4.12

a. Show that the regression R2 in the regression of Y on X is the squared value of the sample correlation between X and Y. That is, show that R2 = r2 XY.

b. Show that the R2 from the regression of Y on X is the same as the R2 from the regression of X on Y.

c. Show that b n

1 = rXY (sY>sX), where rXY is the sample correlation between X and Y, and sX and sY are the sample standard deviations of X and Y.