3.13 (i) Consider the simple regression model y = B+ Bx + u under the first four Gauss-Markov assumptions. For some function g(x), for example g(x) EV = x or g(x) = log(1 + r), define z = g(x). Define a slope estimator as B -(2-3)/(22-3x). Show that B, is linear and unbiased. Remember, because E(ux) = 0, you can treat both x; and z, as nonrandom in your derivation. (ii) Add the homoskedasticity assumption, MLR.5. Show that Var(B) = o((z; - (iii) Show directly that, under the Gauss-Markov assumptions, Var(B) Var(B), where B, is the OLS estimator. [Hint: The Cauchy-Schwartz inequality in Appendix B implies that notice that we can drop & from the sample covariance.] (x ARN