2.2 (E Section 2.1.3) In the regression model the variable y is regressed on the variable x with resulting regression line a bx. Reversing

2.2 (E Section 2.1.3)

In the regression model the variable y is regressed on the variable x with resulting regression line a þ bx. Reversing the role of the two variables, x can be regressed on y with resulting regression line c þ dy.

a. Derive formulas for the least squares estimates of c and d obtained by regressing x on y.

b. Show that bd ¼ R2, where b is the conventional least squares estimator and d the slope estimator in a.

c. Conclude that in general d 6¼ 1=b. Explain this in terms of the criterion functions used to obtain b and d.

d. Finally, check the results in b and c by considering again the excess returns data of Example 2.1.