2. Consider the following simple linear regression model y = Bo + Br2 + for data (xi, yi), i = 1,...,n. Let bo and b be the OLS (Ordinary Least Squares) estimates of Bo and respectively, = bo+b1x be the fitted value, and e = y be the residual. (a) (15 points) Show that 1 ii = 0. (b) (30 points) Let zi = i. Suppose we fit the following simple linear regression model: z=a0a1x + * Obtain OLS estimates of ao and a. What is the coefficient of determination for this regression fit? (c) (15 points) Let corr(x, y) denote the sample correlation coefficient between x and y. Show that R [corr(x, y)] where R is the coefficient of determination. =