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Suppose we want to estimate the effects of alcohol consumption (alcohol) on college grade point average (colGPA). In addition to collecting information on grade point averages and alcohol usage, we also obtain attendance information (say, percentage of lectures attended, called attend). A standardized test score (say, SAT) and high school GPA (hsGPA) are also available.
(i) Should we include attend along with alcohol as explanatory variables in a multiple
regression model? (Think about how you would interpret b alcohol.)
(ii) Should SAT and hsGPA be included as explanatory variables? Explain.
4. The median starting salary for new law school graduates is determined by
log(salary) = B0 + B1 LSAT + B2 GPA + B3 log(libvol) + b4 log(cost)
+ B5 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 an-
nual cost of attending law school, and rank is a law school ranking (with rank = 1 being
(i) Explain why we expect b5 < 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
^ log(salary ) = 8.34 + .0047 * LSAT + .248 GPA + .095 log(libvol)
+ .038 log(cost) - .0033 rank
n = 136, R^2 = .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?