In this exercise, we will explore some of the factors predicting costs at American universities using the data file poolcoll2 and observations outside the great recession. Let \(T C=\) the real (\$2008) total cost per student, \(F T U G=\) number of full-time undergraduate students, FTGRAD = number of full-time graduate students, \(F T E F=\) full-time faculty per 100 students, \(C F=\) number of contract faculty per 100 students, FTENAP = full-time nonacademic professionals per 100 students.

a. Estimate the regression of \(\ln (T C)\) on the remaining variables. What are the predicted effects of additional undergraduate students and graduate students on total cost per student?

b. What are the predicted effects of additional full-time faculty, contract faculty, and nonacademic professionals on total cost per student?

c. Add the indicator variable PRIVATE to the model. Do you predict higher or lower total cost per student at private universities? Is this a statistically significant factor in predicting total cost per student?

d. Add to the model not only PRIVATE but also PRIVATE \(\times\) FTEF. Are these variables individually and jointly significant at the \(5 \%\) level?

e. Add to the model not only PRIVATE but also PRIVATE times all the other variables. Test the joint significance of PRIVATE and PRIVATE times all the other variables using an F-test. What do you conclude about the model in (a) that does not distinguish between private and public universities?

f. Estimate the model in (a) twice, once for private universities and once for public universities. Call the sum of squared residuals for the private universities \(S S E 1\), and the sum of squared residuals for the public universities \(S S E 0\). Compare \(S S E 1+S S E 0\) to the sum of squared residuals in part (e).