In this exercise, we explore some of the factors predicting costs at American public universities using the data file pubcoll. Let \(T C=\) the real \((\$ 2008)\) total cost per student, \(F T U G=\) number of full-time undergraduate students, \(F T G R A D=\) number of full-time graduate students, \(F T E F=\) fulltime faculty per 100 students, \(C F=\) number of contract faculty per 100 students, and 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 indicator variables for the years 1989, 1991, 1999, 2005, 2008, 2010, and 2011. Are these variables jointly and individually significant? Using your favorite site for macroeconomic data, plot the quarterly percentage change in the real U.S. GDP from January 1987 to January 1993. Does this help explain the signs and significance of any of the indicator variable coefficients?

d. The variable \(C R A S H=1\) during 2008, 2010, and 2011. Add to the model in

(c) interactions between CRASH and each of the variables FTEF, CF, and FTENAP. Are these variables individually significant at the \(5 \%\) level? Are they jointly significant?

e. Add to the model in (d) interactions between \(C R A S H\) and each of the variables \(F T U G\) and FTGRAD. Considering all the interaction variables, which are significant at the 5\% level? Test the joint significance of all the interaction variables at the \(5 \%\) level.