The median starting salary for new law school graduates is determined by log(salary)= 0+1 LSAT+2GPA+3log(libvol)+4log(cost)+5rank+u, where LSAT is the median LSAT score for the graduating class, GPA is the median col- lege GPA for the class, libvol is the number of volumes in the law school library, cost is the annual cost of attending law school, and rank is a law school ranking (with rank = 1 being the best).

(i) Explain why we expect 5 <= 0.

(ii) What signs do you expect for the other slope parameters? Justify your answers.

(iii) Using the data in LAWSCH85.RAW, the estimated equation is 2 log(salary) = 8.34 + .0047 LSAT + .248 GPA + .095 log(libvol) + .038 log(cost) - .0033 rank n= 136, R2 = .842. What is the predicted ceteris paribus difference in salary for schools with a median GPA different by one point? (Report your answer as a percentage.)

(iv) Interpret the coefficient on the variable log(libvol).

(v) Would you say it is better to attend a higher ranked law school? How much is a difference in ranking of 20 worth in terms of predicted starting salary?