Use the data in GPA2.RAW for this exercise,
(i) Estimate the model
sat = (0 + (1 hsize + (2 hsize2 + u.
where hsize is the size of the graduating class (in hundreds), and write the results in the usual form. Is the quadratic term statistically significant?
(ii) Using the estimated equation from part (i), what is the "optimal" high school size? Justify your answer.
(iii) Is this analysis representative of the academic performance of all high school seniors? Explain.
(iv) Find the estimated optimal high school size, using log(sat) as the dependent variable. Is it much different from what you obtained in part (ii)?