Question

2.) In this problem, we will perform multiple regression on the Boston housing data. The data contains 506 records with 14 variables. The variable medv is the response variable.

Solve the following problems in R and print out the commands and outputs :

To assess the data use

library(MASS)

data(Boston)

(a) First perform a multiple regression with all the variables, what can you say about the significance of the variables based on only the p-values. Next use the ”step” function to perform backward selection using (1) the AIC criteria and (2) the BIC criteria then compare the results. (By default the step function in R performs variable selection based on AIC criteria. Read the documentation to find out how to do the selection using BIC criteria. )

(b) Now make a histogram of the response variable (use hist()) to see if it is skewed. Using log(medv) as the response variable, perform the stepwise selection as previously using both AIC and BIC criteria. Compare with the previous results in terms of selected variables and adjusted R2.

Answer 1