Problem 2. Download the prostate cancer data set from https://hastie.su.domains/ElemStatLearn/ The data set contains eight predictors (columns 1-8) and the outcome Y (column 9: Ipsa). The last column (column 10) is the train/test indicator. a. Perform the best subset selection with the training data set. In total, how many regres- sion model were fitted? (10 points) b. Report the best models based on BIC, adjusted R2, and Mallow's Cp in subset selection. (10 points) c. Perform the forward stepwise selection with the training data set. In total, how many regression models were fitted? (10 points) d. Report the best models based on BIC, adjusted R2, and Mallow's Cp in forward stepwise selection. (10 points) e. Perform LASSO regression with the training data set. Use 10-fold cross-validation. Report the best lambda value chosen based on cross-validation and the corresponding training MSE. If we the LASSO model with the best lambda as the tuning parameter, which variables stay in the model? (10 points) f. Perform ridge regression with the training data set. Use 10-fold cross-validation. Re- port the best lambda value chosen based on cross-validation and the corresponding train- ing MSE. (10 points) g. Compare the best models selected based on subset selection, forward selection, LASSO regression, and ridge ridge regression in terms of test MSE. (10 points)