Why is it the case that the multiple-correlation coefficient R 2 can never get smaller when an explanatory variable is added to the regression equation? [Hint: Recall that the regression equation is...

Why is it the case that the multiple-correlation coefficient R²
can never get smaller when an explanatory variable is added to the regression equation? [Hint: Recall that the regression equation is fit by minimizing the residual sum of squares, which is equivalent to maximizing R²
(why?).]

Prove that the least-squares fit in simple-regression analysis has the following properties: