Q1. [22 points] Consider a linear estimator B1 = Et=1 Wi yi for B1 in SLR model y = Bo + Bix + u which satisfies Gauss Markov assumptions SLR.1 to SLR.5. E(u) = 0 and Var(u) = 02. The weights for B1 are: W1 = - 1 Xn - X1 w; = 0 for i = 2, 3, 4, ... ....., (n - 1) 1 Wn= + - Xn - X1 (a) (12 points) Substitute the population regression model y = Bo + Bix + u for y in the formula of B1 and derive E(B1|X) and Var(B,|X) under Gauss Markov assumptions, where X stands for a set of sample values of x: X = {xi, i = 1, 2, 3, ..., n}. 02 (b) (8 points) Compare Var (B1 X) to that of OLS estimator $1: CL (xi-x) 2 and proof that B1 is more efficient than B1. (c) (2 points) Is 1 a consistent estimator? Please explain