Suppose that for the model yi = + ei , the errors are independent with mean 0. Also suppose that measurements are taken using one device for the first n1 measurements, and then a more precise instrument was used for the next n2 measurements. Thus Var(ei) = 2 , i = 1, 2, . . . , n1 and Var(ei) = 2/2, i = n1 + 1, n1 + 2, . . . , n. (a) Ignore the fact that the errors have different variances, and derive the least squares estimator for using matrix notation and = (X0X) 1 X0y. (b) Derive the weighted least squares estimator for , WLS. (c) Suppose that n1 = n2. Compute the expected values and variances of the two estimators above. Which is a better estimator and why? (Use theoretical MSE() = Bias2 ( ) + Var() as your definition of "better.")