1. Consider a noisy target y wx+e for generating the data, where e is a noise term with zero mean and 2 variance, independently generated for every example (x,y). The expected error of the best possible linear fit to this target is thus 2. For the data D{(Xyy1), , (XN-JN), denote the noise n yn as en and lete = [1,2, . . . ,ENI", assume that XTX is invertible. By following the steps below, show that the expected in-sample error of linear regression with respect to D is given by d 1 (a) Show that the in-sample estimate of y is given by Xw't He. (H was defined in the exercise two of Homework 6) (b) Show that the in-sample error vector y-y can be expressed by a matrix times e. What is the matrix? (c) Express Ein (Wlin) in terms of e using (b), and simplify the expression using (c) of exercise two of Homework 6. 1. Consider a noisy target y wx+e for generating the data, where e is a noise term with zero mean and 2 variance, independently generated for every example (x,y). The expected error of the best possible linear fit to this target is thus 2. For the data D{(Xyy1), , (XN-JN), denote the noise n yn as en and lete = [1,2, . . . ,ENI", assume that XTX is invertible. By following the steps below, show that the expected in-sample error of linear regression with respect to D is given by d 1 (a) Show that the in-sample estimate of y is given by Xw't He. (H was defined in the exercise two of Homework 6) (b) Show that the in-sample error vector y-y can be expressed by a matrix times e. What is the matrix? (c) Express Ein (Wlin) in terms of e using (b), and simplify the expression using (c) of exercise two of Homework 6