3. Consider the regression model Y= 8, + 3,3, + 14, where z, = X, - X and t4. ~ NID(0, 0'), t= 1, .., n (a) Derive the OLS estimators , and 3,, and the variance-covariance matrix of 3, and 3, (b) Show the properties of 3, regarding bias, efficiency and consistency. (c) Test the hypothesis Ho : 3, = 1 assuming the sample: X, 100 200 300 400 500 600 700 1 40 50 50 70 65 65 80 (d) Compute the R' and F-test and comment. the above model (e) Write down another model that will give you the same p, and residuals as