Consider the regression model:
Yi = BXi + ui
where ui and Xi satisfy Assumptions MLR1-MLR6
i) Let B-hat denote an estimator of B that is constructed as B-hat = Y-bar/X-bar, where Y-bar and X-bar are the sample means of Yi and Xi, respectively. Show that B-hat is conditionally unbiased.
ii) Derive the least squares estimator of B
iii) Show that the estimator is conditionally unbiased
iv) Derive the conditional variance of the estimator