2. Recall that the least squares estimator (Bo, 81) can be obtained by minimizing the criterion function RSS(Bo, B1) = > tyi - (Bo + Bir;) }2. i=1 (a) Prove that Et (x -x)(y: -y) = Ettyi - nay. (b) Let ya, i = 1, ..., n, be the predicted values and e;, i = 1, ..., n, be the residuals. Prove that Enge; = 0, Et me, = 0 and Et, me; = 0. Note that the last relationship implies that the vector of residuals (e1, . .., en) is orthogonal to the vector of predicted values (y1, . . ., Un)