Consider the College data from the ISLR package. These are described on page $54$ of the textbook.

We would like to predict the number of applications received using the other variables.

Problem statements:

All data will be taken as training data.

a$)$ Fit a linear model using least squares and report the LOOCV estimate of the test error.

b$)$ Fit a tree to the data. Summarize the results. Unless the number of terminal nodes is large,

display the tree graphically and explicitly describe the regions corresponding to the terminal

nodes that provide a partition of the predictor space $($i$.$e$.,$ provide expressions for the regions

R$1$

; $...$; RJ

$).$ Report its MSE.

c$)$ Use LOOCV to determine whether pruning is helpful and determine the optimal size for the

pruned tree. Compare the pruned and un$-$pruned trees. Report MSE for the pruned tree. Which

predictors seem to be the most important?

d$)$ Use a bagging approach to analyze the data with B $=500$ and B $=1000.$ Compute the MSE.

Which predictors seem to be the most important?

e$)$ Repeat $($d$)$ with a random forest approach with B $=500$ and B $=1000,$ and m $$ p $=3.$

f$)$ Compare the results from the various methods. Which method would you recommend?