3. Suppose you have a dataset {(x (1), y()), ..., (x(N), y(N))} on which you wish to fit a linear regression model y xB + v. Naturally, you try a least squares data fitting approach: define and solve [1 (x()) A = y = (x(N)) 18- min A Unfortunately, you find that the model does not fit well, so you explore approaches to improve it. One approach is to define an extra feature z as a linear combination of current features x, so z = x + y for some fixed vector y. Let (i) = (x (), 2(i)) where z(i) = (x(i)) Ty for all i = 1,..., N, and define (x(1))] = You then compare the previous model with the one obtained by solving 2 min B,v -Y (a) (5 points) Do you expect the new model to perform better than the old one? Why or why not? Here, "perform better" means that the sum of squared errors is lower.