Using the method of orthogonal polynomials described in Section 7.1.2, fit a third-degree equation to the following data: y (index): 9.8 11.0 13.2 15.1 16.0 (year): 1950 1951 1952 1953 1954 Test the hypothesis that a second-degree equation is adequate. 2. Show that the least squares estimates of B1 and B2 for the model (7.28) are still unbiased even when the true model includes an interaction term B12, that is, E[Y] = Bo + B121 + B2X2 + B120122. Find the least squares estimate of B12. 3. Suppose that the regression curve E[Y] = Bo + BjI + B2x2 has a local maximum at I = Im where I'm is near the origin. If Y is observed at n points 1: (i = 1,2,..., n) in (-a, a), I = 0, and the usual normality assumptions hold, outline a method for finding a confidence interval for Im. Hint: Use the method of Section 6.1.2. (Williams (1959: p. 110])