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 annual cost of attending law school, and rank is a law school ranking (with rank = 1 being the best).

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?.

Step-by-step explanation:

1) we would have the expectation that b₅ < 0 because b₅ shows how salary responds to law school ranking. As the rank of law school increases then median starting salary for new law school graduates declines. there is an inverse relation between salary and rank, Coefficient of rank, b5 will be negative since it is less than 0

ii) B₁ is going to be positive because as median LSAT score for the graduating class goes up, so does the salary of graduates. we have B1 >0

B₂ will be positive as college median GPA rises, so does graduate salary.

B₃ will be positive because if the more volumes of book in library, the greater possibility of getting higher salary, so B₃ >0.

B₄ >0 as if annual cost is high , then there would be indictaes more facilities of learning for students, leading to more chances of high salaries , hence B4 >0.

B5<0 this has been explained in 1.

iii) predicted ceteris paribus difference in salary for schools with a median GPA different by one point

= coefficient of GPA

=0.248

= this 24.8% in percentages B₂ tells us that when other factors are held constant,increasing median gpa by 1 would cause 24.8 percent increase in salary predicted.

iv)holding other variable factors constant, increasing the volume in the law library would bring about predicted salary increase by 0.095%

v) due to the inverse relationship between rank of law school and salary, it is better to attend a law school with lower rank than that with higher rank

difference in ranking of 20 = 20*(-0.0033)

= -0.066  x 100

= -6.6%

if rank is lower by 20 units , then we will have salary to be 6.6% higher