The Cost of Attending Your College Has Once Again Gone

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 $$\begin{array} { l } \widehat { \text { Cost } } = 7,311.17 + 3,985.20 \times \text { Reputation } - 0.20 \times \text { Size } \\+ 8,406.79 \times \text { Dpriv } - 416.38 \times \text { Dlibart } - 2,376.51 \times \text { Dreligion } \\R ^ { 2 } = 0.72 , \text { SER } = 3,773.35\end{array}$$ 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?