The Cost of Attending Your College Has Once Again Gone $\widehat {\operatorname { Cost}}$

Essay

The cost of attending your college has once again gone up. Although you have been told that education is investment in human capital, which carries a return of roughly 10% a year, you (and your parents)are not pleased. One of the administrators at your university/college does not make the situation better by telling you that you pay more because the reputation of your institution is better than that of others. To investigate this hypothesis, you collect data randomly for 100 national universities and liberal arts colleges from the 2000-2001 U.S. News and World Report annual rankings. Next you perform the following regression $\widehat {\operatorname { Cost}}$ = 7,311.17 + 3,985.20 × Reputation - 0.20 × Size + 8,406.79 × Dpriv - 416.38 × Dlibart - 2,376.51 × Dreligion
R²=0.72, SER = 3,773.35
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 university 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? (All liberal arts colleges are private.)
(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?
(d)Eliminating the Size and Dlibart variables from your regression, the estimation regression becomes $\widehat {\operatorname { Cost}}$ = 5,450.35 + 3,538.84 × Reputation + 10,935.70 × Dpriv - 2,783.31 × Dreligion; $R ^ { 2 }$ =0.72, SER = 3,792.68
Why do you think that the effect of attending a private institution has increased now?
(e)What can you say about causation in the above relationship? Is it possible that Cost affects Reputation rather than the other way around?