# Question

Let

R2 = SSR / SST

denote the coefficient of determination for the sample regression line.

a. Using part d of the previous exercise, show that

b. Using the result in part a, show that the coefficient of determination is equal to the square of the sample correlation between X and Y.

c. Let b1 be the slope of the least squares regression of Y on X, b*1 be the slope of the least squares regression of X on Y, and r be the sample correlation between X and Y. Show that b1 ∙ b*1 = r2

R2 = SSR / SST

denote the coefficient of determination for the sample regression line.

a. Using part d of the previous exercise, show that

b. Using the result in part a, show that the coefficient of determination is equal to the square of the sample correlation between X and Y.

c. Let b1 be the slope of the least squares regression of Y on X, b*1 be the slope of the least squares regression of X on Y, and r be the sample correlation between X and Y. Show that b1 ∙ b*1 = r2

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