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Regression Analysis: Interpretation

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The median starting salary (SLRY) for new law school graduates is explained by

log (SLRY) = β0 + β1 LSAT + β3 GPA + β4 log(LIBB) + β5 log(COST) + β6 RANK + e

where LSAT is the median LSAT score for the graduating class, GPA is the median college GPA for the class, LIBB is the number of volumes in the law school library, COST is the annual cost of attending law school, and RANK is the rank of the law school (with rank 1 being the best).

Explain why we expect β5 ≤ 0.

What signs do you expect for the other slope parameters?

Using a sample data of 136 new law school graduates, the estimated equation is

log(SLRY) = 8.34 + 0.0047 LSAT + 0.248 GPA + 0.095 log(LIBB) + 0.038 log( cost) - 0.0033RANK

N = 136; R2= 0.842

What is the predicted ceteris paribus difference in salary for schools with a median GPA different by one point? (Note the dependent variable is in log form)

Interpret the estimated coefficient on the variable log (LIBB).

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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Solution Preview

(i) Explain why we expect β5 ≤ 0.

Here β5 is the coefficient of the rank of the law school in the regression model with rank 1 being the best. A larger rank for a law school means that the school has less prestige; this lowers starting salaries. For example, a rank of 100 means there are 99 schools thought to be better.

(ii) What signs do you expect for the other slope parameters?
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The solution contains the interpretation of a regression analysis problem.

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