Question

Consider the R builtin dataset cars: data(mtcars)

• – Divide the data into training and test data such that 80% of the data is randomly assigned to the training data and the remaining 20% is assigned to the test data. Use set.seed(100) in your code before performing the split to main reproducibility of results. (Hint: use the R function sample)

• – Fit dist vs speed (as the independent variable) using a linear model on the training data and print a summary of this fit.

• – Display the residual plots from the fitting

• – Obtain the mean square error of prediction using the test data.

Answer 1

PFA the complete R code for all parts

library(CARS)
library(Metrics) # It has MSE function

data1=mtcars
set.seed(100)

speed=data1$mpg
distance=data1$disp

n=length(speed) #Total length = 32
training_size=as.integer(0.8*n) #Trainingt sample size = 25
training_index=sample(1:length(speed),size=training_size) #Index vector for training sample
tr_speed=speed[training_index] #training sample speed
tr_distance=distance[training_index] #training samle distance
tr_df=data.frame(tr_speed,tr_distance) #training dataset

test_speed=speed[-training_index]
test_distance=distance[-training_index]
test_df=data.frame(test_speed,test_distance)

fit=lm(tr_distance~tr_speed,data=tr_df) #linear model
summary(fit)

plot(tr_speed,fit$residuals) #residual plot

#predictions
pred_distance=predict.lm(fit,newdata = data.frame(tr_distance=test_distance,tr_speed=test_speed))

pmse=mse(test_distance,pred_distance)
pmse

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The indices for training samle obtained are (10 8 17 2 14 28 22 32 27 4 24 19 6 31 26 12 23 20 15 9 7 21 18 30 16)

The summary of fit is

summary(fit)

Call:
lm(formula = tr_distance ~ tr_speed, data = data.frame(tr_speed,
tr_distance))

Residuals:
Min 1Q Median 3Q Max
-89.503 -36.637 -7.361 42.058 120.703

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 568.594 37.888 15.007 2.26e-13 ***
tr_speed -16.959 1.767 -9.599 1.64e-09 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 58.09 on 23 degrees of freedom
Multiple R-squared: 0.8002,   Adjusted R-squared: 0.7916
F-statistic: 92.14 on 1 and 23 DF, p-value: 1.645e-09

The residual plot is

The mean square error for prediction is 8144.912