4. (6 points) A data set consists of two variables a and y derived from a simple random sample. The observations of a and y are X1, ..., Un, and y1, ..., Un, respectively. Let y be the response variable. A simple linear regression model (using least squares method) is fitted to these data, which yields a coefficient of determination R2. Let y1, ..., Un denote the fitted values and ei = yi - yi, i = 1, ...,n, denote the residuals. Using the fact that EXi ei = 0, prove that (a) Etyiei = 0. (b) Cov(y, y) = Var(y). (c) R2 = [Cor(y, y)12. - SOME GIVEN QUANTILES F2,40(0.01) F2,41 (0.01) F2,40 (0.005) F2,169 (0.1) F2,169(0.025) t171 (0.005) t171 (0.01) 5.178 5.163 6.066 2.334 3.77 2.605 2.348