4. (Statistical Inference) Given the following model, ya = 51 + [3231' + 632;- + 61'.- I have collected data and computed the following moment matrix with M = [1, x, z, y] for you: 120 150 80 450 150 300 250 2000 80 250 600 1200 450 2000 1200 25000 M'M: (a) How many observations have I collected? What are the average values for each variable, that is g, 5:, and 2? (b) Using OLS formula to compute the coeicient estimates, 5'1, 5'2, and ['33. What is the residual variance, the variancecovariance matrix of estimates, and the R2 for this regression? [Hint: 6'6 2 Y'Y ,8'X'Y] (0) Test the hypothesis of 1) 5'3 2 3 and 2))61 + g = 0 separately. (d) Test the hypotheses of {33 = 3 and l + ,82 = 0 simultaneously. Comparing (c) and ((1), what do you conclude