Suppose that Yi = Xi + ui, where (ui, Xi) satisfy the Gauss-Markov conditions. a) Derive the least square estimator of and show that

Suppose that Yi = βXi + ui, where (ui, Xi) satisfy the Gauss-Markov conditions.

a) Derive the least square estimator of β and show that it is a linear function of Y1,...,Yn. 

b) Show that the estimator is conditionally unbiased. 

c) Derive the conditional variance of the estimator. 

d) How would you show that the estimator is the Best Linear conditionally Unbiased Estimator (BLUE)? Provide the basic intuition and discuss the main steps