n . . 20 326.5122 5437.494 92263.52 1593187 We are interested in predicting the value of Y when X = 30. (a) [20 marks] Suppose that the true relationship between Y and X is given by Y=16+3X+Error. Here, the error terms are independent N(0, 2) random variables. Pretend that you do not know the above relationship. You do the prediction by regressing Y against X. Denote the predicted value by ip and the true value by yp. Find E(yp-Up) and Var(yp-up). You may leave the notation in your answer. (b) [20 marks] The true relationship between Y and X assumed in part (a) can be rewritten as Y 16+3X+0 X2 + Error. Now, you do the prediction by regressing Y against both X and X2. Denote the predicted value by up and the true value by up. Find E(yp-p) and Var (pp). You may leave the notation o in your answer. (c) [5 marks] Compare your answers in (a) and (b). If you are very confident that the relationship between Y and X is a straight line, which method, (a) or (b), should you use?