(d) (points: 2) Suppose that random variable x takes on only two possible values, ac and by. In a random sample, there are na and no observations with these values, respectively. When x = ax, the sample average of y is ay; when x = Xb, the sample average of y is by. Calculate 7, the sample average of x, and y, the sample average of y, as a function of these n, a, and b constants. (e) (points: 8) Calculate SSTry and SST,, as defined in the slides. Simplify your answer where possible. (In this problem, all answers should be a function of the n, a, and b constants.) (Hint: reorder the observations so that the first na observations have x = las and the next no observations have x = Xb. Then, divide each summation into two sums: a sum where x = Xa plus a sum where x = = Xb] (f) (points: 4) Use your answers above to calculate the OLS estimate of B1 in the model y = Bo + B1x + u. Simplify your answer where possible. (In this problem, all answers should be a function of the n, a, and b constants.) (g) (points: 6) Now, assume that by = 0 (which simplifies the math). Use your answers above to calculate the OLS estimate of Bo in the model y = Bo + B1x + u. (In this problem, all answers should be a function of the n, a, and b constants.) (h) (points: 4) Continue assuming that b = 0. Use your answers above to calculate the OLS predicted value of y when x = ay, and when x = by = 0. (In this problem, all = x = = answers should be a function of the n, a, and b constants.) =