In this question, we will predict the number of applications received using the other variables in the College data set.

First, we split the data set into a training set and a test set by using the following command lines.

library(ISLR)

data("College")

set.seed(20)

train <- sample(nrow(College), 600)

College.train <- College[train, ]

College.test <- College[-train, ]

(a) Fit a linear model using least squares on the training set, and report the test error obtained.

(b) Fit a ridge regression model on the training set, with chosen by cross-validation. Report the test error obtained.

(c) Fit a lasso model on the training set, with chosen by crossvalidation. Report the test error obtained, along with the number of non-zero coefficient