Attached ppt from the class, please help me solve this question!

2. (5 points) For a new observation X*, F* = , + 82X* + e*. Let X* = {X, X*). We are interested in #* = E[Y'(X ] = B, + 62X*. It is estimated by Y* = , + 2X* . (1). Show that F* is an unbiased estimator for * (conditional on X* ). (2). Compute cov (1, z|X*). (3). What's the distribution of the estimation error #* - Y* conditional on X"? Compute the mean and variance of * - P* conditional on X*.\f. Recall that B1 = Yn - 32Xn cov( Yn, 32 X) = X; - Xn i=1 Sxx cov ( Yn, YilX ) 02 n = nSxx (X; - Xn) = 0 1=1 . Variance and estimated standard error of B1 X2 var(B1|X) = var( Yn|X) + X2var(B2 X) =02 n Sxx se ( B1|X ) = 0 X2 + n Sxx