Please answering the questions (a)~(c)! Thank you very much!!!!!!!

Please answer it very clear! Step by step! With some explanations!

Round off the numerical answers to 4 significant figures. Thank you!!!!

Question 2. We are interested in the relationship between the response Y and the predictor X . 121 Xi 2:121 XE 21:1 XE 21:1 X51 20 326.5122 5437.494 92263.52 1593187 We are interested in predicting the value of Y when X = 30. You are given (a) Suppose that the true relationship between Y and X is given by Y = 16+3X+Err0r. Here, the error terms are independent N (0, 02) 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 391, and the true value by yp . Find E(yp "Qp) and V0.1\"(yp Qp) . You may leave the notation 02 in your answer. (b) 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 X 2. Denote the predicted value by 3);, and the true value by yp. Find E'(yp 32p) and Var(yp 32p) . You may leave the notation 02 in your answer. (c) Compare your answers in (a) and (b). If you are very condent that the relationship between Y and X is a straight line, which method, (a) or (b), should you use