Assignment
Review Chapters 1-3 of Wooldridge and complete the exercises below. (Textbook exercise numbers are given in parenthesis for reference, but the first two are not from our textbook.)
Problem 1. (Studenmund, 1.11) The distinction between the stochastic error term ui and the residual ˆui is one of the most important in this class.
a. List at least two differences between the error term and the residual.
b. Usually, we can never observe the error term, but we can get around this difficulty if we assume values for the true coefficients. Calculate values of the error term and residual for each of the following six observations given that the true β0 equals 0.0, the true β1 equals 1.5, and the estimated regression equation is Y^i = 0.48 + 1.32 • Xi:
Yi 2 6 3 8 5 4
Xi 1 4 2 5 3 4
(Hint: To answer this question, you'll have to solve for ui in the "true model" equation for Yi.)
Problem 2. In order to estimate a regression equation using Ordinary Least Squares (OLS), it must be linear in the coefficients. Determine whether the coefficients in each of the following equations could be estimated using OLS.
a. Yi = β0 +β1lnXi +ui
b. lnYi = β0 +β1lnXi +ui
c. Yi = β0 +β1X β2 i +ui
d. Yβ0i = β1 +β2X2i +ui
e. Yi=β0+β1Xi+β2X2i +ui
Problem 3. (Wooldridge, 3.4) The median starting salary for new law school graduates is determined by
lnSALARY = β0 + β1LSAT+ β2GPA+ β3lnLIBVOL+ β4lnCOST + β5RANK+ 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).
a. Explain why we expect β5 ≤ 0.
b. What signs do you expect for the other slope parameters? Justify your answers.
c. Using the lawsch85 dataset, the estimated equation is
(lnSALARY)^ = 8.34 + 0.0047LSAT + 0.248GPA + 0.095 lnLIBVOL + 0.038 lnCOST - 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? (Report your answer as a percentage.)
d. Interpret the coefficient on the variable lnLIBVOL.
e. 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?
Problem 4. (Wooldridge, C3.2) Use the hprice1 dataset to estimate the model
PRICE = β0 +β1SQRFT+β2BDRMS+ u
where PRICE is the house price measured in thousands of dollars.
a. Write out the results in equation form.
b. What is the estimated increase in price for a house with one more bedroom, holding square footage constant?
c. What is the estimated increase in price for a house with an additional bedroom that is 140 square feet in size? Compare this to your answer in part b.
d. What percentage of the variation in price is explained by square footage and number of bedrooms?
e. The first house in the sample has SQRFT = 2,438 and BDRMS = 4. Find the predicted selling price for this house from the OLS regression line.
f. The actual selling price of the first house in the sample was $300,000 (so PRICE = 300). Find the residual for this house. Does it suggest that the buyer underpaid or overpaid for the house?