Please answer part e, I have included the answer to a. Thanks!

(a) Centering. (5 pts] Let = i=1 X; and x' = x; -. xare called centered since 1=1 * = 0. Let i be the values predicted by Xi, wo, w1: i = wo + wix;. Show that y can be predicted by x as well. That is, there are parameters wo, w such that i = wo + wax, and write wo, w in terms of wo, w1, and, but not xi. (b) Loss function. [5 pts] In (a), we converted linear regression on ti with parameters wo, wi to linear regression on x with ww. Write the loss functions of the both. Specifically, let's assume J is the loss function of the former, and J' is of the latter. (c) Derivative. (5 pts] Take the derivative of J' with respect to wo, w, respectively. you shoume These (d) Finding optimal solution. (10 pts Set the derivatives you found to zero and solve wow. These are the points minimizing the loss function, and thus the solution to the linear regression. You should obtain w'o = and w = 24, where y is the centered version of yi similar to x (Hint: use the fact that x are centered.) ( 2 91 (e) The general case. [5 pts] Use the relation you found in (a), find the solution to the original problem, i.e. the optimal wo and w1. You should find wo = - w and w1 = 2 (1;-) (a) = r; - , I;=x+i substitute I; = x + into i = w, + wir; i = w. +w1(x+2) = w. +12+ wie w + w w * + wifi = we + w124 w = w, + WL wa = 1 W (a) Centering. (5 pts] Let = i=1 X; and x' = x; -. xare called centered since 1=1 * = 0. Let i be the values predicted by Xi, wo, w1: i = wo + wix;. Show that y can be predicted by x as well. That is, there are parameters wo, w such that i = wo + wax, and write wo, w in terms of wo, w1, and, but not xi. (b) Loss function. [5 pts] In (a), we converted linear regression on ti with parameters wo, wi to linear regression on x with ww. Write the loss functions of the both. Specifically, let's assume J is the loss function of the former, and J' is of the latter. (c) Derivative. (5 pts] Take the derivative of J' with respect to wo, w, respectively. you shoume These (d) Finding optimal solution. (10 pts Set the derivatives you found to zero and solve wow. These are the points minimizing the loss function, and thus the solution to the linear regression. You should obtain w'o = and w = 24, where y is the centered version of yi similar to x (Hint: use the fact that x are centered.) ( 2 91 (e) The general case. [5 pts] Use the relation you found in (a), find the solution to the original problem, i.e. the optimal wo and w1. You should find wo = - w and w1 = 2 (1;-) (a) = r; - , I;=x+i substitute I; = x + into i = w, + wir; i = w. +w1(x+2) = w. +12+ wie w + w w * + wifi = we + w124 w = w, + WL wa = 1 W