4 The median starting salary for new law school graduates is determined by log(salary) = Bo + B,LSAT + B,GPA + B,log(libvol) + Bylog(cost) + Bsrank + 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). (i) Explain why we expect ß5 < 0. (ii) What signs do you expect for the other slope parameters? Justify your answers. (iii) Using the data in LAWSCH85, the estimated equation is log(salary) = 8.34 + .0047 LAST + .248 GPA + .095 log(libvol) + .038 log(cost) – .0033 rank n = 136, R? = .842. What is the predicted ceteris paribus difference in salary for schools with a median GPA differ- ent by one point? (Report your answer as a percentage.) (iv) Interpret the coefficient on the variable log(libvol). 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? (v)

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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Problem 1QTC
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Question
5 In a study relating college grade point average to time spent in various activities, you distribute a sur-
vey to several students. The students are asked how many hours they spend each week in four activi-
ties: studying, sleeping, working, and leisure. Any activity is put into one of the four categories, so that
for each student, the sum of hours in the four activities must be 168.
(i) In the model
GPA = Bo + B,study + B,sleep + B3work + B,leisure + u,
does it make sense to hold sleep, work, and leisure fixed, while changing study?
(ii) Explain why this model violates Assumption MLR.3.
(iii) How could you reformulate the model so that its parameters have a useful interpretation and it
satisfies Assumption MLR.3?
Transcribed Image Text:5 In a study relating college grade point average to time spent in various activities, you distribute a sur- vey to several students. The students are asked how many hours they spend each week in four activi- ties: studying, sleeping, working, and leisure. Any activity is put into one of the four categories, so that for each student, the sum of hours in the four activities must be 168. (i) In the model GPA = Bo + B,study + B,sleep + B3work + B,leisure + u, does it make sense to hold sleep, work, and leisure fixed, while changing study? (ii) Explain why this model violates Assumption MLR.3. (iii) How could you reformulate the model so that its parameters have a useful interpretation and it satisfies Assumption MLR.3?
4 The median starting salary for new law school graduates is determined by
log(salary) = Bo + B,LSAT + B,GPA + Bzlog(libvol) + Bąlog(cost)
+ Bsrank + 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).
Explain why we expect B5 < 0.
(i)
What signs do you expect for the other slope parameters? Justify your answers.
(ii)
(iii) Using the data in LAWSCH85, the estimated equation is
log(salary) = 8.34 + .0047 LAST + .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 differ-
ent by one point? (Report your answer as a percentage.)
(iv) Interpret the coefficient on the variable log(libvol).
Would you say it is better to attend a higher ranked law school? How much is a difference in
(v)
ranking of 20 worth in terms of predicted starting salary?
Transcribed Image Text:4 The median starting salary for new law school graduates is determined by log(salary) = Bo + B,LSAT + B,GPA + Bzlog(libvol) + Bąlog(cost) + Bsrank + 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). Explain why we expect B5 < 0. (i) What signs do you expect for the other slope parameters? Justify your answers. (ii) (iii) Using the data in LAWSCH85, the estimated equation is log(salary) = 8.34 + .0047 LAST + .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 differ- ent by one point? (Report your answer as a percentage.) (iv) Interpret the coefficient on the variable log(libvol). Would you say it is better to attend a higher ranked law school? How much is a difference in (v) ranking of 20 worth in terms of predicted starting salary?
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