1. Suppose we perform subset, forward stepwise, and backward stepwise selection on a single data set. For each approach, again we can obtain p + 1 models containing 0, 1, 2, . . . , p predictors. As we know, best subset will give us a best model with k predictors. Call this Mk,subset. Forward stepwise selection will give us a best model with k predictors. Call this Mk,f orward. Backward stepwise selection will give us a best model with k predictors. Call this Mk,backward. Which of these three models has the smallest training MSE? Explain your answer. Hint: Consider the case for k = 0 and k = p first. Then the case for k = 1. Then the case for k = 2, . . . , p 1.

2. Same setup as part (1). Which of these three models has the smallest test MSE? Explain your answer.