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(Solved) The median starting salary for new law school graduates is determined by log (\text salary)=β_0+β_1 L S A T+β_2 G P A+β_3

Question: The median starting salary for new law school graduates is determined by

\[\log (\text { salary })=\beta_{0}+\beta_{1} L S A T+\beta_{2} G P A+\beta_{3} \log (\text { libvol })+\beta_{4} \log (\cos t)+\beta_{5} \operatorname{rank}+u\]

where LSAT is the median LSAT score for the graduating class, GPA is the median college 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).

  1. Explain why we expect \(\beta_{5}\) be non-positive.
  2. What signs do you expect the other slope parameters? Justify your answers.
  3. Using the data set that I have, I obtained the estimated coefficients be:
    8.34,0.0047,0.248,0.095,0.038, and -0.0033 respectively. Moreover, I have \(n=136\) and \(R^{2}=0.842\). 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.)
  4. Based on the information given in part (c), interpret the coefficient on the variable \(\log\) (libvol).
  5. 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?

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