11.65.* Let ¯b∗
i denote the estimated standardized regression coefficient when xi is treated as the response variable and y as an explanatory variable, controlling for the same set of other variables. Then, ¯b∗
i need not equal b∗
i. The squared partial correlation between y and xi, which is symmetric, equals b∗
i ¯b ∗
i .

(a) Explain why the partial correlation must fall between b∗
i and ¯b∗
i . (Note: When a = √
bc, a is said to be the geometric average of b and c.)

(b) Even though b∗
i does not necessarily fall between −1 and +1, explain why b∗
i ¯b ∗
i cannot exceed 1.