Predict the number of applications received using the other variables in the College data set in library ISLR

(a) Split the data set into a training set and a test set using caret library and fit each of the following models using caret and ten fold cross validation.

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

(c) Fit a ridge regression model on the training set, with chosen by cross-validation. Report the test mean squared error obtained. Report the value of used in the model

(d) Fit a lasso model on the training set, with fraction chosen by cross validation. Report the test mean squared error obtained, along with the number of non-zero coefficient estimates and the fraction.

(e) Fit a PCR model on the training set, with no. of principal components M chosen by cross-validation. Report the test mean squared error obtained, along with the value of M selected by cross-validation.

(f) Fit a PLS model on the training set, with M chosen by cross validation. Report the test error obtained, along with the value of M selected by cross-validation.

(g) Comment on the results obtained. Is there much difference among the test errors resulting from these five approaches?