Forward Stepwise Regression. Verify the claim that for the case of AIC selection, step (b)

of the algorithm can be implemented by identifying the regressor in the inactive set with the greatest absolute correlation with the residual from step (a).

Hint: This is challenging. First show that the goal is to find the regressor which will most decrease SSE Æ be0be Æ kbek2. Use a geometric argument to show that the regressor most parallel to be will most decreases kbek. Show that this regressor has the greatest absolute correlation with be.