The cost of attending your university has gone up once again. Although you have been told that education is investment in human capital and carries a return of roughly 10% a year, you (and your parents) are not pleased. An administrators at your school argues that you are paying more for your education because the reputation of your institution is better than that of others. To investigate this hypothesis, you collect data on a random sample of 100 national universities and liberal arts colleges from the 2000-2001 U. S. News and World Report annual ranking. Next you perform the following regression: Cost = 7,311.17 + 3,985.20 × Reputation – 0.20 × Size + 8,406.79 × Dpriv – 416.38 × Dlibart – 2,376.51 × Dreligion
(580.2) (524.4) (0.03) (3502.7) (204.1)
(1200.0)
R2 = 0.72, SER = 3,773.35 and coefficient standard errors are in ().
where Cost is Tuition, Fees, Room and Board in dollars,
Reputation is the index used in U. S. News and World Report (based on a survey of universit presidents and chief academic officers), which ranges from 1 ("marginal") to 5 ("distinguished"), Size is the number of undergraduate students, and Dpriv, Dlibart, and Dreligion are binary variables indicating whether the institution is private, a liberal arts college, and has a religious affiliation.
A. Interpret the results. Do the coefficients have the expected sign?
B. What is the forecasted cost for a liberal arts college, which has no religious affiliation, a size of 1,500 students and a reputation level of 4.5?
C. To save money, you are willing to switch from a private university to a public university, which has a ranking of 0.5 less and 10,000 more students. What is the effect on your cost? Is it substantial (support this)?
D. Do you have a reason to suspect imperfect multicollinearity in the independent variables above? Why or why not? Describe what happens to an independent variable’s estimated coefficient if imperfect multicollinearity is present.
E. Eliminating the Size and Dlibart variables from your regression, the estimation regression becomes
Cost = 5,450.35 + 3,538.84 × Reputation + 10,935.70 × Dpriv – 2,783.31 × Dreligion;
R2 = 0.68, SER = 3,792.68
Why do you think that the effect of attending a private institution has increased now?
F. Describe a variable that you could put into the regression (but won’t!) that would be perfectly collinear with another variable(s) in the original regression. Also, why won’t you add it?