Locally weighted linear regression and bias-variance tradeoff. (20 points) The idea of locally weighted linear regression is that we will give more weight to data points in the training data that are close to the point at which we want to make a prediction. This can improve the bias but will also face a bias-variance tradeoff. This homework question is designed to look into this problem. Denote data point as (xi , yi), xi R p , i = 1, . . . , n. Given a Gaussian kernel function Kh(z) = 1 ( 2h) p e 2 z h 2 2 , z R p . Local linear regression solves 0 R, 1 R p , for a given predictor x R p : b := (b0, b1) = arg min nX i=1 (yi 0 (x x i ) T 1) 2Kh(x xi) (a) (10 points) Show that the solution is given in the form b = (XT W X) 1XT W Y for properly defined X, W, and Y (specify clearly what these need to be)