Consider the simple linear regression model (a) y=i+2w+w If u is homoskedastic, show that the estimated asymptotic variance of the linear prediction 335' = Bl + 5'23: (recall that this is our estimator of E(y|3;)) is minimized at a: = 5: (the sample average). Note that in the case of simple linear regression with homoskedastic u, the estimated (2 x 2) asymptotic covariance matrix is given by A $2 A .57: A 3 \"2 (i + E) \"2% AVAR( A1 ) = 282 _6.2% 62% If u is heteroskedastic, explain why the asymptotic variance of the forecast of y (not E (ylw)) given w may not be minimized at a: = :3. Assume a is homoskedastic with Var(u|$) = 02. You are interested in forecasting the average of three future y outcomes, each with a: = 32*. Provide an estima tor and work out its asymptotic variance. (You may leave things in terms of AVAR(B).) Assume a is homoskedastic with Var(u|3:) = 02. You are interested in forecasting the difference between two future y outcomes, both with w = 3:*. Provide an estimator and work out its asymptotic variance. (You may leave things in terms of AVAR(B).)