12.4 Stepwise Methods: 12.4.1 Forward Selection, 12.4.2 Backward Elimination, 12.4.3 Stepwise Regression

Show that the first step in forward selection is equivalent to selecting the variable most highly correlated with the response.

Show that the variable that increases the difference $\mathrm{RSS}_{p}-\mathrm{RSS}_{p+1}$ by the greatest amount is the one having the greatest partial correlation with the response, given the variables already in the model.

In Example 12.2, verify Algorithm 12.2 and identify the regions corresponding to the subsets chosen by (a) backward elimination, (b) stepwise regression.