074 
##      281      282      283      284      285      286      287      288 
## 121.6994 125.4647 119.2598 119.8250 134.9598 126.0510 135.3131 124.3348 
##      289      290      291      292      293      294      295      296 
## 127.3365 122.7749 122.6141 118.2448 116.0183 115.8635 128.2006 123.5449 
##      297      298      299      300      301      302      303      304 
## 118.5429 124.5121 121.0334 122.1875 111.3567 130.2950 112.0393 125.9923 
##      305      306      307      308      309      310      311      312 
## 129.4228 120.8295 122.2123 114.1345 121.8258 129.3896 120.0897 123.9500 
##      313      314      315      316      317      318      319      320 
## 113.5577 122.6246 127.8383 113.9436 120.4561 121.8194 134.4399 134.3558 
##      321      322      323      324      325      326      327      328 
## 126.9826 120.8850 148.8473 126.3442 127.7985 138.1206 138.7109 132.0071 
##      329      330      331      332      333      334      335      336 
## 121.4102 135.4089 142.3962 126.2505 128.0993 118.5362 138.3866 118.0785 
##      337      338      339      340      341      342      343      344 
## 124.4530 143.7732 135.2382 128.6684 121.2261 141.7751 125.9596 139.2569 
##      345      346      347      348      349      350      351      352 
## 122.0345 137.7126 122.6706 138.1785 132.1516 125.1588 119.2629 126.1635 
##      353      354      355      356      357      358      359      360 
## 129.1783 142.6533 143.3139 129.4163 128.6309 121.6544 122.9127 130.6247 
##      361      362      363      364      365      366      367      368 
## 141.7929 122.2699 121.0375 123.8286 121.4030 122.6387 129.3586 122.7573 
##      369      370      371      372      373      374      375      376 
## 120.0206 119.0443 127.4152 118.2993 120.8705 120.9027 124.5049 123.3774 
##      377      378      379      380      381      382      383      384 
## 119.6337 120.6637 143.1685 121.9596 123.9570 135.3360 121.7853 127.9972 
##      385      386      387      388      389      390      391      392 
## 127.1133 130.2291 114.9419 122.9962 125.8673 137.2797 130.0984 123.1970 
##      393      394      395      396      397      398      399      400 
## 125.7637 124.3499 121.8966 120.5113 126.6985 133.1447 134.6133 124.7213 
##      401      402      403      404      405      406      407      408 
## 137.9138 128.1291 139.0067 123.5449 125.2332 127.4356 122.0215 126.9210 
##      409      410      411      412      413      414      415      416 
## 123.7191 129.2513 126.0667 131.3408 117.0978 122.1882 119.8692 138.0489 
##      417      418      419      420      421      422      423      424 
## 128.5196 128.0093 118.5418 129.8959 142.9489 135.4322 142.5787 132.6544 
##      425      426      427      428      429      430      431      432 
## 129.4548 117.6591 135.4406 136.4929 120.0871 137.3901 128.1619 123.4478 
##      433      434      435      436      437      438      439      440 
## 123.6068 144.2361 125.1975 144.7169 118.3680 142.7674 129.8013 125.8686 
##      441      442      443      444      445      446      447      448 
## 138.2499 130.8100 117.6050 121.3608 131.0980 128.0794 123.9784 136.0660 
##      449      450      451      452      453      454      455      456 
## 115.5078 124.3589 121.4544 135.7492 128.1970 135.7122 131.5057 129.1292 
##      457      458      459      460      461      462      463      464 
## 119.1589 117.4590 119.1717 118.8879 137.4868 122.7327 129.6920 126.7203 
##      465      466      467      468      469      470      471      472 
## 116.7757 141.9853 119.6270 131.2120 120.3187 145.3736 126.0031 123.2202 
##      473      474      475      476      477      478      479      480 
## 141.6033 123.9106 131.2896 136.2385 147.2672 116.5945 125.1863 135.3395 
##      481      482      483      484      485      486      487      488 
## 124.9013 115.0276 120.2832 122.4180 143.9333 128.9958 126.0614 140.5445 
##      489      490      491      492      493      494      495      496 
## 136.7380 134.1159 151.4173 129.2213 144.2238 132.1257 127.5278 134.2806 
##      497      498      499      500      501      502      503      504 
## 139.0932 143.5463 128.0853 126.2927 126.4283 143.3783 121.6951 116.8415 
##      505      506      507      508      509      510      511      512 
## 140.2107 114.5956 124.3754 135.8833 120.9401 127.1973 130.7241 132.9166 
##      513      514      515      516      517      518      519      520 
## 129.9426 131.9385 133.5002 150.3079 114.9786 133.3522 132.4202 134.9065 
##      521      522      523      524      525      526      527      528 
## 139.9466 123.6611 136.6964 136.1102 123.5828 132.2674 118.7956 130.2137 
##      529      530      531      532      533      534      535      536 
## 134.7129 123.8295 132.1113 138.9595 130.4003 129.3367 126.4415 128.3034 
##      537      538      539      540      541      542      543      544 
## 141.1341 130.6604 129.6057 130.1806 131.1613 132.7760 135.6782 143.0540 
##      545      546      547      548      549      550      551      552 
## 134.8134 124.7505 125.4707 134.8145 126.6920 126.3841 120.5989 128.7966 
##      553      554      555      556      557      558      559      560 
## 125.2006 128.9784 130.9314 136.9413 121.7578 120.0724 141.8230 137.5701 
##      561      562      563      564      565      566      567      568 
## 126.0178 131.6750 138.9683 135.4162 129.7796 134.3536 131.5450 132.7099 
##      569      570      571      572      573      574      575      576 
## 135.1362 132.6272 127.5268 120.0964 125.1522 133.5937 118.4046 144.0463 
##      577      578      579      580      581      582      583      584 
## 118.6620 127.2591 124.7271 144.1011 114.6647 113.6124 124.9566 113.4207 
##      585      586      587      588      589      590      591      592 
## 131.4227 121.5796 127.3722 121.9581 129.5293 119.4234 131.8731 122.8067 
##      593      594      595      596      597      598      599      600 
## 133.5646 137.6912 121.3031 125.6888 118.0063 144.9449 136.8489 144.1885 
##      601      602      603      604      605      606      607      608 
## 129.9993 119.1065 137.3849 138.4815 116.8185 137.4423 130.9422 126.3463 
##      609      610      611      612      613      614      615      616 
## 119.3676 133.8715 131.0626 128.0126 139.6805 144.4809 125.6752 127.3024 
##      617      618      619      620      621      622      623      624 
## 141.1802 131.5947 133.6462 142.9806 132.6178 135.3519 128.6878 145.5090 
##      625      626      627      628      629      630      631      632 
## 126.0443 114.0294 120.1081 132.4175 141.9517 139.0194 143.0489 119.8561 
##      633      634      635      636      637      638      639      640 
## 120.8235 146.3959 147.7749 127.8788 126.1516 129.7312 119.3521 114.3995 
##      641      642      643      644      645      646      647      648 
## 120.4068 129.9221 122.7976 128.4397 137.1725 133.9886 120.1485 120.3834 
##      649      650      651      652      653      654      655      656 
## 123.5734 117.1003 121.1854 125.1107 120.3496 119.5084 126.6449 125.3067 
##      657      658      659      660      661      662      663      664 
## 121.6061 119.3195 115.0698 127.9920 128.6119 110.1167 120.4055 125.4270 
##      665      666      667      668      669      670      671      672 
## 117.8609 129.1680 126.3269 120.8827 135.2301 119.8829 122.3181 121.8117 
##      673      674      675      676      677      678      679      680 
## 123.2106 135.3183 113.4645 119.6304 118.1951 118.9736 139.5019 118.3214 
##      681      682      683      684      685      686      687      688 
## 122.7082 128.8716 116.6218 114.7460 123.4463 115.7381 132.2857 118.1039 
##      689      690      691      692      693      694      695      696 
## 122.9988 125.7654 121.9880 119.4421 125.7428 125.6863 129.6436 120.3726 
##      697      698      699      700      701      702      703      704 
## 124.1858 130.1009 121.5735 121.2762 128.3326 124.8509 131.8055 118.6525 
##      705      706      707      708      709      710      711      712 
## 119.8567 124.0988 136.1904 123.1814 123.5179 115.1868 134.9248 122.9599 
##      713      714      715      716      717      718      719      720 
## 117.2676 116.8116 131.6522 130.3028 124.6940 123.7907 127.1121 116.3433 
##      721      722      723      724      725      726      727      728 
## 140.7103 130.0316 121.2304 123.7051 119.1219 124.7193 134.8050 120.4357 
##      729      730      731      732      733      734      735      736 
## 124.9287 123.0324 122.1636 115.3924 116.7740 126.8126 121.4609 117.9838 
##      737      738      739      740      741      742      743      744 
## 132.9761 127.6147 130.1054 124.2912 120.6306 119.9281 128.9470 124.4482 
##      745      746      747      748      749      750      751      752 
## 114.0269 131.2643 137.7191 121.2132 127.8910 125.1490 128.1910 118.1816 
##      753      754      755      756      757      758      759      760 
## 127.5269 134.9001 132.3145 128.4732 133.7527 125.5579 120.1409 118.2878 
##      761      762      763      764      765      766      767      768 
## 123.5439 136.9846 116.9487 127.8199 113.8107 137.3960 124.9044 124.8699 
##      769      770      771      772      773      774      775      776 
## 128.6644 122.8597 126.9858 119.9956 129.0572 119.7831 126.9030 136.9570 
##      777      778      779      780      781      782      783      784 
## 137.6695 128.4800 123.8747 131.7230 134.6931 119.4933 126.2947 120.3477 
##      785      786      787      788      789      790      791      792 
## 127.1977 124.1701 130.8860 113.2432 119.7073 125.8793 134.4141 133.7150 
##      793      794      795      796      797      798      799      800 
## 116.0088 121.6028 131.1394 128.0406 121.4859 124.5738 123.2339 117.1455 
##      801      802      803      804      805      806      807      808 
## 117.8815 125.8529 140.2255 119.2323 127.1787 130.2113 120.6400 128.8636 
##      809      810      811      812      813      814      815      816 
## 131.0213 125.7384 129.8862 120.6658 122.2796 127.4914 140.4144 130.6776 
##      817      818      819      820      821      822      823      824 
## 121.7976 111.6614 130.4046 131.6438 113.8735 127.4246 129.7042 129.9116 
##      825      826      827      828      829      830      831      832 
## 123.6520 127.4418 126.8050 128.0603 126.0468 122.1593 116.1105 133.0852 
##      833      834      835      836      837      838      839      840 
## 134.1873 127.2822 123.6481 136.7466 121.4256 125.2833 138.2272 147.2598 
##      841      842      843      844      845      846      847      848 
## 129.6092 126.9371 115.8736 126.4897 116.6242 121.6316 135.5897 127.0464 
##      849      850      851      852      853      854      855      856 
## 144.5046 143.4418 126.7343 138.5532 128.9211 127.7775 121.0108 122.7993 
##      857      858      859      860      861      862      863      864 
## 139.3379 126.6586 132.6365 134.2401 117.0224 121.2420 135.7759 128.9668 
##      865      866      867      868      869      870      871      872 
## 121.3018 144.0764 122.2502 118.8484 139.4475 130.4989 128.7263 128.3146 
##      873      874      875      876      877      878      879      880 
## 137.2381 123.3165 137.4116 136.1420 124.7897 138.7362 127.5749 124.1443 
##      881      882      883      884      885      886      887      888 
## 122.2006 123.1576 137.6302 140.0140 119.5397 131.2692 133.9833 141.7643 
##      889      890      891      892      893      894      895      896 
## 131.3490 124.6930 133.7085 146.2087 139.9084 127.6864 118.7421 136.8478 
##      897      898      899      900      901      902      903      904 
## 138.2247 142.4628 117.9621 117.5955 116.2767 129.0010 143.8274 123.2439 
##      905      906      907      908      909      910      911      912 
## 126.5878 136.4890 137.9953 125.7751 140.6439 116.9107 130.4776 121.2391 
##      913      914      915      916      917      918      919      920 
## 119.8256 137.6055 123.6943 129.6443 131.9464 117.7753 124.4327 137.3897 
##      921      922      923      924      925      926      927      928 
## 129.4657 123.3811 125.5171 156.6560 135.3266 138.0036 133.3165 131.9208 
##      929      930      931      932      933      934      935      936 
## 133.1406 130.8617 124.3503 137.1334 119.5899 124.7636 118.8364 137.9251 
##      937      938      939      940      941      942      943      944 
## 135.8332 126.0113 141.6837 138.7234 115.7377 115.4909 115.2680 117.3277 
##      945      946      947      948      949      950      951      952 
## 119.7550 113.3722 132.4886 132.3685 132.3290 123.2121 127.8769 122.1482 
##      953      954      955      956      957      958      959      960 
## 126.8068 131.1963 114.9803 143.6367 121.2080 139.9668 138.7774 119.9274 
##      961      962      963      964      965      966      967      968 
## 125.2219 136.1924 137.2078 117.3425 141.3634 144.5977 126.5869 120.7930 
##      969      970      971      972      973      974      975      976 
## 132.7073 124.1448 130.1115 116.8352 127.4090 118.3752 137.4648 124.2307 
##      977      978      979      980      981      982      983      984 
## 134.7286 127.5070 122.3733 133.7341 130.1215 134.8679 133.5279 123.7899 
##      985      986      987      988      989      990      991      992 
## 127.5864 125.4354 123.2357 132.2291 124.5328 118.3577 135.3398 121.1109 
##      993      994      995      996      997      998      999     1000 
## 123.5449 124.6701 124.2844 116.9077 125.6571 124.8636 150.8950 137.2569 
##     1001     1002     1003     1004     1005     1006     1007     1008 
## 141.2353 128.2842 111.7854 122.1932 142.7372 121.5221 141.9797 141.5166 
##     1009     1010     1011     1012     1013     1014     1015     1016 
## 125.9937 127.1736 126.5879 128.7740 120.0623 137.4106 127.3424 126.5645 
##     1017     1018     1019     1020     1021     1022     1023     1024 
## 127.6062 129.6737 119.1909 127.2944 145.3603 136.7432 131.1121 138.8623 
##     1025     1026     1027     1028     1029     1030     1031     1032 
## 129.7827 120.4700 121.1576 127.3741 141.0422 120.1467 122.7122 129.1645 
##     1033     1034     1035     1036     1037     1038     1039     1040 
## 123.3443 124.6805 131.8128 124.4413 123.9308 126.3455 130.3326 136.0183 
##     1041     1042     1043     1044     1045     1046     1047     1048 
## 136.5104 141.8063 119.1962 126.0114 127.7218 132.1321 121.3897 140.5267 
##     1049     1050     1051     1052     1053     1054     1055     1056 
## 127.6928 120.9927 117.4232 130.1628 140.0277 127.7851 143.3681 128.8835 
##     1057     1058     1059     1060     1061     1062     1063     1064 
## 116.0556 134.3339 132.3804 127.7992 134.2762 111.2972 136.6532 135.5828 
##     1065     1066     1067     1068     1069     1070     1071     1072 
## 127.8878 125.9042 139.3651 124.4713 115.3537 126.6985 128.8110 125.8152 
##     1073     1074     1075     1076     1077     1078     1079     1080 
## 139.4019 132.1280 135.1146 118.2343 137.2892 130.3314 139.0636 136.7411 
##     1081     1082     1083     1084     1085     1086     1087     1088 
## 128.3075 143.0426 120.9295 133.5725 132.6709 130.6694 127.6164 135.5441 
##     1089     1090     1091     1092     1093     1094     1095     1096 
## 136.7404 144.0001 138.4447 136.0281 137.3582 137.5260 157.3531 117.6765 
##     1097     1098     1099     1100     1101     1102     1103     1104 
## 127.5172 124.6931 123.9875 142.1653 121.7002 146.4571 135.9192 146.3290 
##     1105     1106     1107     1108     1109     1110     1111     1112 
## 139.8325 114.8228 128.3953 121.3110 148.1762 132.3004 119.9363 128.1450 
##     1113     1114     1115     1116     1117     1118     1119     1120 
## 119.5709 120.6742 117.7201 122.7793 124.9962 123.9861 124.2784 124.0521 
##     1121     1122     1123     1124     1125     1126     1127     1128 
## 146.8873 114.1736 130.0645 148.0763 125.3038 134.7459 136.2603 130.9498 
##     1129     1130     1131     1132     1133     1134     1135     1136 
## 119.9203 139.1938 132.5943 143.0218 119.0639 123.1050 131.2974 136.7016 
##     1137     1138     1139     1140     1141     1142     1143     1144 
## 126.6562 124.5313 124.8512 129.7955 138.4792 119.4118 127.4153 124.7946 
##     1145     1146     1147     1148     1149     1150     1151     1152 
## 128.1014 131.6375 129.6534 138.5599 126.5629 121.7536 124.2608 136.5423 
##     1153     1154     1155     1156     1157     1158     1159     1160 
## 119.6684 127.5748 133.7881 124.4395 120.1205 126.7428 125.7126 119.8597 
##     1161     1162     1163     1164     1165     1166     1167     1168 
## 122.9152 126.5852 130.4497 123.1803 128.8729 122.0146 141.9316 127.5387 
##     1169     1170     1171     1172     1173     1174     1175     1176 
## 135.0285 131.3949 127.7846 130.3495 124.4243 125.2385 125.0723 149.5262 
##     1177     1178     1179     1180     1181     1182     1183     1184 
## 140.5287 142.6666 121.2054 137.2826 131.4763 126.7461 125.2552 119.8770 
##     1185     1186     1187     1188     1189     1190     1191     1192 
## 119.9325 111.7981 119.4373 112.0047 111.4575 116.2672 121.3849 113.4014 
##     1193     1194     1195     1196     1197     1198     1199     1200 
## 119.8515 123.1286 114.4116 120.7714 119.5260 114.5889 116.4268 123.0137 
##     1201     1202     1203     1204     1205     1206     1207     1208 
## 116.5805 121.0969 113.5201 120.6373 125.3620 118.2495 118.1919 115.2174 
##     1209     1210     1211     1212     1213     1214     1215     1216 
## 136.2472 124.3009 120.9114 117.4203 118.1212 134.6220 125.1574 135.2795 
##     1217     1218     1219     1220     1221     1222     1223     1224 
## 125.4342 120.6842 123.0585 114.7554 122.4885 119.6483 118.0270 125.4596 
##     1225     1226     1227     1228     1229     1230     1231     1232 
## 117.5975 125.6965 123.4361 130.4463 127.6893 133.1954 115.5841 118.1822 
##     1233     1234     1235     1236     1237     1238     1239     1240 
## 123.1218 128.8580 127.8513 130.1044 124.6919 123.8639 133.3785 125.9244 
##     1241     1242     1243     1244     1245     1246     1247     1248 
## 133.3005 122.8140 144.0659 126.7525 125.7128 120.0652 118.1333 123.0536 
##     1249     1250     1251     1252     1253     1254     1255     1256 
## 131.1280 136.4649 125.3718 114.1663 118.6001 134.2158 121.1104 121.4621 
##     1257     1258     1259     1260     1261     1262     1263     1264 
## 139.4966 127.1723 127.5446 120.9176 115.5620 129.8573 122.1501 131.9667 
##     1265     1266     1267     1268     1269     1270     1271     1272 
## 145.1612 149.1257 124.0127 152.9539 130.1939 139.6176 128.6764 141.1774 
##     1273     1274     1275     1276     1277     1278     1279     1280 
## 127.2985 133.2633 132.8411 127.6051 142.5861 140.6336 138.8953 121.3389 
##     1281     1282     1283     1284     1285     1286     1287     1288 
## 122.4851 118.5291 143.5406 134.5501 135.0302 131.8046 128.7886 144.3877 
##     1289     1290     1291     1292     1293     1294     1295     1296 
## 117.5303 134.9852 137.8279 146.1404 133.2004 125.1095 120.0496 120.4896 
##     1297     1298     1299     1300     1301     1302     1303     1304 
## 137.5434 133.3050 127.7777 132.0577 129.4331 126.2409 123.8998 127.2066 
##     1305     1306     1307     1308     1309     1310     1311     1312 
## 121.7905 141.8666 124.1752 133.8162 125.3126 121.7467 129.1396 133.1500 
##     1313     1314     1315     1316     1317     1318     1319     1320 
## 126.9682 138.2604 132.7340 126.2130 117.9780 126.1874 123.7316 126.7855 
##     1321     1322     1323     1324     1325     1326     1327     1328 
## 140.4500 122.7749 136.7319 138.3717 136.1913 142.5027 126.4342 124.9193 
##     1329     1330     1331     1332     1333     1334     1335     1336 
## 127.3227 130.2360 116.3088 130.4787 125.0170 130.6926 139.1933 119.0409 
##     1337     1338     1339     1340     1341     1342     1343     1344 
## 122.6874 126.2451 132.9880 128.7473 123.2414 122.1309 130.3449 114.8894 
##     1345     1346     1347     1348     1349     1350     1351     1352 
## 116.9551 124.8018 125.9860 139.2323 121.7830 137.5780 119.3737 122.9116 
##     1353     1354     1355     1356     1357     1358     1359     1360 
## 119.5139 122.8223 128.9601 126.4676 122.7139 117.2543 125.6793 126.8736 
##     1361     1362     1363     1364     1365     1366     1367     1368 
## 118.7406 121.2321 133.1186 124.7063 132.3258 136.7255 116.3237 129.1583 
##     1369     1370     1371     1372     1373     1374     1375     1376 
## 132.1709 131.9673 138.4882 123.4163 113.9103 127.8284 131.4517 130.5829 
##     1377     1378     1379     1380     1381     1382     1383     1384 
## 131.5942 112.4629 132.4247 123.1736 138.0186 128.0176 134.9654 136.8331 
##     1385     1386     1387     1388     1389     1390     1391     1392 
## 129.2341 126.2495 122.3450 134.3291 131.0349 130.7912 129.8998 122.8387 
##     1393     1394     1395     1396     1397     1398     1399     1400 
## 113.5856 122.5824 125.4117 119.2525 127.1100 141.5975 123.8649 129.3276 
##     1401     1402     1403     1404     1405     1406     1407     1408 
## 119.1063 115.1353 137.3677 128.6737 125.5740 123.9334 126.2553 141.1609 
##     1409     1410     1411     1412     1413     1414     1415     1416 
## 124.8647 115.5366 124.7515 124.4263 114.5198 137.9797 129.6154 114.6921 
##     1417     1418     1419     1420     1421     1422     1423     1424 
## 138.0866 148.3047 120.3234 141.6351 126.0686 118.8814 146.3212 116.7410 
##     1425     1426     1427     1428     1429     1430     1431     1432 
## 144.4722 117.7014 118.6348 143.7877 139.4333 135.1699 115.7876 133.6132 
##     1433     1434     1435     1436     1437     1438     1439     1440 
## 121.9872 132.6489 120.6258 119.3468 115.7752 122.7436 142.0166 115.2995 
##     1441     1442     1443     1444     1445     1446     1447     1448 
## 118.9332 123.1582 129.5427 131.6504 121.3023 124.4897 130.9998 126.4822 
##     1449     1450     1451     1452     1453     1454     1455     1456 
## 146.0794 147.8265 131.4069 147.8656 148.4661 122.1846 134.5329 133.4711 
##     1457     1458     1459     1460     1461     1462     1463     1464 
## 127.9354 139.7474 133.3806 128.0131 118.9655 120.3188 119.7923 130.7404 
##     1465     1466     1467     1468     1469     1470     1471     1472 
## 133.1066 125.7164 127.4557 119.0535 135.4216 124.5980 116.3460 116.7568 
##     1473     1474     1475     1476     1477     1478     1479     1480 
## 131.5278 130.6067 135.6167 140.1426 124.8508 130.3437 132.5443 115.3121 
##     1481     1482     1483     1484     1485     1486     1487     1488 
## 134.0488 123.9391 126.6438 125.3790 128.0036 141.3323 117.9072 128.1006 
##     1489     1490     1491     1492     1493     1494     1495     1496 
## 124.3916 127.4727 142.3022 132.7382 130.6555 132.4484 131.5330 138.8264 
##     1497     1498     1499     1500     1501     1502     1503     1504 
## 134.7124 119.0028 134.2987 139.3852 128.3089 129.3737 112.1460 146.7605 
##     1505     1506     1507     1508     1509     1510     1511     1512 
## 115.5843 120.2947 138.4535 142.8160 124.0890 146.8691 130.0179 139.0465 
##     1513     1514     1515     1516     1517     1518     1519     1520 
## 147.0676 143.6780 125.9928 120.0774 134.2081 135.6396 123.9462 124.4228 
##     1521     1522     1523     1524     1525     1526     1527     1528 
## 130.6117 134.9634 127.7413 134.6305 139.5463 131.3619 125.1607 121.9753 
##     1529     1530     1531     1532     1533     1534     1535     1536 
## 122.9223 127.6785 117.0711 110.3985 140.7018 126.3139 117.1286 115.0783 
##     1537     1538     1539     1540     1541     1542     1543     1544 
## 122.7525 112.8200 113.6203 125.4724 118.9969 114.5966 118.1490 122.2535 
##     1545     1546     1547     1548     1549     1550     1551     1552 
## 120.3674 119.7450 116.5812 115.6996 143.7571 125.6442 116.8711 126.7211 
##     1553     1554     1555     1556     1557     1558     1559     1560 
## 117.8816 112.7833 112.6747 128.3547 121.8219 124.5270 118.8102 112.2786 
##     1561     1562     1563     1564     1565     1566     1567     1568 
## 112.3573 117.0255 117.1545 129.3776 120.2231 119.7542 114.9704 117.8225 
##     1569     1570     1571     1572     1573     1574     1575     1576 
## 118.9013 116.9544 128.3576 128.0046 127.3931 119.3487 122.4178 119.5699 
##     1577     1578     1579     1580     1581     1582     1583     1584 
## 138.7309 132.2311 121.8524 127.6377 141.1812 120.8563 149.9470 132.3962 
##     1585     1586     1587     1588     1589     1590     1591     1592 
## 123.8361 138.9992 131.1037 112.9134 115.8833 116.6924 124.8417 137.8410 
##     1593     1594     1595     1596     1597     1598     1599     1600 
## 118.7141 128.9830 134.2282 124.1367 115.8124 123.4210 125.8751 112.9315 
##     1601     1602     1603     1604     1605     1606     1607     1608 
## 129.5939 137.6773 128.6658 134.4098 119.7081 137.9120 129.9538 135.9467 
##     1609     1610     1611     1612     1613     1614     1615     1616 
## 132.3189 143.3973 143.4827 123.2477 121.2880 117.8233 139.2881 119.3915 
##     1617     1618     1619     1620     1621     1622     1623     1624 
## 120.4062 128.8286 120.0004 121.9800 120.9240 125.2664 148.3316 124.2008 
##     1625     1626     1627     1628     1629     1630     1631     1632 
## 121.3135 134.1595 119.9268 130.5541 123.7714 142.4477 123.2043 134.4505 
##     1633     1634     1635     1636     1637     1638     1639     1640 
## 128.8561 122.2775 117.6210 119.1014 127.5316 126.3627 130.1361 132.2799 
##     1641     1642     1643     1644     1645     1646     1647     1648 
## 128.0345 129.2255 118.0144 127.7471 126.1179 121.9637 124.0064 127.6446 
##     1649     1650     1651     1652     1653     1654     1655     1656 
## 129.0363 123.2734 124.2062 121.2102 132.6784 123.4123 134.1209 121.0940 
##     1657     1658     1659     1660     1661     1662     1663     1664 
## 116.1989 122.9457 123.9348 135.2814 133.9756 127.5990 130.8969 125.2677 
##     1665     1666     1667     1668     1669     1670     1671     1672 
## 118.3170 131.4273 137.9843 123.7223 135.4751 131.1716 121.6365 117.6927 
##     1673     1674     1675     1676     1677     1678     1679     1680 
## 119.7805 119.3236 124.0677 118.5135 127.4711 126.6963 128.8844 121.2111 
##     1681     1682     1683     1684     1685     1686     1687     1688 
## 127.5843 127.9313 134.2680 132.4555 121.2935 113.3483 139.2963 123.6462 
##     1689     1690     1691     1692     1693     1694     1695     1696 
## 125.8994 125.2808 126.5684 129.8003 143.0780 127.5615 136.3439 131.4936 
##     1697     1698     1699     1700     1701     1702     1703     1704 
## 125.4782 120.5306 115.5115 124.4056 123.2194 123.8169 120.7600 117.1561 
##     1705     1706     1707     1708     1709     1710     1711     1712 
## 130.2383 116.7821 128.2387 116.4771 126.0148 124.6221 117.9950 134.9625 
##     1713     1714     1715     1716     1717     1718     1719     1720 
## 129.4268 133.4197 122.6105 121.5723 113.3670 129.8988 117.6139 111.5551 
##     1721     1722     1723     1724     1725     1726     1727     1728 
## 135.2436 118.9180 125.0990 120.3980 140.3377 134.3817 133.0794 125.2656 
##     1729     1730     1731     1732     1733     1734     1735     1736 
## 124.2805 114.1583 112.8338 132.7050 125.3922 130.5725 125.6618 119.8912 
##     1737     1738     1739     1740     1741     1742     1743     1744 
## 122.2835 117.2743 133.8245 131.8675 130.1462 143.6222 112.6787 118.1795 
##     1745     1746     1747     1748     1749     1750     1751     1752 
## 122.1092 114.4696 118.1537 136.3949 115.6907 119.1303 126.6813 120.1321 
##     1753     1754     1755     1756     1757     1758     1759     1760 
## 118.9563 116.9192 119.5318 121.0440 126.2880 122.3596 114.6122 124.6596 
##     1761     1762     1763     1764     1765     1766     1767     1768 
## 134.1747 124.6745 138.1023 151.2302 128.3871 123.2127 131.9103 122.9395 
##     1769     1770     1771     1772     1773     1774     1775     1776 
## 118.1903 134.4426 117.1881 121.4048 116.0966 128.1528 131.0038 137.1621 
##     1777     1778     1779     1780     1781     1782     1783     1784 
## 137.4318 140.8200 115.7461 117.4299 121.1086 114.7419 145.0825 138.7645 
##     1785     1786     1787     1788     1789     1790     1791     1792 
## 119.3402 122.9874 119.9706 120.7626 121.5898 140.7752 128.9633 117.2328 
##     1793     1794     1795     1796     1797     1798     1799     1800 
## 114.9567 128.9389 122.0550 125.1547 129.2834 133.9987 119.1435 122.0381 
##     1801     1802     1803     1804     1805     1806     1807     1808 
## 128.8149 122.8439 134.5119 127.1173 131.5453 120.9448 119.8841 123.8274 
##     1809     1810     1811     1812     1813     1814     1815     1816 
## 118.6148 119.0477 133.9058 137.4133 118.4818 126.0560 118.9742 113.7358 
##     1817     1818     1819     1820     1821     1822     1823     1824 
## 125.2712 122.2749 120.9810 131.6642 116.8045 127.9919 125.4015 113.0813 
##     1825     1826     1827     1828     1829     1830     1831     1832 
## 113.6719 137.0570 131.9157 127.3335 125.2865 119.4980 125.1919 129.9897 
##     1833     1834     1835     1836     1837     1838     1839     1840 
## 128.8754 135.1858 119.0176 120.9847 124.6088 118.2169 119.1384 128.1327 
##     1841     1842     1843     1844     1845     1846     1847     1848 
## 120.9967 124.1279 117.9577 113.2236 112.6035 113.8835 125.0949 120.9992 
##     1849     1850     1851     1852     1853     1854     1855     1856 
## 119.9995 124.9915 124.0294 117.0443 130.8068 131.8311 125.0659 124.0661 
##     1857     1858     1859     1860     1861     1862     1863     1864 
## 148.8452 123.3717 141.1042 120.1500 147.2003 123.6870 130.9858 119.8806 
##     1865     1866     1867     1868     1869     1870     1871     1872 
## 116.2395 136.2624 120.4745 115.9965 117.5721 117.7333 137.9049 115.9780 
##     1873     1874     1875     1876     1877     1878     1879     1880 
## 121.9134 122.7842 122.5846 128.5729 143.9872 123.1486 141.4340 114.9150 
##     1881     1882     1883     1884     1885     1886     1887     1888 
## 123.3350 134.6533 117.6657 127.8077 122.9003 121.6799 136.9128 128.0359 
##     1889     1890     1891     1892     1893     1894     1895     1896 
## 122.6322 120.8676 120.4657 119.9312 137.7352 128.0184 126.5706 128.9755 
##     1897     1898     1899     1900     1901     1902     1903     1904 
## 131.0571 120.7716 128.5107 131.1853 126.3428 133.6207 116.1408 130.3547 
##     1905     1906     1907     1908     1909     1910     1911     1912 
## 125.0094 131.1719 126.6981 125.9718 136.3754 126.6408 135.2056 128.0185 
##     1913     1914     1915     1916     1917     1918     1919     1920 
## 126.3890 125.0707 123.5788 123.8740 124.0992 129.1715 116.7277 126.8955 
##     1921     1922     1923     1924     1925     1926     1927     1928 
## 132.4821 116.3963 133.6325 132.4895 127.0653 133.2096 126.5176 137.0407 
##     1929     1930     1931     1932     1933     1934     1935     1936 
## 142.6168 119.5627 138.7889 129.3237 121.7611 125.8278 132.7741 152.9685 
##     1937     1938     1939     1940     1941     1942     1943     1944 
## 120.1544 118.6556 136.6437 114.7516 128.3437 123.1048 129.3472 130.2927 
##     1945     1946     1947     1948     1949     1950     1951     1952 
## 118.7084 135.9066 141.4072 136.0197 109.2866 122.9888 124.8642 122.4351 
##     1953     1954     1955     1956     1957     1958     1959     1960 
## 121.7136 135.2917 120.8685 135.9217 126.5017 119.0776 133.7876 127.1660 
##     1961     1962     1963     1964     1965     1966     1967     1968 
## 124.1490 121.1991 124.0987 190.3617 121.2900 129.0708 133.8187 139.0864 
##     1969     1970     1971     1972     1973     1974     1975     1976 
## 146.3822 130.4776 127.2699 129.5826 133.4613 141.7372 114.2397 119.0734 
##     1977     1978     1979     1980     1981     1982     1983     1984 
## 136.8547 125.9214 124.1564 112.1717 129.5892 124.1851 114.7646 115.0317 
##     1985     1986     1987     1988     1989     1990     1991     1992 
## 115.5240 126.5582 122.3769 110.4027 120.7787 123.5067 124.1006 121.0487 
##     1993     1994     1995     1996     1997     1998     1999     2000 
## 131.4679 131.6127 117.0574 130.9150 125.0094 128.9082 127.6038 128.3917 
##     2001     2002     2003     2004     2005     2006     2007     2008 
## 138.1095 114.2401 132.6792 120.2848 125.9936 129.9492 119.5328 138.3708 
##     2009     2010     2011     2012     2013     2014     2015     2016 
## 130.5580 117.6970 130.1845 128.8230 126.8747 113.9869 127.2786 122.8953 
##     2017     2018     2019     2020     2021     2022     2023     2024 
## 128.9070 126.2909 119.6683 143.6503 120.1857 114.4377 123.6759 121.2162 
##     2025     2026     2027     2028     2029     2030     2031     2032 
## 115.6669 116.5807 135.3468 122.7989 136.7870 130.6280 129.0505 135.4065 
##     2033     2034     2035     2036     2037     2038     2039     2040 
## 122.6808 122.6465 144.5351 124.4193 128.1887 129.3226 118.2239 120.5919 
##     2041     2042     2043     2044     2045     2046     2047     2048 
## 121.5561 131.1990 123.2369 128.4292 126.5412 133.0604 117.9089 126.9755 
##     2049     2050     2051     2052     2053     2054     2055     2056 
## 114.3634 143.9033 120.6637 124.2922 115.3306 123.7193 121.3606 119.6882 
##     2057     2058     2059     2060     2061     2062     2063     2064 
## 128.7003 131.8805 115.8667 131.6532 139.2069 121.8349 133.3445 122.6777 
##     2065     2066     2067     2068     2069     2070     2071     2072 
## 125.3296 115.7844 120.8120 120.0066 121.7592 127.2646 116.2413 132.0430 
##     2073     2074     2075     2076     2077     2078     2079     2080 
## 119.2000 128.3414 118.2645 126.1936 137.9122 116.9811 129.8466 123.9753 
##     2081     2082     2083     2084     2085     2086     2087     2088 
## 127.2005 111.4587 114.0768 123.0530 117.4309 116.5815 114.6408 124.8909 
##     2089     2090     2091     2092     2093     2094     2095     2096 
## 112.5453 128.0576 122.8561 128.5196 122.1921 124.3206 137.0772 128.2229 
##     2097     2098     2099     2100     2101     2102     2103     2104 
## 129.7715 115.3198 137.4406 123.9433 125.6386 118.4449 134.0708 117.1544 
##     2105     2106     2107     2108     2109     2110     2111     2112 
## 130.5425 128.3324 142.0850 124.3489 122.3650 127.7915 130.1080 124.8265 
##     2113     2114     2115     2116     2117     2118     2119     2120 
## 136.6646 127.3554 122.8585 147.4909 133.9273 122.2769 121.3768 116.4081 
##     2121     2122     2123     2124     2125     2126     2127     2128 
## 127.9770 130.8960 127.6744 134.0890 118.1288 123.7647 124.9201 127.0343 
##     2129     2130     2131     2132     2133     2134     2135     2136 
## 131.8398 121.8570 118.9042 127.9191 118.1880 123.3191 140.2537 116.7614 
##     2137     2138     2139     2140     2141     2142     2143     2144 
## 136.5060 127.4708 117.9598 132.9678 122.5961 130.7721 127.1354 120.0444 
##     2145     2146     2147     2148     2149     2150     2151     2152 
## 137.7346 128.4078 127.2366 115.1641 119.4034 116.0861 122.5693 125.0094 
##     2153     2154     2155     2156     2157     2158     2159     2160 
## 121.4473 130.5583 139.4226 136.1220 117.6349 119.3010 120.3382 124.4801 
##     2161     2162     2163     2164     2165     2166     2167     2168 
## 126.1823 121.7723 132.0542 120.8642 139.4525 118.0596 122.8742 118.7736 
##     2169     2170     2171     2172     2173     2174     2175     2176 
## 129.4109 129.4889 143.6263 134.8279 135.0999 122.8805 134.2894 125.1004 
##     2177     2178     2179     2180     2181     2182     2183     2184 
## 134.7290 131.6460 127.7267 124.0412 122.4246 118.9766 120.2810 129.8741 
##     2185     2186     2187     2188     2189     2190     2191     2192 
## 123.7897 132.5229 118.1275 130.3052 135.6051 123.2571 127.4244 121.3776 
##     2193     2194     2195     2196     2197     2198     2199     2200 
## 118.7010 141.0493 140.9559 144.2080 115.0895 126.0803 127.4941 132.6615 
##     2201     2202     2203     2204     2205     2206     2207     2208 
## 122.2561 128.9272 134.3818 120.4441 117.2357 116.8390 135.2058 124.4475 
##     2209     2210     2211     2212     2213     2214     2215     2216 
## 119.3984 124.5697 125.5504 140.9573 136.5759 139.0053 139.7481 120.9936 
##     2217     2218     2219     2220     2221     2222     2223     2224 
## 139.2055 122.3468 132.8423 114.1991 127.2122 125.3362 128.8967 122.6115 
##     2225     2226     2227     2228     2229     2230     2231     2232 
## 124.4663 130.4125 133.5311 133.3318 119.6879 138.6646 121.8264 141.0902 
##     2233     2234     2235     2236     2237     2238     2239     2240 
## 122.3992 125.7679 141.4799 124.5923 142.5193 121.8634 129.2471 119.8453 
##     2241     2242     2243     2244     2245     2246     2247     2248 
## 126.5526 123.6814 131.0703 142.0614 127.0009 126.4775 118.9886 140.2173 
##     2249     2250     2251     2252     2253     2254     2255     2256 
## 115.5515 116.1556 119.7700 134.7226 123.6533 131.4010 136.0363 125.2207 
##     2257     2258     2259     2260     2261     2262     2263     2264 
## 118.4880 126.8157 126.4454 155.5428 120.1701 127.6435 118.1418 121.6846 
##     2265     2266     2267     2268     2269     2270     2271     2272 
## 121.5048 143.0063 138.6494 127.7908 126.6671 119.9693 130.6835 121.0689 
##     2273     2274     2275     2276     2277     2278     2279     2280 
## 123.5527 127.4774 124.1098 121.1368 130.9088 119.4324 128.3060 118.5123 
##     2281     2282     2283     2284     2285     2286     2287     2288 
## 122.8011 124.6499 132.4249 138.0134 120.9468 128.2863 120.7226 135.9239 
##     2289     2290     2291     2292     2293     2294     2295     2296 
## 125.0513 117.6852 136.3944 122.7807 136.2267 129.6996 120.7276 122.1051 
##     2297     2298     2299     2300     2301     2302     2303     2304 
## 135.3596 142.4816 134.4716 135.9821 130.6274 132.4226 120.3936 136.6665 
##     2305     2306 
## 139.7150 132.6837
# Print the ANOVA table of the model
anova(lm_rural)
## Analysis of Variance Table
## 
## Response: sbp
##             Df     Sum Sq   Mean Sq  F value    Pr(>F)    
## age          1  410870815 410870815 298.4807 < 2.2e-16 ***
## male         1   27086789  27086789  19.6774   9.6e-06 ***
## bmi          1  180890810 180890810 131.4097 < 2.2e-16 ***
## dm           1    5258476   5258476   3.8201  0.050763 .  
## smk          1   13587439  13587439   9.8707  0.001701 ** 
## tc           1    9729862   9729862   7.0683  0.007900 ** 
## age:smk      1   12941661  12941661   9.4016  0.002193 ** 
## Residuals 2298 3163290623   1376541                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Print the diagnostic plots of the model
par(mfrow=c(2,2))
plot(lm_rural)

# Fit a linear regression model for predicting sbp for hypertensive population-adjusted for clusturing using survey weights

# Fit a linear regression model for predicting sbp for hypertensive population
lm_hypertensive <- lm(sbp~age+male+bmi+dm+smk+tc+age*smk, data = hypertensive_data, weights = weights)
# Print the summary of the model
summary(lm_hypertensive)
## 
## Call:
## lm(formula = sbp ~ age + male + bmi + dm + smk + tc + age * smk, 
##     data = hypertensive_data, weights = weights)
## 
## Weighted Residuals:
##     Min      1Q  Median      3Q     Max 
## -4809.4  -536.3  -146.2   389.8  7011.0 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 121.85033    3.14893  38.696   <2e-16 ***
## age           0.49559    0.03985  12.435   <2e-16 ***
## male          2.67279    1.05659   2.530   0.0115 *  
## bmi           0.12924    0.09926   1.302   0.1932    
## dm           -0.18557    2.28633  -0.081   0.9353    
## smk          -0.54307    4.90548  -0.111   0.9119    
## tc            0.21219    0.50876   0.417   0.6767    
## age:smk      -0.05863    0.11330  -0.517   0.6049    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1033 on 1287 degrees of freedom
## Multiple R-squared:  0.1338, Adjusted R-squared:  0.1291 
## F-statistic:  28.4 on 7 and 1287 DF,  p-value: < 2.2e-16
# Print the coefficients of the model
coef(lm_hypertensive)
##  (Intercept)          age         male          bmi           dm          smk 
## 121.85032558   0.49559047   2.67279090   0.12923508  -0.18557206  -0.54307377 
##           tc      age:smk 
##   0.21219045  -0.05863273

11 Model diagnostics

# Model diagnostics
# Print the residuals of the model
residuals(lm_hypertensive)
##            1            2            3            4            5            6 
##  55.50920368  24.69737819 -17.18824858  71.81579273   9.29719247  -6.38286641 
##            7            8            9           10           11           12 
##  -7.32886599   7.56467182  -9.43223126  22.19035525 -11.40611107   1.30215725 
##           13           14           15           16           17           18 
## -22.30708377  -8.22490015   5.92449351  31.12384605  -3.20168657 -16.17672763 
##           19           20           21           22           23           24 
## -29.46310596  -8.90807871  -4.83101033  18.72553549   4.70971921 -17.02977472 
##           25           26           27           28           29           30 
##  22.92802187   8.37760484 -14.94702880 -16.24141948 -22.24813902   7.06091485 
##           31           32           33           34           35           36 
##  16.06562453 -17.01132080   6.56826555  -9.64473561   0.26775542  -9.26630007 
##           37           38           39           40           41           42 
##  28.42726874  17.63922991   5.20300533 -13.63443868  20.28581333 -12.48906947 
##           43           44           45           46           47           48 
##   9.86821022   7.01621973  -7.04156393 -10.56183081  -6.13218176  28.60933375 
##           49           50           51           52           53           54 
## -22.98572046  53.00425305 -16.60122778   4.71790041 -23.37554196  -1.21186880 
##           55           56           57           58           59           60 
## -16.94816404  -7.29014099 -11.59883345  -5.12749214  22.01793074  10.45828578 
##           61           62           63           64           65           66 
## -10.45487102  -8.20489555   3.81917626  -1.60744098   0.70566847  -9.00572612 
##           67           68           69           70           71           72 
##  -9.33497710  -4.35492109 -17.04987646  -3.70857426  37.31570619  35.98370633 
##           73           74           75           76           77           78 
## -10.29777468 -14.69581653   9.74846540   9.61289468 -24.24968389  52.81403698 
##           79           80           81           82           83           84 
##  38.32383711 -15.40703500 -17.14852660 -14.97252711 -23.59779432   4.21366664 
##           85           86           87           88           89           90 
## -22.86155748   0.49244512 -12.39119341  -8.79952651   1.32426016  12.13006598 
##           91           92           93           94           95           96 
##  -8.80611737  22.36334123  12.05879594  -9.59923219 -20.99215255 -28.51947760 
##           97           98           99          100          101          102 
## -31.72551120   3.02859301  35.75398934  -8.68152115 -13.76926477 -10.90666145 
##          103          104          105          106          107          108 
##   7.72469346 -16.27693943  -4.54692049  -4.38066583  -7.46487622  -1.91073427 
##          109          110          111          112          113          114 
##  -5.10062152 -18.50384311  16.21296043 -19.58490731   9.66055800   6.81066248 
##          115          116          117          118          119          120 
##  -8.98729888 -11.89641228   9.46544480  -5.64698906  -5.17662810  -4.63769460 
##          121          122          123          124          125          126 
##  -3.88009542   2.87058908 -20.47140445 -24.89504652  -3.77243012 -26.20625340 
##          127          128          129          130          131          132 
## -24.26533569  35.92022257  47.43842106  14.12490513  -2.18192522  10.99509059 
##          133          134          135          136          137          138 
##  11.07386914  -8.06138636  -5.76858811  -1.56215065  -2.59674097  -4.50717548 
##          139          140          141          142          143          144 
##   6.35204777   2.03373997  -1.14866900  14.48926640 -12.12227164  10.13288634 
##          145          146          147          148          149          150 
##   2.18062264  -6.87326750 -11.38292373  -6.40697801 -14.59763699 107.28324216 
##          151          152          153          154          155          156 
##   1.62578209 -12.35951430  24.35807298  34.77827509 -16.78657239  24.80700621 
##          157          158          159          160          161          162 
##   5.80706889  10.50890328  35.00490685  45.94803266  -0.37975775  -3.73019148 
##          163          164          165          166          167          168 
##  16.75799306  38.04335440 -12.04828977   4.77088214  26.14491593  -4.12666297 
##          169          170          171          172          173          174 
## -15.34706278   4.02182271  -9.51812408  10.32635074  27.56469616  -6.78709681 
##          175          176          177          178          179          180 
## -14.79806112  16.12222035 -10.50250073  15.54923044   4.14279936 -10.39785398 
##          181          182          183          184          185          186 
##  -6.47614982   2.05883840 -16.55507106 -10.67531033  -5.52041723  56.73042896 
##          187          188          189          190          191          192 
##  -9.06688274 -12.13097846  -0.11340781 -12.47240543   6.37394322  -4.06416677 
##          193          194          195          196          197          198 
##  13.63792972 -17.29150465  -5.22574259   8.63083488  -8.03763452 -19.23264669 
##          199          200          201          202          203          204 
##  -0.60729056 -14.68690336  -8.93765370 -13.84907288  -1.71507415  -5.66959754 
##          205          206          207          208          209          210 
## -17.77466794 -14.30348000   3.10072411  -6.60916500 -26.96624542 -15.84967495 
##          211          212          213          214          215          216 
## -21.96718919  -4.29109683 -13.84822445 -33.72681103  -9.16524661 -18.68843377 
##          217          218          219          220          221          222 
##  15.98297990  -7.74348635  -9.16751039 -11.48353434 -12.86460497  -8.39050114 
##          223          224          225          226          227          228 
##  37.29512186  -1.48875237 -13.62675143  -8.62888959 -31.61705833  38.35713417 
##          229          230          231          232          233          234 
##   1.40913192 -13.78015199  -6.65655465 -10.51490345  -2.40433175  -4.17566296 
##          235          236          237          238          239          240 
## -20.98085989  10.62985152  -7.06693122  10.21624399   0.98824025  -6.67501094 
##          241          242          243          244          245          246 
##  -9.83425806  33.42063001 -24.76381878  -2.23234489  28.00210347  -1.56934382 
##          247          248          249          250          251          252 
##   8.09277517 -19.94534099 -17.03608684  -4.42322472 -13.64531979  -6.42328269 
##          253          254          255          256          257          258 
##  -4.21446212 -11.57531588  -5.68475035 -21.66879200   2.25318334 -12.26186025 
##          259          260          261          262          263          264 
## -18.05452202  32.65464024  -6.99183517  -5.94781625  -1.71329932 -12.36599561 
##          265          266          267          268          269          270 
##   1.57862001 -27.27301062  -6.90747175  -8.33524362  -8.63493199  43.67338466 
##          271          272          273          274          275          276 
##  -7.29720052  34.89451696 -20.47100515 -28.58200921  13.81204070 -17.44591972 
##          277          278          279          280          281          282 
##  -4.88471265  -6.95385574 -15.67452703  32.37091352   2.25894977  -2.24653310 
##          283          284          285          286          287          288 
##   5.78663267  -8.97387478  26.27576125  42.50011703  72.09506764  17.40188842 
##          289          290          291          292          293          294 
## -15.96660918  13.03065013  42.35310249  29.32391800 -18.42717209 -38.43170079 
##          295          296          297          298          299          300 
##   7.87979984 -13.96274341   6.69708662  -9.01002129  74.33995579  -2.17946712 
##          301          302          303          304          305          306 
##   3.40469674  23.99092874 -12.99817796 -12.47201106 -11.70618692  50.75456883 
##          307          308          309          310          311          312 
##  -9.83593651   7.07232923 -10.31611771  -3.57581975  25.92315879 -10.06121517 
##          313          314          315          316          317          318 
##  -5.20056512  -9.83039120  -6.45120994 -14.70356546 -21.17910318  13.39422383 
##          319          320          321          322          323          324 
## -17.54180373  -7.67687890 -26.10672468 -12.26589009  -4.89311669   0.49038636 
##          325          326          327          328          329          330 
##  -4.88203443  -5.18135744   9.77745766  10.42307815  -3.04186347  11.99846566 
##          331          332          333          334          335          336 
##  -2.40760351  -3.06074975 -27.76118217  14.20923922  34.69888219  28.81644100 
##          337          338          339          340          341          342 
##   7.93764157  22.81341089  25.93505260 -14.40529467   1.35087975  -1.05438557 
##          343          344          345          346          347          348 
##  -6.16895989 -10.22769121   7.71661800  -5.76196297  -3.88643149 -12.04831549 
##          349          350          351          352          353          354 
## -21.61998631   0.98941463  -1.22463030   1.98722845  10.72143077   6.59432620 
##          355          356          357          358          359          360 
##  24.06574477  36.12393001  -6.50182273  -0.11735520  -2.03476630  18.92732870 
##          361          362          363          364          365          366 
## -25.21052224 -15.88740130 -16.55791373  -9.60184839 -11.30711432  -9.29215905 
##          367          368          369          370          371          372 
## -19.83027506   0.50717250 -27.05227346   3.16274171   6.90155898  -6.18662930 
##          373          374          375          376          377          378 
##  54.49851890   8.02149094  16.21703987 -17.42373809  24.95211461 -20.36718675 
##          379          380          381          382          383          384 
##  -9.48550038 -21.57687785 -22.93508771  -2.66987775 -11.51367460  10.66469131 
##          385          386          387          388          389          390 
## -17.16907503  -4.82460365 -34.07422748  -3.69475926  36.47727878  -9.69060892 
##          391          392          393          394          395          396 
##  40.48739795 -13.11724504   0.66791740  19.29085900   1.44635604  -1.19322001 
##          397          398          399          400          401          402 
##  -9.96517531  13.13340715  56.12816879 -17.62404254  -4.18380957   5.59723894 
##          403          404          405          406          407          408 
##  -2.23604400 -10.62560340 -20.05203157 -11.10426639 -11.66027001  -1.51171274 
##          409          410          411          412          413          414 
## -19.25325905   0.60850054   8.02060439  -6.49540023   2.10346471 -14.53066704 
##          415          416          417          418          419          420 
## -20.40259889   6.29164371  20.96284785   7.75619127  -5.85991740  -5.39344579 
##          421          422          423          424          425          426 
##   7.84407443 -10.49716125  -1.72228023 -14.51677539  24.13366554  44.75970784 
##          427          428          429          430          431          432 
##  -0.31323831  -1.32071087  -6.73556894   3.65779525  12.81756349  11.78223706 
##          433          434          435          436          437          438 
##   9.64753670  11.76171939 -16.05132322 -15.19684023   1.57849346  14.04168912 
##          439          440          441          442          443          444 
## -18.83190125   7.32603190  -8.92789128  13.46725311  -5.32673505 -12.98235629 
##          445          446          447          448          449          450 
## -16.40567503 -15.52094487   5.46065742  40.99915418 -18.58698703 -14.98245459 
##          451          452          453          454          455          456 
##  59.07124933   5.43937273 -16.90411676  -6.82674266   1.75046473  54.68020019 
##          457          458          459          460          461          462 
##  -8.41208353 -22.60015821   7.35014205  -4.90379251  10.46565918 -13.24751445 
##          463          464          465          466          467          468 
##  -2.84574021  24.07322178  30.56472582 -26.83578360  91.73858301   6.85423400 
##          469          470          471          472          473          474 
##   1.98954445 -11.96880826  12.27094778   8.77672709   9.14627472   2.44404595 
##          475          476          477          478          479          480 
##   1.58634691 -16.61182444  27.68685798  17.66405452   9.10567619   6.81485673 
##          481          482          483          484          485          486 
##  -0.89641016   6.15970825 -17.36331524  -8.20709637   4.39820746 -11.99651729 
##          487          488          489          490          491          492 
##   1.09381363  23.20771559 -12.22215949  19.77890282  -8.03354919   3.90091932 
##          493          494          495          496          497          498 
##  14.93820620  11.87895377   2.24347811  16.48440418 -25.91519388 -12.96746360 
##          499          500          501          502          503          504 
##  13.73490510 -13.52063397  29.90806254   7.67872904 -21.87919151 106.36450281 
##          505          506          507          508          509          510 
## -31.65047106 -17.44663668 -14.59341546 -30.36151419  -2.37956837  -6.50363002 
##          511          512          513          514          515          516 
##  -7.35088433 -18.89703438 -14.31148336 -11.39034822 -12.94614322  -7.37901241 
##          517          518          519          520          521          522 
##  44.54390832 -12.58139009 -25.38390025  -8.53758750  -8.90862860   0.31285562 
##          523          524          525          526          527          528 
##  -1.62084445  16.29536232 -19.26170942  11.99676705   9.33132572   0.05100987 
##          529          530          531          532          533          534 
## -10.90724122 -11.82673563 -10.27906597 -28.58380142   4.49809843   0.78903553 
##          535          536          537          538          539          540 
## -11.50868224  -8.22221103 -18.83807367 -13.28855807  37.73211775 -17.53947959 
##          541          542          543          544          545          546 
## -19.05778637  -7.81056147  -1.98065103 -15.10874021   2.22812148 -20.19061067 
##          547          548          549          550          551          552 
##  -2.48761936 -19.25299079 -24.44224939 -19.06183525  -1.74658515 -19.75795338 
##          553          554          555          556          557          558 
## -11.63994125  -7.11363711  15.37427297   0.69875712  -2.05781769  15.36073994 
##          559          560          561          562          563          564 
## -16.78054984   4.25492240  -6.69870731  26.09665114  22.75048881 -14.90721385 
##          565          566          567          568          569          570 
## -18.44091279  -2.86923011 -16.12786985  -5.91438303   5.85820515 -15.86617098 
##          571          572          573          574          575          576 
##   0.96447178 -15.70589126  -4.66490660  -6.35811158  -5.69086640 -16.37356515 
##          577          578          579          580          581          582 
##  -2.32633336  13.29587831 -11.60798960  42.95224369   9.29613249   1.07956942 
##          583          584          585          586          587          588 
##  30.35579208  -2.39150926 -12.95394764   3.00179988  -5.62823402  23.99512824 
##          589          590          591          592          593          594 
## -15.35459512 -22.71021725 -12.51012747  -1.79848280  41.85104274  -2.31929631 
##          595          596          597          598          599          600 
##  15.60088911  -4.55883189  18.70269276 -12.41746503  -3.35293200   6.62529475 
##          601          602          603          604          605          606 
##   0.25285846 -11.00074072  16.29359928  -0.45966698  -3.94663454  15.66446512 
##          607          608          609          610          611          612 
##  -2.22144924  -7.14171444 -21.32750088 -13.93186653  -8.25994953 -21.88712222 
##          613          614          615          616          617          618 
## -16.45853852   6.63178261 -11.00163729   5.58474232   2.95386969 -10.98217731 
##          619          620          621          622          623          624 
## -15.78576412   2.86972952 -17.29435911 -14.13536263 -19.33825491   5.01469119 
##          625          626          627          628          629          630 
## -11.15937842 -11.50827187  -3.58599749  22.96629320 -23.40430606  13.37905830 
##          631          632          633          634          635          636 
##  -9.74967973  54.94673245  48.33334685  11.61398088  -0.58069477   8.09150933 
##          637          638          639          640          641          642 
## -13.12383081  58.05836065  89.31572039  -5.95165648  -1.98812043  14.79335450 
##          643          644          645          646          647          648 
##  -1.28539656 -26.46982182  -9.70409311 -10.27976222  -7.06048533  -7.82967477 
##          649          650          651          652          653          654 
## -14.77611026  -1.85317450  -4.72325794 -22.56049117  39.10235153   1.56963700 
##          655          656          657          658          659          660 
##  -1.39280734 -27.23798544  11.82206929 -15.66591642  27.23355716 -26.43175342 
##          661          662          663          664          665          666 
##  -4.86007721   6.41028794  34.10338871 -14.14835664   7.72700440  34.91980557 
##          667          668          669          670          671          672 
##   0.82140608  -8.30086304  25.73983404  -7.68803331  -6.61455889   4.10366674 
##          673          674          675          676          677          678 
##   5.38058853  -8.84881688  15.82999312   8.31014599  16.12567272 -22.43531076 
##          679          680          681          682          683          684 
##   0.98820572 -20.01896207   9.10187173 -16.97567646  27.48866464  56.29028163 
##          685          686          687          688          689          690 
##  17.07896471 -17.25080424  41.10722361   7.11794676 -20.75428670   1.13291859 
##          691          692          693          694          695          696 
##  11.12262685 -15.09434777  -3.66192766  -1.53763405   7.49882374  -6.74345034 
##          697          698          699          700          701          702 
##  -0.46138862 -14.73096394  -7.86690355  21.01240044 -10.31693869  26.99769787 
##          703          704          705          706          707          708 
##  25.90520072  -1.58914815 -12.09617916  56.82484079  14.39272645  -5.02753628 
##          709          710          711          712          713          714 
## -15.79573261   2.20197300   5.36078705   6.47015324  76.01289297   6.28286778 
##          715          716          717          718          719          720 
##  20.42426213  80.98285411 -33.32189587  55.43496525  -4.64939655   5.05340779 
##          721          722          723          724          725          726 
##  -4.59045837 -14.75812163   8.65088618  33.04618558  -1.82353512  -1.82008425 
##          727          728          729          730          731          732 
##   0.37087311  -9.85838413  37.97735582   3.73512605  21.82149010 -13.22978774 
##          733          734          735          736          737          738 
##  -0.26125150  -1.33959718   5.76959569   8.00943839   7.57929321  -7.71499757 
##          739          740          741          742          743          744 
##   6.38120365 -16.48182523 -21.19171116  -0.11538328 -14.49462967 -15.53446360 
##          745          746          747          748          749          750 
##  -5.11743264 -18.71257458  -3.03966713 -14.06636814  -9.80251509 -19.00942203 
##          751          752          753          754          755          756 
##  -1.39114137  -6.37916839 -13.31646303 -17.37419479  12.94187935  19.96020896 
##          757          758          759          760          761          762 
## -11.63351959  -3.31240369  10.54019247  -7.80659868  -9.26504190  -4.80750947 
##          763          764          765          766          767          768 
##  10.53237607 -13.57889711  -9.62580193 -17.85293217  52.91866213  -3.04627988 
##          769          770          771          772          773          774 
##  23.59052455 -26.60080016  22.55829892 -13.75421458 -17.45120993 -31.44551334 
##          775          776          777          778          779          780 
##  -0.35654550   1.53812916  -1.03563732 -13.33126976   2.24733527  63.74716762 
##          781          782          783          784          785          786 
##   3.24584585   5.11256680 -12.71126493 -12.38393649  -0.76150666  -8.26032349 
##          787          788          789          790          791          792 
## -12.11510288  -5.54263247 -18.58162017   6.01454260 -12.20061623 -14.43191408 
##          793          794          795          796          797          798 
## -30.06494739 -25.81263380 -12.03081318 -10.93606472 -21.19897925  -9.51864760 
##          799          800          801          802          803          804 
## -35.33617028  -3.16781248 -20.63760120 -25.17209465 -14.31962750   5.10263880 
##          805          806          807          808          809          810 
##  -8.93701385 -24.33965749 -19.98360663  12.89950811  38.67912588   5.24633046 
##          811          812          813          814          815          816 
##   4.69015996  -8.56517252  -3.19599785 -16.58368778   1.33375661   4.30683094 
##          817          818          819          820          821          822 
##  -5.59208040   4.08456223  13.73156268  -7.57942854   0.84598322   8.73321018 
##          823          824          825          826          827          828 
##  -7.45358176 -12.63430558  44.61608788 -13.36346293 -16.25438798 -26.44849261 
##          829          830          831          832          833          834 
## -13.70281535  -2.38551495  36.89521600  11.21943931   1.20502382  -2.90208551 
##          835          836          837          838          839          840 
##  10.27584412 -17.90784586   6.03429311  -2.21928080 -10.61316271  16.89457745 
##          841          842          843          844          845          846 
##  -4.51618480  11.99442619   1.97109924  -1.01282482  -5.57666000 -17.04962167 
##          847          848          849          850          851          852 
##  -6.69267514 -12.96372889  10.09912387   1.98440242 -18.10830664  -3.24144901 
##          853          854          855          856          857          858 
##   1.32350837 -12.82248461  -4.63935258  -9.65380757  -3.04879856 -11.62385382 
##          859          860          861          862          863          864 
##  59.43009125 -27.84421526  -7.28412623   4.45015929  -1.23864026  -2.87623874 
##          865          866          867          868          869          870 
##  -7.62772508 -10.67092498  -7.74258538  13.15860225  -7.23499700   4.84518125 
##          871          872          873          874          875          876 
## -11.85441668 -14.58975033  -2.86825437  -3.13846054  24.42832840  31.49705958 
##          877          878          879          880          881          882 
##   3.16755453  11.95902138   4.98363645  -8.84596504  -8.46789755  10.70355786 
##          883          884          885          886          887          888 
##   4.52976286  -6.17108708  27.49685987 -18.34495868   3.38978625   2.56020107 
##          889          890          891          892          893          894 
## -25.17337034   0.19667921 -20.41732901  -8.17533295 -26.12507568  -7.57510905 
##          895          896          897          898          899          900 
##  31.53969964 -14.53117273 -12.94589666 -20.83612647   6.90453395  -0.96993121 
##          901          902          903          904          905          906 
## -13.59891617   6.32458057  22.78142938 -10.41934129  95.21962061  26.97788016 
##          907          908          909          910          911          912 
## -16.79727123  -3.29264163   3.99663783  19.27490005 -14.32134635   7.55620331 
##          913          914          915          916          917          918 
## -17.02738278  22.40185777  35.17354490  -5.11058193 -17.30428828  34.19238484 
##          919          920          921          922          923          924 
##   1.78381794  -4.25207590  -2.67484182   6.01279875  35.33107585 -20.51887653 
##          925          926          927          928          929          930 
## -15.20631315 -16.85061407 -10.91801485   7.75710259 -22.74977251 -21.92400390 
##          931          932          933          934          935          936 
##  18.67490011 -10.57931023  -9.14503853   6.81557326  22.10202804  -8.92141295 
##          937          938          939          940          941          942 
## -15.48951633  -8.67027082  23.35284263  -5.49941399  -7.40280404 -14.70199216 
##          943          944          945          946          947          948 
##   4.17917601  13.97383198 -27.82635140 -17.37104952 -13.15142726   4.71745877 
##          949          950          951          952          953          954 
##  35.50829070  -4.25767934  -9.32344862   3.07267938 -17.54196134 -21.59852396 
##          955          956          957          958          959          960 
##  -8.11472737   8.77569264 -14.23315782 -18.00257578  -7.95541012  -5.66923388 
##          961          962          963          964          965          966 
##   7.93481332  -5.26101359 -17.17082056  24.10896926  -9.00571832  -0.22423107 
##          967          968          969          970          971          972 
##   9.93590552  15.68871253 -11.90518024 -14.63364898 -21.49447167 -20.17492091 
##          973          974          975          976          977          978 
##  -5.43606585 -10.15573932  -5.42145448  -2.81614981  -3.44062150 -13.33582560 
##          979          980          981          982          983          984 
##  -2.23869224   1.22961920 -13.59144237  -7.02063905 -21.49517174   9.35505513 
##          985          986          987          988          989          990 
##  42.69183514  13.90123392   1.27396188  51.73563738 -12.54622533  20.38412449 
##          991          992          993          994          995          996 
##   7.95302373 -18.62214119 -10.47495004 -13.01537714  15.05379956 -20.25641787 
##          997          998          999         1000         1001         1002 
## -31.00200942 -14.56054997  -4.29309975  -9.11116307 -21.43666828  -3.16322959 
##         1003         1004         1005         1006         1007         1008 
##  -2.40983870  25.96315400 -14.67450332  -9.45243591   7.79678775 -22.94622294 
##         1009         1010         1011         1012         1013         1014 
##  15.78289547   4.06307011 -11.81894395   8.05906017   9.68874166  -9.23408155 
##         1015         1016         1017         1018         1019         1020 
##  -0.48996539  10.88102088  60.05821719  17.60245815  15.93554469   0.48448921 
##         1021         1022         1023         1024         1025         1026 
## -15.87572445 -14.63577914  18.77139677 -15.74938772  15.98946011  37.06649536 
##         1027         1028         1029         1030         1031         1032 
## -11.12650466   7.57528813 -14.70998282 -16.51927185   2.01673751  -7.50552181 
##         1033         1034         1035         1036         1037         1038 
##  14.99499743  -8.22159933  -1.32391552  26.88933467  10.28830983  -2.52005864 
##         1039         1040         1041         1042         1043         1044 
##   8.70873528  -2.29059714 -11.81921479  12.31049659 -13.88782815 -10.02982946 
##         1045         1046         1047         1048         1049         1050 
##  20.85483654  -3.02652703 -18.16216319  30.07424988  26.36380246  -5.58266448 
##         1051         1052         1053         1054         1055         1056 
##  -1.76612434  -2.39099203  -1.87960740  21.46013577  -5.63833342  11.23192044 
##         1057         1058         1059         1060         1061         1062 
## -20.36012545 -13.27891482   6.31526173  -1.88898107   9.48389595  45.96375945 
##         1063         1064         1065         1066         1067         1068 
##  35.10114626 -14.97356854  -6.32491443 -18.66153061 -11.05860855 -16.20572539 
##         1069         1070         1071         1072         1073         1074 
##  17.88566822  -0.62763231 -14.00497050 -12.77067621 -25.45778204  -0.76129052 
##         1075         1076         1077         1078         1079         1080 
##  -3.47210866  31.33992410   0.26062901 -14.25745647  72.58214556   0.80895691 
##         1081         1082         1083         1084         1085         1086 
##   1.56316592  11.33081561  -8.62249171  30.62966023  -4.50824217 -12.22556571 
##         1087         1088         1089         1090         1091         1092 
##  19.10489683  29.80155201  -7.13352447 -17.07327064   4.86309466  -5.59218108 
##         1093         1094         1095         1096         1097         1098 
## -22.66082686  -3.20002707  13.26224223   4.48355835  31.21695245  -6.49510518 
##         1099         1100         1101         1102         1103         1104 
## -10.36650073 -11.22877108  -6.53495184  10.86996713  -5.73548698 -17.12207839 
##         1105         1106         1107         1108         1109         1110 
##  -1.70105238   7.84329009 -14.41077778 -10.28446192   8.07686580  14.23650725 
##         1111         1112         1113         1114         1115         1116 
##  84.53280592  14.93210669   1.46596573 -15.80654832 -21.69597021   1.71922921 
##         1117         1118         1119         1120         1121         1122 
##  70.15594753 -25.64520431 -11.83503095  54.35502090  29.50479159  55.41592359 
##         1123         1124         1125         1126         1127         1128 
##  19.16779233 -10.31381862 -16.78988632 -13.37687714   8.36447343 -10.80785997 
##         1129         1130         1131         1132         1133         1134 
## -16.48113156  17.39069476  12.90310228  -5.67099266  15.19775974  -8.55299077 
##         1135         1136         1137         1138         1139         1140 
## -18.66758834 -15.68742766   9.76075801 -24.13380428  -9.21624968  12.21532565 
##         1141         1142         1143         1144         1145         1146 
## -13.02286419  -6.53841296  10.64224410 -17.12059817   9.06997341  19.28390523 
##         1147         1148         1149         1150         1151         1152 
##   8.33115097  26.77012462  -7.69342796   8.06375224  18.20695742  28.07613675 
##         1153         1154         1155         1156         1157         1158 
##  22.54599584   6.12159613  43.93210980  -4.04199109 -13.01017178  18.14544392 
##         1159         1160         1161         1162         1163         1164 
##  -3.34493138  41.51535980 -10.85810459 -10.25507806 -19.04466995  12.30129755 
##         1165         1166         1167         1168         1169         1170 
## -13.61560507  -8.42171909   3.96438445  14.09371246  -6.29163551   3.08487334 
##         1171         1172         1173         1174         1175         1176 
## -11.14470961   1.78928929 -10.30300425 -19.88553200 -22.80874629 -25.13481550 
##         1177         1178         1179         1180         1181         1182 
##  -9.47607262  15.88758863 -14.00910464   2.34478266  16.18289326  -5.35128206 
##         1183         1184         1185         1186         1187         1188 
##  -8.73601471  10.19807026  -4.01164524 -16.03752389  10.81733193 -13.08531140 
##         1189         1190         1191         1192         1193         1194 
## -14.87672222  11.09506527   4.18515893   6.29741767  -0.12386456  -6.36115976 
##         1195         1196         1197         1198         1199         1200 
## -21.88260970 -10.57723699   4.62453022 -14.30305679 -25.96399767   8.43415262 
##         1201         1202         1203         1204         1205         1206 
##  -2.32085261 -11.33949973  -0.09326921  13.23622169 -18.01304130   6.78028501 
##         1207         1208         1209         1210         1211         1212 
##  17.64667148  -1.48991690  -6.72043429  13.49006472  -0.26055887  -2.01218911 
##         1213         1214         1215         1216         1217         1218 
## -16.48304679  10.17838506  46.43564704  -6.36767144  -2.30425730  -8.42487446 
##         1219         1220         1221         1222         1223         1224 
##  -1.01765088  -6.71605256 -20.15598726  10.26681524  -8.02297791  31.95670378 
##         1225         1226         1227         1228         1229         1230 
##  28.18370505  21.74521951   0.13682639  -9.24000593   1.30799055  -1.01590726 
##         1231         1232         1233         1234         1235         1236 
##   0.87340129  -0.78002538  -0.37296499 -12.80999851 -10.12366542  57.30913475 
##         1237         1238         1239         1240         1241         1242 
##  26.89947683  -3.75409785   5.65575857 -12.15943672 -10.80797168  -2.81956624 
##         1243         1244         1245         1246         1247         1248 
##  -9.21451082 -11.08404799   7.57365791  -0.28999457 -12.62783236  21.37572432 
##         1249         1250         1251         1252         1253         1254 
##  -3.20190777   4.07079202  65.03203324  -1.77729823  -6.09075347 -10.17750500 
##         1255         1256         1257         1258         1259         1260 
##  -0.77148791  45.54798446   5.70281176  -0.42162639  26.83349429  -7.87347897 
##         1261         1262         1263         1264         1265         1266 
##  -0.87037825 -19.06486837  12.47825507   2.41089392  16.87555936   1.74779259 
##         1267         1268         1269         1270         1271         1272 
##  -8.13987641  21.16333642  -1.59438452  29.53750719  -1.02867892  -6.29323324 
##         1273         1274         1275         1276         1277         1278 
##  -4.48299044 -12.75376479  -8.55928981   3.24152804 -10.00143038  -1.67825857 
##         1279         1280         1281         1282         1283         1284 
## -17.43255418  22.27752164  10.07798192  -9.46426039  39.83014740  41.13762307 
##         1285         1286         1287         1288         1289         1290 
##   9.10935277  11.18464452 -13.08791541   4.50064136 -11.90846331  18.04164594 
##         1291         1292         1293         1294         1295 
##  -7.93909808 -13.25729789  14.59281273  24.23818903 -13.98417875
# Print the fitted values of the model
fitted(lm_hypertensive)
##        1        2        3        4        5        6        7        8 
## 157.4908 150.3026 148.1882 147.1842 138.7028 139.3829 140.3289 144.4353 
##        9       10       11       12       13       14       15       16 
## 143.4322 156.8096 134.4061 142.6978 144.3071 159.2249 134.0755 139.8762 
##       17       18       19       20       21       22       23       24 
## 145.2017 149.1767 149.4631 150.9081 139.8310 138.2745 156.2903 157.0298 
##       25       26       27       28       29       30       31       32 
## 145.0720 161.6224 144.9470 143.2414 152.2481 148.9391 158.9344 145.0113 
##       33       34       35       36       37       38       39       40 
## 140.4317 155.6447 158.7322 137.2663 136.5727 158.3608 147.7970 157.6344 
##       41       42       43       44       45       46       47       48 
## 135.7142 155.4891 141.1318 139.9838 158.0416 151.5618 136.1322 140.3907 
##       49       50       51       52       53       54       55       56 
## 143.9857 138.9957 147.6012 142.2821 148.3755 148.2119 143.9482 152.2901 
##       57       58       59       60       61       62       63       64 
## 157.5988 142.1275 145.9821 154.5417 151.4549 150.2049 151.1808 153.6074 
##       65       66       67       68       69       70       71       72 
## 157.2943 136.0057 147.3350 145.3549 148.0499 142.7086 155.6843 146.0163 
##       73       74       75       76       77       78       79       80 
## 140.2978 157.6958 140.2515 137.3871 156.2497 151.1860 147.6762 142.4070 
##       81       82       83       84       85       86       87       88 
## 148.1485 141.9725 146.5978 138.7863 148.8616 150.5076 136.3912 141.7995 
##       89       90       91       92       93       94       95       96 
## 137.6757 149.8699 144.8061 147.6367 158.9412 144.5992 146.9922 156.5195 
##       97       98       99      100      101      102      103      104 
## 155.7255 138.9714 144.2460 148.6815 142.7693 143.9067 144.2753 160.2769 
##      105      106      107      108      109      110      111      112 
## 144.5469 143.3807 158.4649 135.9107 146.1006 149.5038 147.7870 138.5849 
##      113      114      115      116      117      118      119      120 
## 159.3394 147.1893 150.9873 160.8964 145.5346 151.6470 143.1766 150.6377 
##      121      122      123      124      125      126      127      128 
## 152.8801 148.1294 145.4714 157.8950 141.7724 147.2063 151.2653 142.0798 
##      129      130      131      132      133      134      135      136 
## 153.5616 159.8751 156.1819 149.0049 150.9261 150.0614 143.7686 142.5622 
##      137      138      139      140      141      142      143      144 
## 148.5967 149.5072 155.6480 147.9663 149.1487 154.5107 143.1223 136.8671 
##      145      146      147      148      149      150      151      152 
## 143.8194 148.8733 143.3829 154.4070 152.5976 150.7168 159.3742 150.3595 
##      153      154      155      156      157      158      159      160 
## 147.6419 152.2217 155.7866 153.1930 151.1929 139.4911 148.9951 158.0520 
##      161      162      163      164      165      166      167      168 
## 144.3798 159.7302 139.2420 146.9566 151.0483 138.2291 159.8551 158.1267 
##      169      170      171      172      173      174      175      176 
## 156.3471 137.9782 151.5181 158.6736 140.4353 151.7871 153.7981 148.8778 
##      177      178      179      180      181      182      183      184 
## 148.5025 157.4508 149.8572 160.3979 137.4761 156.9412 159.5551 137.6753 
##      185      186      187      188      189      190      191      192 
## 137.5204 152.2696 141.0669 145.1310 151.1134 157.4724 137.6261 147.0642 
##      193      194      195      196      197      198      199      200 
## 137.3621 145.2915 139.2257 145.3692 148.0376 140.2326 144.6073 153.6869 
##      201      202      203      204      205      206      207      208 
## 145.9377 155.8491 142.7151 153.6696 137.7747 145.3035 138.8993 141.6092 
##      209      210      211      212      213      214      215      216 
## 148.9662 156.8497 144.9672 139.2911 144.8482 149.7268 144.1652 140.6884 
##      217      218      219      220      221      222      223      224 
## 151.0170 144.7435 157.1675 138.4835 147.8646 158.3905 145.7049 154.4888 
##      225      226      227      228      229      230      231      232 
## 151.6268 152.6289 148.6171 145.6429 140.5909 150.7802 152.6566 152.5149 
##      233      234      235      236      237      238      239      240 
## 159.4043 142.1757 154.9809 156.3701 156.0669 147.7838 140.0118 151.6750 
##      241      242      243      244      245      246      247      248 
## 138.8343 160.5794 157.7638 143.2323 150.9979 141.5693 148.9072 146.9453 
##      249      250      251      252      253      254      255      256 
## 158.0361 154.4232 150.6453 148.4233 145.2145 160.5753 147.6848 149.6688 
##      257      258      259      260      261      262      263      264 
## 157.7468 140.2619 158.0545 140.3454 139.9918 147.9478 147.7133 141.3660 
##      265      266      267      268      269      270      271      272 
## 157.4214 150.2730 148.9075 141.3352 150.6349 156.3266 160.2972 138.1055 
##      273      274      275      276      277      278      279      280 
## 146.4710 148.5820 143.1880 161.4459 137.8847 159.9539 154.6745 157.6291 
##      281      282      283      284      285      286      287      288 
## 154.7411 138.2465 147.2134 151.9739 148.7242 151.4999 155.9049 148.5981 
##      289      290      291      292      293      294      295      296 
## 142.9666 145.9693 161.6469 155.6761 158.4272 159.4317 147.1202 143.9627 
##      297      298      299      300      301      302      303      304 
## 146.3029 157.0100 158.6600 155.1795 152.5953 145.0091 153.9982 156.4720 
##      305      306      307      308      309      310      311      312 
## 157.7062 159.2454 157.8359 152.9277 152.3161 157.5758 156.0768 145.0612 
##      313      314      315      316      317      318      319      320 
## 159.2006 152.8304 139.4512 152.7036 154.1791 148.6058 142.5418 145.6769 
##      321      322      323      324      325      326      327      328 
## 149.1067 137.2659 152.8931 139.5096 139.8820 153.1814 147.2225 151.5769 
##      329      330      331      332      333      334      335      336 
## 144.0419 143.0015 141.4076 145.0607 147.7612 150.7908 140.3011 157.1836 
##      337      338      339      340      341      342      343      344 
## 136.0624 155.1866 160.0649 153.4053 158.6491 145.0544 152.1690 141.2277 
##      345      346      347      348      349      350      351      352 
## 138.2834 146.7620 150.8864 137.0483 153.6200 144.0106 144.2246 138.0128 
##      353      354      355      356      357      358      359      360 
## 142.2786 151.4057 151.9343 144.8761 145.5018 146.1174 142.0348 145.0727 
##      361      362      363      364      365      366      367      368 
## 141.2105 138.8874 142.5579 149.6018 135.3071 143.2922 159.8303 140.4928 
##      369      370      371      372      373      374      375      376 
## 158.0523 155.8373 137.0984 149.1866 141.5015 160.9785 158.7830 149.4237 
##      377      378      379      380      381      382      383      384 
## 143.0479 146.3672 143.4855 152.5769 150.9351 157.6699 156.5137 159.3353 
##      385      386      387      388      389      390      391      392 
## 144.1691 159.8246 145.0742 149.6948 154.5227 144.6906 141.5126 148.1172 
##      393      394      395      396      397      398      399      400 
## 146.3321 159.7091 147.5536 146.1932 147.9652 151.8666 139.8718 140.6240 
##      401      402      403      404      405      406      407      408 
## 148.1838 143.4028 154.2360 143.6256 146.0520 141.1043 153.6603 151.5117 
##      409      410      411      412      413      414      415      416 
## 146.2533 148.3915 145.9794 151.4954 138.8965 136.5307 152.4026 146.7084 
##      417      418      419      420      421      422      423      424 
## 149.0372 139.2438 149.8599 148.3934 151.1559 145.4972 151.7223 150.5168 
##      425      426      427      428      429      430      431      432 
## 144.8663 155.2403 142.3132 142.3207 156.7356 146.3422 159.1824 155.2178 
##      433      434      435      436      437      438      439      440 
## 143.3525 155.2383 147.0513 156.1968 142.4215 150.9583 148.8319 143.6740 
##      441      442      443      444      445      446      447      448 
## 155.9279 148.5327 151.3267 148.9824 143.4057 150.5209 141.5393 157.0008 
##      449      450      451      452      453      454      455      456 
## 145.5870 144.9825 148.9288 156.5606 148.9041 137.8267 145.2495 151.3198 
##      457      458      459      460      461      462      463      464 
## 140.4121 149.6002 147.6499 150.9038 148.5343 139.2475 152.8457 145.9268 
##      465      466      467      468      469      470      471      472 
## 150.4353 144.8358 157.2614 139.1458 135.0105 140.9688 142.7291 139.2233 
##      473      474      475      476      477      478      479      480 
## 138.8537 134.5560 144.4137 145.6118 142.3131 141.3359 153.8943 145.1851 
##      481      482      483      484      485      486      487      488 
## 140.8964 140.8403 141.3633 137.2071 158.6018 144.9965 157.9062 142.7923 
##      489      490      491      492      493      494      495      496 
## 137.2222 147.2211 150.0335 140.0991 139.0618 145.1210 136.7565 140.5156 
##      497      498      499      500      501      502      503      504 
## 151.9152 156.9675 163.2651 159.5206 137.0919 157.3213 157.8792 157.6355 
##      505      506      507      508      509      510      511      512 
## 160.6505 153.4466 163.5934 155.3615 157.3796 153.5036 148.3509 157.8970 
##      513      514      515      516      517      518      519      520 
## 151.3115 138.3903 153.9461 140.3790 153.4561 140.5814 154.3839 146.5376 
##      521      522      523      524      525      526      527      528 
## 146.9086 137.6871 141.6208 141.7046 149.2617 156.0032 152.6687 140.9490 
##      529      530      531      532      533      534      535      536 
## 153.9072 154.8267 148.2791 144.5838 138.5019 159.2110 144.5087 151.2222 
##      537      538      539      540      541      542      543      544 
## 144.8381 138.2886 156.2679 153.5395 147.0578 147.8106 134.9807 138.1087 
##      545      546      547      548      549      550      551      552 
## 142.7719 135.1906 149.4876 138.2530 148.4422 155.0618 154.7466 147.7580 
##      553      554      555      556      557      558      559      560 
## 137.6399 154.1136 150.6257 143.3012 142.0578 141.6393 146.7805 159.7451 
##      561      562      563      564      565      566      567      568 
## 138.6987 153.9033 156.2495 145.9072 143.4409 142.8692 142.1279 144.9144 
##      569      570      571      572      573      574      575      576 
## 160.1418 149.8662 137.0355 154.7059 146.6649 139.3581 153.6909 143.3736 
##      577      578      579      580      581      582      583      584 
## 147.3263 149.7041 139.6080 149.0478 137.7039 139.9204 150.6442 154.3915 
##      585      586      587      588      589      590      591      592 
## 155.9539 148.9982 158.6282 150.0049 145.3546 156.7102 136.5101 155.7985 
##      593      594      595      596      597      598      599      600 
## 150.1490 156.3193 155.3991 139.5588 138.2973 139.4175 144.3529 156.3747 
##      601      602      603      604      605      606      607      608 
## 143.7471 147.0007 147.7064 153.4597 148.9466 139.3355 151.2214 154.1417 
##      609      610      611      612      613      614      615      616 
## 145.3275 150.9319 154.2599 150.8871 157.4585 153.3682 136.0016 159.4153 
##      617      618      619      620      621      622      623      624 
## 146.0461 156.9822 160.7858 138.1303 145.2944 159.1354 142.3383 158.9853 
##      625      626      627      628      629      630      631      632 
## 140.1594 149.5083 155.5860 153.0337 155.4043 152.6209 151.7497 141.0533 
##      633      634      635      636      637      638      639      640 
## 148.6667 146.3860 151.5807 158.9085 159.1238 141.9416 144.6843 139.9517 
##      641      642      643      644      645      646      647      648 
## 153.9881 152.2066 142.2854 155.4698 159.7041 143.2798 156.0605 151.8297 
##      649      650      651      652      653      654      655      656 
## 138.7761 151.8532 152.7233 156.5605 158.8976 159.4304 149.3928 154.2380 
##      657      658      659      660      661      662      663      664 
## 151.1779 148.6659 152.7664 157.4318 140.8601 158.5897 157.8966 157.1484 
##      665      666      667      668      669      670      671      672 
## 155.2730 153.0802 142.1786 144.3009 157.2602 140.6880 147.6146 143.8963 
##      673      674      675      676      677      678      679      680 
## 156.6194 151.8488 153.1700 149.6899 158.8743 153.4353 162.0118 141.0190 
##      681      682      683      684      685      686      687      688 
## 149.8981 149.9757 149.5113 142.7097 147.9210 157.2508 140.8928 150.8821 
##      689      690      691      692      693      694      695      696 
## 148.7543 142.8671 145.8774 141.0943 143.6619 137.5376 140.5012 142.7435 
##      697      698      699      700      701      702      703      704 
## 156.4614 155.7310 148.8669 150.9876 152.3169 158.0023 147.0948 153.5891 
##      705      706      707      708      709      710      711      712 
## 144.0962 142.1752 141.6073 149.0275 159.7957 143.7980 150.6392 159.5298 
##      713      714      715      716      717      718      719      720 
## 147.9871 148.7171 152.5757 153.0171 158.3219 152.5650 154.6494 153.9466 
##      721      722      723      724      725      726      727      728 
## 160.5905 151.7581 147.3491 158.9538 142.8235 145.8201 159.6291 155.8584 
##      729      730      731      732      733      734      735      736 
## 145.0226 161.2649 162.1785 148.2298 150.2613 138.3396 145.2304 147.9906 
##      737      738      739      740      741      742      743      744 
## 142.4207 158.7150 142.6188 155.4818 145.1917 143.1154 159.4946 152.5345 
##      745      746      747      748      749      750      751      752 
## 151.1174 151.7126 140.0397 156.0664 142.8025 161.0094 150.3911 152.3792 
##      753      754      755      756      757      758      759      760 
## 151.3165 162.3742 158.0581 152.0398 153.6335 157.3124 152.4598 143.8066 
##      761      762      763      764      765      766      767      768 
## 135.2650 138.8075 144.4676 145.5789 146.6258 158.8529 157.0813 155.0463 
##      769      770      771      772      773      774      775      776 
## 137.4095 161.6008 154.4417 154.7542 134.4512 155.4455 140.3565 154.4619 
##      777      778      779      780      781      782      783      784 
## 160.0356 161.3313 140.7527 155.2528 136.7542 136.8874 158.7113 154.3839 
##      785      786      787      788      789      790      791      792 
## 152.7615 145.2603 143.1151 142.5426 150.5816 137.9855 141.2006 148.4319 
##      793      794      795      796      797      798      799      800 
## 149.0649 146.8126 145.0308 142.9361 154.1990 146.5186 157.3362 151.1678 
##      801      802      803      804      805      806      807      808 
## 144.6376 155.1721 148.3196 142.8974 134.9370 147.3397 144.9836 149.1005 
##      809      810      811      812      813      814      815      816 
## 136.3209 137.7537 147.3098 151.5652 143.1960 135.5837 149.6662 154.6932 
##      817      818      819      820      821      822      823      824 
## 136.5921 153.9154 156.2684 154.5794 141.1540 155.2668 158.4536 142.6343 
##      825      826      827      828      829      830      831      832 
## 158.3839 143.3635 153.2544 142.4485 133.7028 149.3855 160.1048 162.7806 
##      833      834      835      836      837      838      839      840 
## 148.7950 134.9021 142.7242 158.9078 148.9657 143.2193 155.6132 139.1054 
##      841      842      843      844      845      846      847      848 
## 150.5162 145.0056 142.0289 156.0128 152.5767 150.0496 147.6927 154.9637 
##      849      850      851      852      853      854      855      856 
## 136.9009 147.0156 155.1083 154.2414 143.6765 145.8225 142.6394 139.6538 
##      857      858      859      860      861      862      863      864 
## 137.0488 155.6239 151.5699 143.8442 151.2841 150.5498 149.2386 133.8762 
##      865      866      867      868      869      870      871      872 
## 147.6277 144.6709 148.7426 144.8414 152.2350 144.1548 152.8544 148.5898 
##      873      874      875      876      877      878      879      880 
## 136.8683 145.1385 144.5717 142.5029 139.8324 149.0410 139.0164 142.8460 
##      881      882      883      884      885      886      887      888 
## 157.4679 157.2964 148.4702 141.1711 142.5031 159.3450 142.6102 145.4398 
##      889      890      891      892      893      894      895      896 
## 144.1734 150.8033 159.4173 143.1753 148.1251 143.5751 153.4603 149.5312 
##      897      898      899      900      901      902      903      904 
## 142.9459 147.8361 135.0955 140.9699 137.5989 157.6754 153.2186 142.4193 
##      905      906      907      908      909      910      911      912 
## 151.7804 160.0221 146.7973 145.2926 137.0034 137.7251 145.3213 156.4438 
##      913      914      915      916      917      918      919      920 
## 150.0274 145.5981 147.8265 135.1106 146.3043 160.8076 142.2162 144.2521 
##      921      922      923      924      925      926      927      928 
## 144.6748 148.9872 151.6689 153.5189 146.2063 156.8506 142.9180 136.2429 
##      929      930      931      932      933      934      935      936 
## 144.7498 144.9240 138.3251 137.5793 152.1450 136.1844 141.8980 146.9214 
##      937      938      939      940      941      942      943      944 
## 149.4895 138.6703 145.6472 134.4994 142.4028 137.7020 137.8208 144.0262 
##      945      946      947      948      949      950      951      952 
## 147.8264 155.3710 149.1514 146.2825 149.4917 158.2577 152.3234 146.9273 
##      953      954      955      956      957      958      959      960 
## 146.5420 140.5985 137.1147 153.2243 152.2332 148.0026 148.9554 145.6692 
##      961      962      963      964      965      966      967      968 
## 150.0652 141.2610 157.1708 140.8910 147.0057 158.2242 142.0641 151.3113 
##      969      970      971      972      973      974      975      976 
## 148.9052 141.6336 141.4945 148.1749 138.4361 144.1557 149.4215 153.8161 
##      977      978      979      980      981      982      983      984 
## 153.4406 155.3358 154.2387 152.7704 143.5914 149.0206 143.4952 143.6449 
##      985      986      987      988      989      990      991      992 
## 156.3082 143.0988 146.7260 153.2644 143.5462 154.6159 142.0470 138.6221 
##      993      994      995      996      997      998      999     1000 
## 142.4750 155.0154 139.9462 149.2564 155.0020 149.5605 141.2931 148.1112 
##     1001     1002     1003     1004     1005     1006     1007     1008 
## 157.4367 149.1632 146.4098 151.0368 152.6745 137.4524 147.2032 135.9462 
##     1009     1010     1011     1012     1013     1014     1015     1016 
## 140.2171 160.9369 134.8189 140.9409 162.3113 140.2341 137.4900 138.1190 
##     1017     1018     1019     1020     1021     1022     1023     1024 
## 159.9418 158.3975 143.0645 139.5155 153.8757 144.6358 151.2286 137.7494 
##     1025     1026     1027     1028     1029     1030     1031     1032 
## 157.0105 153.9335 146.1265 148.4247 141.7100 137.5193 148.9833 141.5055 
##     1033     1034     1035     1036     1037     1038     1039     1040 
## 160.0050 154.2216 149.3239 151.1107 155.7117 142.5201 140.2913 155.2906 
##     1041     1042     1043     1044     1045     1046     1047     1048 
## 141.8192 136.6895 136.8878 146.0298 145.1452 145.0265 141.1622 142.9258 
##     1049     1050     1051     1052     1053     1054     1055     1056 
## 151.6362 140.5827 141.7661 144.3910 139.8796 146.5399 157.6383 162.7681 
##     1057     1058     1059     1060     1061     1062     1063     1064 
## 158.3601 160.2789 151.6847 142.8890 147.5161 146.0362 144.8989 142.9736 
##     1065     1066     1067     1068     1069     1070     1071     1072 
## 141.3249 152.6615 153.0586 160.2057 142.1143 135.6276 146.0050 159.7707 
##     1073     1074     1075     1076     1077     1078     1079     1080 
## 150.4578 157.7613 134.4721 158.6601 157.7394 138.2575 156.4179 148.1910 
##     1081     1082     1083     1084     1085     1086     1087     1088 
## 139.4368 137.6692 147.6225 149.3703 159.5082 144.2256 138.8951 156.1984 
##     1089     1090     1091     1092     1093     1094     1095     1096 
## 155.1335 147.0733 151.1369 143.5922 145.6608 153.2000 135.7378 147.5164 
##     1097     1098     1099     1100     1101     1102     1103     1104 
## 146.7830 148.4951 156.3665 145.2288 145.5350 137.1300 154.7355 158.1221 
##     1105     1106     1107     1108     1109     1110     1111     1112 
## 144.7011 160.1567 151.4108 134.2845 149.9231 150.7635 149.4672 153.0679 
##     1113     1114     1115     1116     1117     1118     1119     1120 
## 145.5340 149.8065 152.6960 147.2808 143.8441 153.6452 139.8350 147.6450 
##     1121     1122     1123     1124     1125     1126     1127     1128 
## 150.4952 152.5841 154.8322 152.3138 150.7899 141.3769 146.6355 154.8079 
##     1129     1130     1131     1132     1133     1134     1135     1136 
## 158.4811 146.6093 156.0969 140.6710 159.8022 141.5530 143.6676 152.6874 
##     1137     1138     1139     1140     1141     1142     1143     1144 
## 151.2392 150.1338 153.2162 144.7847 158.0229 161.5384 153.3578 144.1206 
##     1145     1146     1147     1148     1149     1150     1151     1152 
## 138.9300 154.7161 149.6688 137.2299 149.6934 143.9362 134.7930 159.9239 
##     1153     1154     1155     1156     1157     1158     1159     1160 
## 151.4540 138.8784 147.0679 148.0420 154.0102 142.8546 144.3449 156.4846 
##     1161     1162     1163     1164     1165     1166     1167     1168 
## 141.8581 151.2551 143.0447 156.6987 137.6156 139.4217 137.0356 146.9063 
##     1169     1170     1171     1172     1173     1174     1175     1176 
## 140.2916 148.9151 146.1447 158.2107 155.3030 159.8855 148.8087 157.1348 
##     1177     1178     1179     1180     1181     1182     1183     1184 
## 152.4761 158.1124 158.0091 148.6552 153.8171 144.3513 140.7360 139.8019 
##     1185     1186     1187     1188     1189     1190     1191     1192 
## 159.0116 154.0375 135.1827 151.0853 143.8767 139.9049 149.8148 151.7026 
##     1193     1194     1195     1196     1197     1198     1199     1200 
## 150.1239 153.3612 147.8826 157.5772 147.3755 155.3031 149.9640 144.5658 
##     1201     1202     1203     1204     1205     1206     1207     1208 
## 136.3209 157.3395 150.0933 157.7638 154.0130 143.2197 137.3533 142.4899 
##     1209     1210     1211     1212     1213     1214     1215     1216 
## 147.7204 139.5099 137.2606 161.0122 157.4830 157.8216 141.5644 143.3677 
##     1217     1218     1219     1220     1221     1222     1223     1224 
## 153.3043 156.4249 155.0177 158.7161 144.1560 138.7332 148.0230 160.0433 
##     1225     1226     1227     1228     1229     1230     1231     1232 
## 157.8163 152.2548 148.8632 143.2400 148.6920 148.0159 159.1266 157.7800 
##     1233     1234     1235     1236     1237     1238     1239     1240 
## 139.3730 153.8100 154.1237 151.6909 146.1005 149.7541 137.3442 159.1594 
##     1241     1242     1243     1244     1245     1246     1247     1248 
## 141.8080 142.8196 154.2145 150.0840 154.4263 145.2900 143.6278 136.6243 
##     1249     1250     1251     1252     1253     1254     1255     1256 
## 154.2019 155.9292 155.9680 144.7773 162.0908 140.1775 150.7715 159.4520 
##     1257     1258     1259     1260     1261     1262     1263     1264 
## 155.2972 140.4216 152.1665 158.8735 159.8704 142.0649 136.5217 138.5891 
##     1265     1266     1267     1268     1269     1270     1271     1272 
## 155.1244 140.2522 144.1399 152.8367 156.5944 154.4625 155.0287 143.2932 
##     1273     1274     1275     1276     1277     1278     1279     1280 
## 140.4830 155.7538 137.5593 146.7585 157.0014 140.6783 146.4326 158.7225 
##     1281     1282     1283     1284     1285     1286     1287     1288 
## 157.9220 156.4643 156.1699 152.8624 135.8906 139.8154 147.0879 142.4994 
##     1289     1290     1291     1292     1293     1294     1295 
## 148.9085 135.9584 144.9391 139.2573 153.4072 150.7618 148.9842
# Print the ANOVA table of the model
anova(lm_hypertensive)
## Analysis of Variance Table
## 
## Response: sbp
##             Df     Sum Sq   Mean Sq  F value  Pr(>F)    
## age          1  200940904 200940904 188.2952 < 2e-16 ***
## male         1    3327698   3327698   3.1183 0.07766 .  
## bmi          1    3280429   3280429   3.0740 0.07979 .  
## dm           1        731       731   0.0007 0.97912    
## smk          1    4124095   4124095   3.8646 0.04953 *  
## tc           1     196968    196968   0.1846 0.66754    
## age:smk      1     285777    285777   0.2678 0.60491    
## Residuals 1287 1373433631   1067159                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Print the diagnostic plots of the model
par(mfrow=c(2,2))
plot(lm_hypertensive)

# Fit a linear regression model for predicting sbp for patients on hypertension treatment

# Fit a linear regression model for predicting sbp for patients on hypertension treatment
lm_htn_treatment <- lm(sbp~age+male+bmi+dm+smk+tc+age*smk, data = htn_treatment_data, weights = weights)
# Print the summary of the model
summary(lm_htn_treatment)
## 
## Call:
## lm(formula = sbp ~ age + male + bmi + dm + smk + tc + age * smk, 
##     data = htn_treatment_data, weights = weights)
## 
## Weighted Residuals:
##     Min      1Q  Median      3Q     Max 
## -1644.7  -670.1  -302.3   293.7  6591.6 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  98.8112    26.8123   3.685 0.000443 ***
## age           0.8332     0.2608   3.195 0.002090 ** 
## male          0.7102     6.7887   0.105 0.916975    
## bmi           0.2665     0.5387   0.495 0.622393    
## dm           20.3132     9.5125   2.135 0.036179 *  
## smk         -44.5203    76.8025  -0.580 0.563970    
## tc            1.8926     3.5514   0.533 0.595759    
## age:smk       0.5867     1.3887   0.422 0.673951    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1270 on 71 degrees of freedom
## Multiple R-squared:  0.2433, Adjusted R-squared:  0.1687 
## F-statistic: 3.262 on 7 and 71 DF,  p-value: 0.004637
# Print the coefficients of the model
coef(lm_htn_treatment)
## (Intercept)         age        male         bmi          dm         smk 
##  98.8111609   0.8332405   0.7102136   0.2664772  20.3131509 -44.5203192 
##          tc     age:smk 
##   1.8926029   0.5867187

12 Fit a linear regression model for predicting sbp for diabetic population

# Fit a linear regression model for predicting sbp for diabetic population
lm_diabetic <- lm(sbp~age+male+bmi+smk+tc+htn+age*smk, data = diabetic_data, weights = weights)
# Print the summary of the model
summary(lm_diabetic)
## 
## Call:
## lm(formula = sbp ~ age + male + bmi + smk + tc + htn + age * 
##     smk, data = diabetic_data, weights = weights)
## 
## Weighted Residuals:
##     Min      1Q  Median      3Q     Max 
## -2731.8  -380.8   -66.6   318.7  3856.2 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  84.8727    11.1392   7.619 3.38e-12 ***
## age           0.4431     0.1692   2.619  0.00979 ** 
## male          0.2563     3.9150   0.065  0.94789    
## bmi           0.7154     0.3039   2.354  0.01997 *  
## smk          -7.4500    16.5305  -0.451  0.65291    
## tc           -0.1330     1.4352  -0.093  0.92632    
## htn          25.3806     3.7437   6.779 3.05e-10 ***
## age:smk       0.1748     0.3532   0.495  0.62146    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 989.4 on 141 degrees of freedom
## Multiple R-squared:  0.4884, Adjusted R-squared:  0.463 
## F-statistic: 19.23 on 7 and 141 DF,  p-value: < 2.2e-16
# Print the coefficients of the model
coef(lm_diabetic)
## (Intercept)         age        male         bmi         smk          tc 
##  84.8726644   0.4430917   0.2563199   0.7153838  -7.4499727  -0.1329507 
##         htn     age:smk 
##  25.3805508   0.1747985

13 Model diagnostics

# Model diagnostics
# Print the residuals of the model
residuals(lm_diabetic)
##             1             2             3             4             5 
##  -6.581864741 -11.792841433  -9.348683643  11.637934338   0.661652304 
##             6             7             8             9            10 
## -25.763900212  -4.791593175  -7.655485886  13.550319070  14.878846709 
##            11            12            13            14            15 
## -29.566085721  -9.161048773 -10.722685137 -22.889764790 -31.647106939 
##            16            17            18            19            20 
##  -3.300930748 -16.513177080 -15.175234009 -18.409713130  -0.101982886 
##            21            22            23            24            25 
##  -4.688032416 -14.857667650  -1.328853721   0.740078745  -1.114109457 
##            26            27            28            29            30 
##  -7.335795862 -23.197020085  -8.137836251   9.260260767   5.790084257 
##            31            32            33            34            35 
##  45.840582273  -2.114029003  -2.948441683 -17.736790336   6.247475047 
##            36            37            38            39            40 
## -13.058885389  32.433539779  -2.459953772   4.371775639   3.371910147 
##            41            42            43            44            45 
##  14.319732192  -7.673623046  -0.029155609   7.076360078  14.051340048 
##            46            47            48            49            50 
##  -5.817716601 -18.741778766 -15.306692859   6.430235024   4.981642058 
##            51            52            53            54            55 
##  27.512730151  -6.581291244  -7.426754468   3.345372814   3.991595526 
##            56            57            58            59            60 
##  -6.198035280   7.188354809  -2.507363271 -20.195913375  41.001335594 
##            61            62            63            64            65 
##  82.907669097   5.427365801   1.890935285   6.941445354  -5.604328899 
##            66            67            68            69            70 
## -17.840695178  -9.954749813 -11.070834045 -12.317653440   9.087849498 
##            71            72            73            74            75 
##   6.837420961  -7.410856293 -24.231424804  10.178993477 -10.465371641 
##            76            77            78            79            80 
##  -7.972554860   6.919903959 -10.928211242 -11.657184337   6.794752292 
##            81            82            83            84            85 
##  15.041433032   4.361927927  -6.794870136  39.528415490  12.032475976 
##            86            87            88            89            90 
##  -2.747851940  14.287889320  -4.780936002  15.426370522   1.459874137 
##            91            92            93            94            95 
## -29.273501388  54.913708914  -5.422278464  15.676849861   4.841967031 
##            96            97            98            99           100 
##  70.144500952 -13.375007228  -8.054177336   4.484175156   4.875802091 
##           101           102           103           104           105 
##  -0.488546253 -16.271673055  52.560638259 -25.800920083 -20.701795339 
##           106           107           108           109           110 
##  -8.181838197 -14.257714380   9.556688433  32.600984779 -18.372451312 
##           111           112           113           114           115 
##  35.150758954  18.349580475  -0.525722913  -3.210733240   3.782259602 
##           116           117           118           119           120 
##   2.738831669  -7.304363384 -10.457221827 -14.945676862   4.308074400 
##           121           122           123           124           125 
##  13.822370564  24.827656519  -6.560050213 -21.462501487  14.750210465 
##           126           127           128           129           130 
## -16.139441618  -9.939759389  12.143245651  -1.092903016  -6.705908580 
##           131           132           133           134           135 
##  19.641184724  -4.793782975  11.020498975  -9.730113757  10.297157995 
##           136           137           138           139           140 
## -12.447378841  -4.070455122  -3.863403465  -0.003253542  -5.384887029 
##           141           142           143           144           145 
##  53.511952732   0.044520163  -2.112332084  15.631818142  -2.492509070 
##           146           147           148           149 
##  14.297888489  16.176596016   7.704264058   0.694931743
# Print the fitted values of the model
fitted(lm_diabetic)
##        1        2        3        4        5        6        7        8 
## 121.5819 145.7928 114.3487 105.3621 107.3383 116.7639 114.7916 153.6555 
##        9       10       11       12       13       14       15       16 
## 125.4497 155.1212 153.5661 158.1610 156.7227 155.8898 152.6471 127.3009 
##       17       18       19       20       21       22       23       24 
## 122.5132 153.1752 125.4097 115.1020 121.6880 113.8577 110.3289 152.2599 
##       25       26       27       28       29       30       31       32 
## 158.1141 131.3358 150.1970 137.1378 115.7397 147.2099 158.1594 126.1140 
##       33       34       35       36       37       38       39       40 
## 115.9484 150.7368 122.7525 161.0589 153.5665 141.4600 155.6282 109.6281 
##       41       42       43       44       45       46       47       48 
## 120.6803 118.6736 125.0292 114.9236 160.9487 129.8177 127.7418 160.3067 
##       49       50       51       52       53       54       55       56 
## 111.5698 127.0184 163.4873 150.5813 119.4268 149.6546 120.0084 156.1980 
##       57       58       59       60       61       62       63       64 
## 159.8116 116.5074 150.1959 156.9987 166.0923 117.5726 125.1091 118.0586 
##       65       66       67       68       69       70       71       72 
## 120.6043 153.8407 142.9547 149.0708 142.3177 117.9122 131.1626 122.4109 
##       73       74       75       76       77       78       79       80 
## 158.2314 120.8210 122.4654 153.9726 131.0801 155.9282 153.6572 160.2052 
##       81       82       83       84       85       86       87       88 
## 151.9586 127.6381 119.7949 158.4716 112.9675 163.7479 122.7121 127.7809 
##       89       90       91       92       93       94       95       96 
## 153.5736 131.5401 154.2735 153.0863 155.4223 140.3232 119.1580 148.8555 
##       97       98       99      100      101      102      103      104 
## 159.3750 150.0542 113.5158 115.1242 131.4885 158.2717 158.4394 122.8009 
##      105      106      107      108      109      110      111      112 
## 159.7018 114.1818 145.2577 154.4433 154.3990 156.3725 149.8492 148.6504 
##      113      114      115      116      117      118      119      120 
## 125.5257 153.2107 150.2177 125.2612 129.3044 132.4572 136.9457 151.6919 
##      121      122      123      124      125      126      127      128 
## 161.1776 153.1723 159.5601 136.4625 115.2498 163.1394 124.9398 123.8568 
##      129      130      131      132      133      134      135      136 
## 128.0929 156.7059 111.3588 159.7938 152.9795 133.7301 117.7028 127.4474 
##      137      138      139      140      141      142      143      144 
## 109.0705 143.8634 134.0033 149.3849 155.4880 149.9555 161.1123 156.3682 
##      145      146      147      148      149 
## 157.4925 114.7021 134.8234 160.2957 132.3051
# Print the ANOVA table of the model
anova(lm_diabetic)
## Analysis of Variance Table
## 
## Response: sbp
##            Df    Sum Sq  Mean Sq F value    Pr(>F)    
## age         1  62467107 62467107 63.8144 4.389e-13 ***
## male        1    628522   628522  0.6421    0.4243    
## bmi         1  21436440 21436440 21.8988 6.673e-06 ***
## smk         1   1020568  1020568  1.0426    0.3090    
## tc          1     22886    22886  0.0234    0.8787    
## htn         1  45960447 45960447 46.9517 2.083e-10 ***
## age:smk     1    239727   239727  0.2449    0.6215    
## Residuals 141 138023136   978887                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Print the diagnostic plots of the model
par(mfrow=c(2,2))
plot(lm_diabetic)

14 Create hypertension grade variable based on sbp and dbp

# Create a new variable for hypertension grade based on sbp and dbp
steps_data <- steps_data %>%
  mutate(htn_grade = case_when(
    sbp < 120 & dbp < 80 ~ "Normal",
    sbp >= 120 & sbp < 140 | dbp >= 80 & dbp<90  ~ "Prehypertension",
    sbp >= 140 & sbp < 160 | dbp >= 90 & dbp < 100 ~ "Stage 1",
    sbp >= 160 | dbp >= 100 ~ "Stage 2",
    TRUE ~ "Unknown"
  ))
# Check the distribution of the new variable
htn_grade_distribution <- steps_data %>%
  group_by(htn_grade) %>%
  summarise(count = n()) %>%
  mutate(percentage = count / sum(count) * 100)
# Print the distribution
htn_grade_distribution
## # A tibble: 4 × 3
##   htn_grade       count percentage
##   <chr>           <int>      <dbl>
## 1 Normal           1303       29.0
## 2 Prehypertension  2500       55.6
## 3 Stage 1           517       11.5
## 4 Stage 2           180        4

Create hypertension grade variable based on sbp only

# Create a new variable for hypertension grade based on sbp only
steps_data <- steps_data %>%
  mutate(htn_grade_sbp = case_when(
    sbp < 120 ~ "Optimal",
    sbp >= 120 & sbp < 130 ~ "Normal",
    sbp >= 130 & sbp < 140 ~ "Elevated",
    sbp >= 140 & sbp < 160 ~ "Grade 1",
    sbp >= 160 & sbp < 180 ~ "Grade 2",
    sbp >= 180 ~ "Grade 3",
    TRUE ~ "Unknown"
  ))
# Check the distribution of the new variable
htn_grade_sbp_distribution <- steps_data %>%
  group_by(htn_grade_sbp) %>%
  summarise(count = n()) %>%
  mutate(percentage = count / sum(count) * 100)
# Print the distribution
htn_grade_sbp_distribution
## # A tibble: 6 × 3
##   htn_grade_sbp count percentage
##   <chr>         <int>      <dbl>
## 1 Elevated        727      16.2 
## 2 Grade 1         564      12.5 
## 3 Grade 2         179       3.98
## 4 Grade 3         107       2.38
## 5 Normal         1215      27   
## 6 Optimal        1708      38.0

15 Create five year age groups

# Create five year age groups
steps_data <- steps_data %>%
  mutate(age_group = case_when(
    age < 20 ~ "20 and below",
    age >= 20 & age < 25 ~ "20-24",
    age >= 25 & age < 30 ~ "25-29",
    age >= 30 & age < 35 ~ "30-34",
    age >= 35 & age < 40 ~ "35-39",
    age >= 40 & age < 45 ~ "40-44",
    age >= 45 & age < 50 ~ "45-49",
    age >= 50 & age < 55 ~ "50-54",
    age >= 55 & age < 60 ~ "55-59",
    age >= 60 & age < 65 ~ "60-64",
    TRUE ~ "65+"
  ))
# Check the distribution of the new variable
age_group_distribution <- steps_data %>%
  group_by(age_group) %>%
  summarise(count = n()) %>%
  mutate(percentage = count / sum(count) * 100)
# Print the distribution
age_group_distribution
## # A tibble: 11 × 3
##    age_group    count percentage
##    <chr>        <int>      <dbl>
##  1 20 and below   217       4.82
##  2 20-24          593      13.2 
##  3 25-29          688      15.3 
##  4 30-34          666      14.8 
##  5 35-39          588      13.1 
##  6 40-44          459      10.2 
##  7 45-49          334       7.42
##  8 50-54          285       6.33
##  9 55-59          256       5.69
## 10 60-64          226       5.02
## 11 65+            188       4.18

16 Summarise mean sbp by age group for those with normal hypertension grade

# Summarise mean sbp by age group for those with normal hypertension grade-add number of observations
mean_sbp_optimal <- steps_data %>%
  filter(htn_grade_sbp == "Optimal") %>%
  group_by(age_group) %>%
  summarise(mean_sbp = mean(sbp, na.rm = TRUE), n = n()) %>%
  arrange(age_group)
# Print the summary
mean_sbp_optimal
## # A tibble: 11 × 3
##    age_group    mean_sbp     n
##    <chr>           <dbl> <int>
##  1 20 and below     109.   110
##  2 20-24            111.   301
##  3 25-29            111.   336
##  4 30-34            110.   293
##  5 35-39            110.   228
##  6 40-44            112.   160
##  7 45-49            110.    91
##  8 50-54            110.    69
##  9 55-59            109.    55
## 10 60-64            110.    43
## 11 65+              107.    22

17 Summarise mean sbp by age group for those with prehypertension grade

# Summarise mean sbp by age group for those with prehypertension grade-add number of observations
mean_sbp_normal <- steps_data %>%
  filter(sbp == "Normal") %>%
  group_by(age_group) %>%
  summarise(mean_sbp = mean(sbp, na.rm = TRUE), n = n()) %>%
  arrange(age_group)
# Print the summary
mean_sbp_normal
## # A tibble: 0 × 3
## # ℹ 3 variables: age_group <chr>, mean_sbp <dbl>, n <int>

18 Summarise mean sbp by age group for those with elevated bp

# Summarise mean sbp by age group for those with elevated bp-add number of observations
mean_sbp_elevated <- steps_data %>%
  filter(htn_grade_sbp == "Elevated") %>%
  group_by(age_group) %>%
  summarise(mean_sbp = mean(sbp, na.rm = TRUE), n = n()) %>%
  arrange(age_group)
# Print the summary
mean_sbp_elevated
## # A tibble: 11 × 3
##    age_group    mean_sbp     n
##    <chr>           <dbl> <int>
##  1 20 and below     133.    24
##  2 20-24            134.    95
##  3 25-29            134.    92
##  4 30-34            134.   107
##  5 35-39            133.   115
##  6 40-44            134.    81
##  7 45-49            134.    58
##  8 50-54            135.    51
##  9 55-59            135.    47
## 10 60-64            134.    30
## 11 65+              134.    27

19 Summarise mean sbp by age group for those with grade 1 hypertension

# Summarise mean sbp by age group for those with grade 1 hypertension-add number of observations
mean_sbp_grade1 <- steps_data %>%
  filter(htn_grade_sbp == "Grade 1") %>%
  group_by(age_group) %>%
  summarise(mean_sbp = mean(sbp, na.rm = TRUE), n = n()) %>%
  arrange(age_group)
# Print the summary
mean_sbp_grade1
## # A tibble: 11 × 3
##    age_group    mean_sbp     n
##    <chr>           <dbl> <int>
##  1 20 and below     146.    13
##  2 20-24            147.    40
##  3 25-29            147.    50
##  4 30-34            145.    43
##  5 35-39            148.    63
##  6 40-44            148.    60
##  7 45-49            148.    56
##  8 50-54            147.    66
##  9 55-59            149.    57
## 10 60-64            149.    61
## 11 65+              149.    55

20 Summarise mean sbp by age group for those with grade 2 hypertension

# Summarise mean sbp by age group for those with grade 2 hypertension-add number of observations
mean_sbp_grade2 <- steps_data %>%
  filter(htn_grade_sbp == "Grade 2") %>%
  group_by(age_group) %>%
  summarise(mean_sbp = mean(sbp, na.rm = TRUE), n = n()) %>%
  arrange(age_group)
# Print the summary
mean_sbp_grade2
## # A tibble: 11 × 3
##    age_group    mean_sbp     n
##    <chr>           <dbl> <int>
##  1 20 and below     164      2
##  2 20-24            168      4
##  3 25-29            170      5
##  4 30-34            170.     9
##  5 35-39            166.    13
##  6 40-44            168.    16
##  7 45-49            168.    25
##  8 50-54            170.    14
##  9 55-59            169.    28
## 10 60-64            168.    29
## 11 65+              169.    34

21 Summarise mean sbp by age group for those with grade 3 hypertension

# Summarise mean sbp by age group for those with grade 3 hypertension-add number of observations
mean_sbp_grade3 <- steps_data %>%
  filter(htn_grade_sbp == "Grade 3") %>%
  group_by(age_group) %>%
  summarise(mean_sbp = mean(sbp, na.rm = TRUE), n = n()) %>%
  arrange(age_group)
# Print the summary
mean_sbp_grade3
## # A tibble: 9 × 3
##   age_group mean_sbp     n
##   <chr>        <dbl> <int>
## 1 25-29         192.     6
## 2 30-34         190.     4
## 3 35-39         190.     7
## 4 40-44         190.     8
## 5 45-49         210.    14
## 6 50-54         194.    17
## 7 55-59         204.    13
## 8 60-64         205.    17
## 9 65+           195.    21

22 Fit a linear regression model for predicting sbp by age group for those with optimal hypertension grade

# Fit a linear regression model for predicting sbp by age group for those with optimal hypertension grade
lm_optimal <- lm(sbp~age, data = steps_data %>% filter(htn_grade_sbp == "Optimal"), weights = weights)
# Print the summary of the model
summary(lm_optimal)
## 
## Call:
## lm(formula = sbp ~ age, data = steps_data %>% filter(htn_grade_sbp == 
##     "Optimal"), weights = weights)
## 
## Weighted Residuals:
##      Min       1Q   Median       3Q      Max 
## -2227.12  -195.12    69.86   246.12  1226.78 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 111.59797    0.49278 226.468   <2e-16 ***
## age          -0.03327    0.01510  -2.203   0.0277 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 417.7 on 1706 degrees of freedom
## Multiple R-squared:  0.002838,   Adjusted R-squared:  0.002253 
## F-statistic: 4.855 on 1 and 1706 DF,  p-value: 0.0277
# Print the coefficients of the model
coef(lm_optimal)
##  (Intercept)          age 
## 111.59796906  -0.03326639
# Model diagnostics
par(mfrow=c(2,2))
plot(lm_optimal)

# Print the ANOVA table of the model
anova(lm_optimal)
## Analysis of Variance Table
## 
## Response: sbp
##             Df    Sum Sq Mean Sq F value Pr(>F)  
## age          1    847235  847235  4.8552 0.0277 *
## Residuals 1706 297695166  174499                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Print the diagnostic plots of the model

23 Fit a linear regression model for predicting sbp by age group for those with normal hypertension grade

# Fit a linear regression model for predicting sbp by age group for those with normal hypertension grade
lm_normal <- lm(sbp~age, data = steps_data %>% filter(sbp <130), weights = weights)
# Print the summary of the model
summary(lm_normal)
## 
## Call:
## lm(formula = sbp ~ age, data = steps_data %>% filter(sbp < 130), 
##     weights = weights)
## 
## Weighted Residuals:
##      Min       1Q   Median       3Q      Max 
## -2740.29  -267.98    48.25   314.58  3082.24 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 114.57928    0.48300 237.226  < 2e-16 ***
## age           0.05046    0.01428   3.535 0.000415 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 541.1 on 2921 degrees of freedom
## Multiple R-squared:  0.004259,   Adjusted R-squared:  0.003918 
## F-statistic: 12.49 on 1 and 2921 DF,  p-value: 0.0004145
# Print the coefficients of the model
coef(lm_normal)
##  (Intercept)          age 
## 114.57927783   0.05046211
# Model diagnostics
par(mfrow=c(2,2))
plot(lm_normal)

# Print the ANOVA table of the model
anova(lm_normal)
## Analysis of Variance Table
## 
## Response: sbp
##             Df    Sum Sq Mean Sq F value    Pr(>F)    
## age          1   3658496 3658496  12.494 0.0004145 ***
## Residuals 2921 855309248  292814                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Print the diagnostic plots of the model

24 Fit a linear regression model for predicting sbp by age group for those with elevated hypertension grade

# Fit a linear regression model for predicting sbp by age group for those with elevated hypertension grade
lm_elevated <- lm(sbp~age, data = steps_data %>% filter(htn_grade_sbp == "Elevated"), weights = weights)
# Print the summary of the model
summary(lm_elevated)
## 
## Call:
## lm(formula = sbp ~ age, data = steps_data %>% filter(htn_grade_sbp == 
##     "Elevated"), weights = weights)
## 
## Weighted Residuals:
##     Min      1Q  Median      3Q     Max 
## -801.59 -102.66  -15.87   98.69  695.78 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 1.329e+02  3.051e-01  435.57  < 2e-16 ***
## age         2.705e-02  8.273e-03    3.27  0.00113 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 179.2 on 725 degrees of freedom
## Multiple R-squared:  0.01453,    Adjusted R-squared:  0.01317 
## F-statistic: 10.69 on 1 and 725 DF,  p-value: 0.001127
# Print the coefficients of the model
coef(lm_elevated)
##  (Intercept)          age 
## 132.88040555   0.02705233
# Model diagnostics
par(mfrow=c(2,2))
plot(lm_elevated)

# Print the ANOVA table of the model
anova(lm_elevated)
## Analysis of Variance Table
## 
## Response: sbp
##            Df   Sum Sq Mean Sq F value   Pr(>F)   
## age         1   343299  343299  10.693 0.001127 **
## Residuals 725 23277156   32106                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Print the diagnostic plots of the model

25 Fit a linear regression model for predicting sbp by age group for those with grade 1 hypertension

# Fit a linear regression model for predicting sbp by age group for those with grade 1 hypertension
lm_grade1 <- lm(sbp~age, data = steps_data %>% filter(htn_grade_sbp == "Grade 1"), weights = weights)
# Print the summary of the model
summary(lm_grade1)
## 
## Call:
## lm(formula = sbp ~ age, data = steps_data %>% filter(htn_grade_sbp == 
##     "Grade 1"), weights = weights)
## 
## Weighted Residuals:
##      Min       1Q   Median       3Q      Max 
## -1388.76  -212.38   -20.57   194.66  1669.85 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 145.15147    0.71770 202.244  < 2e-16 ***
## age           0.05112    0.01636   3.124  0.00187 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 326.9 on 562 degrees of freedom
## Multiple R-squared:  0.01707,    Adjusted R-squared:  0.01532 
## F-statistic: 9.762 on 1 and 562 DF,  p-value: 0.001873
# Print the coefficients of the model
coef(lm_grade1)
## (Intercept)         age 
## 145.1514730   0.0511182
# Model diagnostics
par(mfrow=c(2,2))
plot(lm_grade1)

# Print the ANOVA table of the model
anova(lm_grade1)
## Analysis of Variance Table
## 
## Response: sbp
##            Df   Sum Sq Mean Sq F value   Pr(>F)   
## age         1  1043199 1043199  9.7621 0.001873 **
## Residuals 562 60056473  106862                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Print the diagnostic plots of the model

26 Fit a linear regression model for predicting sbp by age group for those with grade 2 hypertension

# Fit a linear regression model for predicting sbp by age group for those with grade 2 hypertension
lm_grade2 <- lm(sbp~age, data = steps_data %>% filter(htn_grade_sbp == "Grade 2"), weights = weights)
# Print the summary of the model
summary(lm_grade2)
## 
## Call:
## lm(formula = sbp ~ age, data = steps_data %>% filter(htn_grade_sbp == 
##     "Grade 2"), weights = weights)
## 
## Weighted Residuals:
##     Min      1Q  Median      3Q     Max 
## -869.41 -149.02   31.66  197.94  789.19 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 166.77675    1.47716 112.904   <2e-16 ***
## age           0.00932    0.03040   0.307     0.76    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 302.3 on 177 degrees of freedom
## Multiple R-squared:  0.0005308,  Adjusted R-squared:  -0.005116 
## F-statistic: 0.094 on 1 and 177 DF,  p-value: 0.7595
# Print the coefficients of the model
coef(lm_grade2)
##  (Intercept)          age 
## 166.77675266   0.00932042
# Model diagnostics
par(mfrow=c(2,2))
plot(lm_grade2)

# Print the ANOVA table of the model
anova(lm_grade2)
## Analysis of Variance Table
## 
## Response: sbp
##            Df   Sum Sq Mean Sq F value Pr(>F)
## age         1     8590    8590   0.094 0.7595
## Residuals 177 16174444   91381
# Print the diagnostic plots of the model

27 Fit a linear regression model for predicting sbp by age group for those with grade 3 hypertension

# Fit a linear regression model for predicting sbp by age group for those with grade 3 hypertension
lm_grade3 <- lm(sbp~age, data = steps_data %>% filter(htn_grade_sbp == "Grade 3"), weights = weights)
# Print the summary of the model
summary(lm_grade3)
## 
## Call:
## lm(formula = sbp ~ age, data = steps_data %>% filter(htn_grade_sbp == 
##     "Grade 3"), weights = weights)
## 
## Weighted Residuals:
##     Min      1Q  Median      3Q     Max 
## -1360.0  -539.6  -174.8   258.1  3925.0 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 192.0140     7.1763   26.76   <2e-16 ***
## age           0.1234     0.1356    0.91    0.365    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 807.5 on 105 degrees of freedom
## Multiple R-squared:  0.007825,   Adjusted R-squared:  -0.001624 
## F-statistic: 0.8281 on 1 and 105 DF,  p-value: 0.3649
# Print the coefficients of the model
coef(lm_grade3)
## (Intercept)         age 
## 192.0140279   0.1234323
# Model diagnostics
par(mfrow=c(2,2))
plot(lm_grade3)

# Print the ANOVA table of the model
anova(lm_grade3)
## Analysis of Variance Table
## 
## Response: sbp
##            Df   Sum Sq Mean Sq F value Pr(>F)
## age         1   539901  539901  0.8281 0.3649
## Residuals 105 68458048  651981
# Print the diagnostic plots of the model