Consider estimating a simple linear regression model a) Derive the OLS estimators that minimize the sum of squared residuals? Also derive the variance of OLS estimator, b) Show that OLS estimators for are unbiased and efficient estimators. c) What Gauss-Markov assumptions are needed for question b? Only include assumptions if actually required. d) State assumptions and show the sufficient conditions for OLS estimator to be consistent. e) Differentiate between unbiasedness and consistency of OLS estimator f) Assume that ( | ) , but all other Gauss Markov assumptions are satisfied. Show that OLS estimator for is still unbiased, but it is inefficient. g) Correct the problem of heteroskedasticity in question d and show that random error satisfies mean of the error term is zero and constant variance assumption.