Last Assignment in R
Niyomufasha Emerance ,ID: 20251MBI019
2026-06-04
Assignment 1
Find a data set of which you can fit multiple linear regression and interpret your results
#install.packages("readxl")
library(readxl)
data <- read_excel("D:/Emerance - personal stuffs/Big data/R Programming/Last Assignment/pathogen_dataset.xlsx")
str(data)## tibble [3,040 × 31] (S3: tbl_df/tbl/data.frame)
## $ Var1 : num [1:3040] 63.5 46.1 60.3 49.3 52.1 ...
## $ Var2 : num [1:3040] 37 34.2 64.9 54.4 47.3 ...
## $ Var3 : num [1:3040] 37.5 58.1 46.7 30.4 60.2 ...
## $ Var4 : num [1:3040] 57.2 36.5 62.3 52.9 51.4 ...
## $ Var5 : num [1:3040] 59.7 59.5 41.5 75 35.1 ...
## $ Var6 : num [1:3040] 64.2 54.9 53.3 64.9 53.9 ...
## $ Var7 : num [1:3040] 46.5 54.2 61.3 37.9 52.3 ...
## $ Var8 : num [1:3040] 65.2 51.3 72.6 51.3 71.7 ...
## $ Var9 : num [1:3040] 54.9 37.9 32.2 55 41.9 ...
## $ Var10 : num [1:3040] 38.9 59.7 44.4 60.2 55.8 ...
## $ Var11 : num [1:3040] 54.5 24.6 49.2 47.5 47.9 ...
## $ Var12 : num [1:3040] 30.1 43.9 44.4 51.3 49.8 ...
## $ Var13 : num [1:3040] 28.7 50.3 49.3 68.6 47.4 ...
## $ Var14 : num [1:3040] 33.3 47.2 31.5 52.7 62.9 ...
## $ Var15 : num [1:3040] 48.8 42.6 48.8 62.8 41.7 ...
## $ Var16 : num [1:3040] 49.4 41.1 56.4 47.1 49.6 ...
## $ Var17 : num [1:3040] 58.3 51 51.5 49.5 62.3 ...
## $ Var18 : num [1:3040] 40.7 39.7 58.4 57.3 29.1 ...
## $ Var19 : num [1:3040] 53.2 57.8 47.9 56 53.1 ...
## $ Var20 : num [1:3040] 50.5 51.9 41.1 53 46.7 ...
## $ ID : num [1:3040] 1782 1860 2878 2297 1492 ...
## $ Year : num [1:3040] 2013 2011 2023 2020 2019 ...
## $ Sex : chr [1:3040] "Female" "Male" "Female" "Male" ...
## $ Education : chr [1:3040] "Tertiary" "None" "Primary" "Secondary" ...
## $ WaterSource : chr [1:3040] "Borehole" "Borehole" "Tap" "Tap" ...
## $ BoiledWater : chr [1:3040] "No" "No" "No" "No" ...
## $ HandWashing : chr [1:3040] "No" "Yes" "Yes" "No" ...
## $ ToiletType : chr [1:3040] "Pit Latrine" "Pit Latrine" "Flush" "Pit Latrine" ...
## $ Age : num [1:3040] 23 59 21 26 28 64 39 76 19 19 ...
## $ Site : chr [1:3040] "Hospital B" "Hospital B" "Hospital A" "Clinic C" ...
## $ bact_isolated: chr [1:3040] "None" "E.coli" "None" "E.coli" ...head(data)## # A tibble: 6 × 31
## Var1 Var2 Var3 Var4 Var5 Var6 Var7 Var8 Var9 Var10 Var11 Var12 Var13
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 63.5 37.0 37.5 57.2 59.7 64.2 46.5 65.2 54.9 38.9 54.5 30.1 28.7
## 2 46.1 34.2 58.1 36.5 59.5 54.9 54.2 51.3 37.9 59.7 24.6 43.9 50.3
## 3 60.3 64.9 46.7 62.3 41.5 53.3 61.3 72.6 32.2 44.4 49.2 44.4 49.3
## 4 49.3 54.4 30.4 52.9 75.0 64.9 37.9 51.3 55.0 60.2 47.5 51.3 68.6
## 5 52.1 47.3 60.2 51.4 35.1 53.9 52.3 71.7 41.9 55.8 47.9 49.8 47.4
## 6 44.9 36.5 55.0 55.2 66.7 57.9 60.0 57.2 30.8 37.9 39.3 44.6 56.0
## # ℹ 18 more variables: Var14 <dbl>, Var15 <dbl>, Var16 <dbl>, Var17 <dbl>,
## # Var18 <dbl>, Var19 <dbl>, Var20 <dbl>, ID <dbl>, Year <dbl>, Sex <chr>,
## # Education <chr>, WaterSource <chr>, BoiledWater <chr>, HandWashing <chr>,
## # ToiletType <chr>, Age <dbl>, Site <chr>, bact_isolated <chr>#Check for missing values
colSums(is.na(data))## Var1 Var2 Var3 Var4 Var5
## 0 0 0 0 153
## Var6 Var7 Var8 Var9 Var10
## 0 0 0 0 0
## Var11 Var12 Var13 Var14 Var15
## 0 0 0 0 0
## Var16 Var17 Var18 Var19 Var20
## 0 0 0 0 0
## ID Year Sex Education WaterSource
## 0 0 50 30 0
## BoiledWater HandWashing ToiletType Age Site
## 0 0 0 0 0
## bact_isolated
## 0#Using Var1 as the dependent variable:
model <- lm(Var1 ~ Var2 + Var3 + Var4 + Var5 + Age + Year,
data = data)
summary(model)##
## Call:
## lm(formula = Var1 ~ Var2 + Var3 + Var4 + Var5 + Age + Year, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -35.642 -7.496 -1.017 5.782 115.823
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 149.52032 118.71592 1.259 0.2080
## Var2 0.01899 0.02630 0.722 0.4704
## Var3 0.02203 0.02689 0.819 0.4128
## Var4 -0.04848 0.02666 -1.819 0.0691 .
## Var5 0.04581 0.02662 1.721 0.0853 .
## Age 0.01504 0.01158 1.298 0.1943
## Year -0.05010 0.05882 -0.852 0.3944
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 14.36 on 2880 degrees of freedom
## (153 observations deleted due to missingness)
## Multiple R-squared: 0.00353, Adjusted R-squared: 0.001454
## F-statistic: 1.7 on 6 and 2880 DF, p-value: 0.1169#Include categorical variables
model2 <- lm(Var1 ~ Var2 + Var3 + Age + Year +
Sex + Education + WaterSource +
BoiledWater + HandWashing +
ToiletType + Site,
data = data)
summary(model2)##
## Call:
## lm(formula = Var1 ~ Var2 + Var3 + Age + Year + Sex + Education +
## WaterSource + BoiledWater + HandWashing + ToiletType + Site,
## data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -35.373 -7.454 -0.755 6.002 116.185
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 148.623267 112.159642 1.325 0.18524
## Var2 0.031090 0.025089 1.239 0.21538
## Var3 0.019473 0.025527 0.763 0.44563
## Age 0.009809 0.011031 0.889 0.37397
## Year -0.049384 0.055584 -0.888 0.37437
## SexMale 0.271239 0.507234 0.535 0.59287
## EducationPrimary 0.796523 0.709823 1.122 0.26189
## EducationSecondary 0.957072 0.724872 1.320 0.18683
## EducationTertiary 0.884035 0.715501 1.236 0.21673
## WaterSourceRiver -2.274560 0.725014 -3.137 0.00172 **
## WaterSourceTap -1.970834 0.710251 -2.775 0.00556 **
## WaterSourceWell -2.173780 0.722993 -3.007 0.00266 **
## BoiledWaterYes -0.483528 0.507197 -0.953 0.34050
## HandWashingYes -0.132203 0.507326 -0.261 0.79443
## ToiletTypeNone -0.036528 0.622172 -0.059 0.95319
## ToiletTypePit Latrine -0.294781 0.618160 -0.477 0.63349
## SiteHospital A 0.832230 0.625417 1.331 0.18340
## SiteHospital B -0.419027 0.620120 -0.676 0.49927
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.77 on 2942 degrees of freedom
## (80 observations deleted due to missingness)
## Multiple R-squared: 0.008628, Adjusted R-squared: 0.0029
## F-statistic: 1.506 on 17 and 2942 DF, p-value: 0.08286#Check regression assumptions:Residual plots
par(mfrow = c(2,2))
plot(model)
#Check multicollinearity
#install.packages("car")
library(car)## Loading required package: carDatavif(model)## Var2 Var3 Var4 Var5 Age Year
## 1.002086 1.002513 1.001141 1.001107 1.002167 1.000534It’s acceptable since the VIF <5
#Obtain predicted values
predicted_values <- predict(model)
head(predicted_values)## 1 2 3 4 5 6
## 50.50058 52.53551 49.62061 51.27420 50.12604 52.06168#Obtain residuals
residuals_model <- residuals(model)
head(residuals_model)## 1 2 3 4 5 6
## 13.027259 -6.402198 10.655525 -1.991431 2.014692 -7.188180summary(model)##
## Call:
## lm(formula = Var1 ~ Var2 + Var3 + Var4 + Var5 + Age + Year, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -35.642 -7.496 -1.017 5.782 115.823
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 149.52032 118.71592 1.259 0.2080
## Var2 0.01899 0.02630 0.722 0.4704
## Var3 0.02203 0.02689 0.819 0.4128
## Var4 -0.04848 0.02666 -1.819 0.0691 .
## Var5 0.04581 0.02662 1.721 0.0853 .
## Age 0.01504 0.01158 1.298 0.1943
## Year -0.05010 0.05882 -0.852 0.3944
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 14.36 on 2880 degrees of freedom
## (153 observations deleted due to missingness)
## Multiple R-squared: 0.00353, Adjusted R-squared: 0.001454
## F-statistic: 1.7 on 6 and 2880 DF, p-value: 0.1169The interpretation
The multiple linear regression model shows a very weak relationship between Var1 and the independent variables (Var2, Var3, Var4, Var5, Age, and Year). The model explains only 0.35% of the variation in Var1, and the overall model is not statistically significant (p = 0.1169). None of the predictors are statistically significant at the 5% level, although Var4 and Var5 show weak (marginal) effects. Therefore, these variables are not strong predictors of Var1 in this dataset.
Assignment 2 : Read about variable selection method
Variable selection is the process of choosing the most important independent variables (predictors) in a regression model.
Main Variable Selection Methods:
data(mtcars)
# Full model (all variables)
full_model <- lm(mpg ~ ., data = mtcars)
summary(full_model)##
## Call:
## lm(formula = mpg ~ ., data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.4506 -1.6044 -0.1196 1.2193 4.6271
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.30337 18.71788 0.657 0.5181
## cyl -0.11144 1.04502 -0.107 0.9161
## disp 0.01334 0.01786 0.747 0.4635
## hp -0.02148 0.02177 -0.987 0.3350
## drat 0.78711 1.63537 0.481 0.6353
## wt -3.71530 1.89441 -1.961 0.0633 .
## qsec 0.82104 0.73084 1.123 0.2739
## vs 0.31776 2.10451 0.151 0.8814
## am 2.52023 2.05665 1.225 0.2340
## gear 0.65541 1.49326 0.439 0.6652
## carb -0.19942 0.82875 -0.241 0.8122
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.65 on 21 degrees of freedom
## Multiple R-squared: 0.869, Adjusted R-squared: 0.8066
## F-statistic: 13.93 on 10 and 21 DF, p-value: 3.793e-07#Backward Elimination
step_backward <- step(full_model, direction = "backward")## Start: AIC=70.9
## mpg ~ cyl + disp + hp + drat + wt + qsec + vs + am + gear + carb
##
## Df Sum of Sq RSS AIC
## - cyl 1 0.0799 147.57 68.915
## - vs 1 0.1601 147.66 68.932
## - carb 1 0.4067 147.90 68.986
## - gear 1 1.3531 148.85 69.190
## - drat 1 1.6270 149.12 69.249
## - disp 1 3.9167 151.41 69.736
## - hp 1 6.8399 154.33 70.348
## - qsec 1 8.8641 156.36 70.765
## <none> 147.49 70.898
## - am 1 10.5467 158.04 71.108
## - wt 1 27.0144 174.51 74.280
##
## Step: AIC=68.92
## mpg ~ disp + hp + drat + wt + qsec + vs + am + gear + carb
##
## Df Sum of Sq RSS AIC
## - vs 1 0.2685 147.84 66.973
## - carb 1 0.5201 148.09 67.028
## - gear 1 1.8211 149.40 67.308
## - drat 1 1.9826 149.56 67.342
## - disp 1 3.9009 151.47 67.750
## - hp 1 7.3632 154.94 68.473
## <none> 147.57 68.915
## - qsec 1 10.0933 157.67 69.032
## - am 1 11.8359 159.41 69.384
## - wt 1 27.0280 174.60 72.297
##
## Step: AIC=66.97
## mpg ~ disp + hp + drat + wt + qsec + am + gear + carb
##
## Df Sum of Sq RSS AIC
## - carb 1 0.6855 148.53 65.121
## - gear 1 2.1437 149.99 65.434
## - drat 1 2.2139 150.06 65.449
## - disp 1 3.6467 151.49 65.753
## - hp 1 7.1060 154.95 66.475
## <none> 147.84 66.973
## - am 1 11.5694 159.41 67.384
## - qsec 1 15.6830 163.53 68.200
## - wt 1 27.3799 175.22 70.410
##
## Step: AIC=65.12
## mpg ~ disp + hp + drat + wt + qsec + am + gear
##
## Df Sum of Sq RSS AIC
## - gear 1 1.565 150.09 63.457
## - drat 1 1.932 150.46 63.535
## <none> 148.53 65.121
## - disp 1 10.110 158.64 65.229
## - am 1 12.323 160.85 65.672
## - hp 1 14.826 163.35 66.166
## - qsec 1 26.408 174.94 68.358
## - wt 1 69.127 217.66 75.350
##
## Step: AIC=63.46
## mpg ~ disp + hp + drat + wt + qsec + am
##
## Df Sum of Sq RSS AIC
## - drat 1 3.345 153.44 62.162
## - disp 1 8.545 158.64 63.229
## <none> 150.09 63.457
## - hp 1 13.285 163.38 64.171
## - am 1 20.036 170.13 65.466
## - qsec 1 25.574 175.67 66.491
## - wt 1 67.572 217.66 73.351
##
## Step: AIC=62.16
## mpg ~ disp + hp + wt + qsec + am
##
## Df Sum of Sq RSS AIC
## - disp 1 6.629 160.07 61.515
## <none> 153.44 62.162
## - hp 1 12.572 166.01 62.682
## - qsec 1 26.470 179.91 65.255
## - am 1 32.198 185.63 66.258
## - wt 1 69.043 222.48 72.051
##
## Step: AIC=61.52
## mpg ~ hp + wt + qsec + am
##
## Df Sum of Sq RSS AIC
## - hp 1 9.219 169.29 61.307
## <none> 160.07 61.515
## - qsec 1 20.225 180.29 63.323
## - am 1 25.993 186.06 64.331
## - wt 1 78.494 238.56 72.284
##
## Step: AIC=61.31
## mpg ~ wt + qsec + am
##
## Df Sum of Sq RSS AIC
## <none> 169.29 61.307
## - am 1 26.178 195.46 63.908
## - qsec 1 109.034 278.32 75.217
## - wt 1 183.347 352.63 82.790summary(step_backward)##
## Call:
## lm(formula = mpg ~ wt + qsec + am, data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.4811 -1.5555 -0.7257 1.4110 4.6610
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.6178 6.9596 1.382 0.177915
## wt -3.9165 0.7112 -5.507 6.95e-06 ***
## qsec 1.2259 0.2887 4.247 0.000216 ***
## am 2.9358 1.4109 2.081 0.046716 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.459 on 28 degrees of freedom
## Multiple R-squared: 0.8497, Adjusted R-squared: 0.8336
## F-statistic: 52.75 on 3 and 28 DF, p-value: 1.21e-11#Forward Selection
null_model <- lm(mpg ~ 1, data = mtcars)
full_model <- lm(mpg ~ ., data = mtcars)
step_forward <- step(null_model,
scope = list(lower = null_model, upper = full_model),
direction = "forward")## Start: AIC=115.94
## mpg ~ 1
##
## Df Sum of Sq RSS AIC
## + wt 1 847.73 278.32 73.217
## + cyl 1 817.71 308.33 76.494
## + disp 1 808.89 317.16 77.397
## + hp 1 678.37 447.67 88.427
## + drat 1 522.48 603.57 97.988
## + vs 1 496.53 629.52 99.335
## + am 1 405.15 720.90 103.672
## + carb 1 341.78 784.27 106.369
## + gear 1 259.75 866.30 109.552
## + qsec 1 197.39 928.66 111.776
## <none> 1126.05 115.943
##
## Step: AIC=73.22
## mpg ~ wt
##
## Df Sum of Sq RSS AIC
## + cyl 1 87.150 191.17 63.198
## + hp 1 83.274 195.05 63.840
## + qsec 1 82.858 195.46 63.908
## + vs 1 54.228 224.09 68.283
## + carb 1 44.602 233.72 69.628
## + disp 1 31.639 246.68 71.356
## <none> 278.32 73.217
## + drat 1 9.081 269.24 74.156
## + gear 1 1.137 277.19 75.086
## + am 1 0.002 278.32 75.217
##
## Step: AIC=63.2
## mpg ~ wt + cyl
##
## Df Sum of Sq RSS AIC
## + hp 1 14.5514 176.62 62.665
## + carb 1 13.7724 177.40 62.805
## <none> 191.17 63.198
## + qsec 1 10.5674 180.60 63.378
## + gear 1 3.0281 188.14 64.687
## + disp 1 2.6796 188.49 64.746
## + vs 1 0.7059 190.47 65.080
## + am 1 0.1249 191.05 65.177
## + drat 1 0.0010 191.17 65.198
##
## Step: AIC=62.66
## mpg ~ wt + cyl + hp
##
## Df Sum of Sq RSS AIC
## <none> 176.62 62.665
## + am 1 6.6228 170.00 63.442
## + disp 1 6.1762 170.44 63.526
## + carb 1 2.5187 174.10 64.205
## + drat 1 2.2453 174.38 64.255
## + qsec 1 1.4010 175.22 64.410
## + gear 1 0.8558 175.76 64.509
## + vs 1 0.0599 176.56 64.654summary(step_forward)##
## Call:
## lm(formula = mpg ~ wt + cyl + hp, data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.9290 -1.5598 -0.5311 1.1850 5.8986
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 38.75179 1.78686 21.687 < 2e-16 ***
## wt -3.16697 0.74058 -4.276 0.000199 ***
## cyl -0.94162 0.55092 -1.709 0.098480 .
## hp -0.01804 0.01188 -1.519 0.140015
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.512 on 28 degrees of freedom
## Multiple R-squared: 0.8431, Adjusted R-squared: 0.8263
## F-statistic: 50.17 on 3 and 28 DF, p-value: 2.184e-11#Stepwise Selection
stepwise_model <- step(null_model,
scope = list(lower = null_model, upper = full_model),
direction = "both")## Start: AIC=115.94
## mpg ~ 1
##
## Df Sum of Sq RSS AIC
## + wt 1 847.73 278.32 73.217
## + cyl 1 817.71 308.33 76.494
## + disp 1 808.89 317.16 77.397
## + hp 1 678.37 447.67 88.427
## + drat 1 522.48 603.57 97.988
## + vs 1 496.53 629.52 99.335
## + am 1 405.15 720.90 103.672
## + carb 1 341.78 784.27 106.369
## + gear 1 259.75 866.30 109.552
## + qsec 1 197.39 928.66 111.776
## <none> 1126.05 115.943
##
## Step: AIC=73.22
## mpg ~ wt
##
## Df Sum of Sq RSS AIC
## + cyl 1 87.15 191.17 63.198
## + hp 1 83.27 195.05 63.840
## + qsec 1 82.86 195.46 63.908
## + vs 1 54.23 224.09 68.283
## + carb 1 44.60 233.72 69.628
## + disp 1 31.64 246.68 71.356
## <none> 278.32 73.217
## + drat 1 9.08 269.24 74.156
## + gear 1 1.14 277.19 75.086
## + am 1 0.00 278.32 75.217
## - wt 1 847.73 1126.05 115.943
##
## Step: AIC=63.2
## mpg ~ wt + cyl
##
## Df Sum of Sq RSS AIC
## + hp 1 14.551 176.62 62.665
## + carb 1 13.772 177.40 62.805
## <none> 191.17 63.198
## + qsec 1 10.567 180.60 63.378
## + gear 1 3.028 188.14 64.687
## + disp 1 2.680 188.49 64.746
## + vs 1 0.706 190.47 65.080
## + am 1 0.125 191.05 65.177
## + drat 1 0.001 191.17 65.198
## - cyl 1 87.150 278.32 73.217
## - wt 1 117.162 308.33 76.494
##
## Step: AIC=62.66
## mpg ~ wt + cyl + hp
##
## Df Sum of Sq RSS AIC
## <none> 176.62 62.665
## - hp 1 14.551 191.17 63.198
## + am 1 6.623 170.00 63.442
## + disp 1 6.176 170.44 63.526
## - cyl 1 18.427 195.05 63.840
## + carb 1 2.519 174.10 64.205
## + drat 1 2.245 174.38 64.255
## + qsec 1 1.401 175.22 64.410
## + gear 1 0.856 175.76 64.509
## + vs 1 0.060 176.56 64.654
## - wt 1 115.354 291.98 76.750summary(stepwise_model)##
## Call:
## lm(formula = mpg ~ wt + cyl + hp, data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.9290 -1.5598 -0.5311 1.1850 5.8986
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 38.75179 1.78686 21.687 < 2e-16 ***
## wt -3.16697 0.74058 -4.276 0.000199 ***
## cyl -0.94162 0.55092 -1.709 0.098480 .
## hp -0.01804 0.01188 -1.519 0.140015
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.512 on 28 degrees of freedom
## Multiple R-squared: 0.8431, Adjusted R-squared: 0.8263
## F-statistic: 50.17 on 3 and 28 DF, p-value: 2.184e-11##Conclusion: Variable selection helps build a better regression model by identifying the most important predictors while removing irrelevant ones. Stepwise selection is the most commonly used method in R because it balances accuracy and simplicity.