4. Locally weighted linear regression and bias-variance tradeoff. (30 points) Consider a dataset with n data points (xi, yi), xi E RP, following the following linear model yi = B* xitti, i = 1, ...,n, where ci ~N(0, o? ) are independent (but not identically distributed) Gaussian noise with zero mean and variance oz. (a) (5 points) Show that the ridge regression which introduces a squared 42 norm penalty on the parameter in the maximum likelihood estimate of S can be written as follows B(A) = arg min { (XB - y)TW(XB - y) + >llBl13} B for property defined diagonal matrix W, matrix X and vector y. (b) (5 points) Find the close-form solution for B(A) and its distribution conditioning on {xi}. (c) (5 points) Derive the bias as a function of ) and some fixed test point x