A sample of 200 Chicago households was taken to investigate how far American households tend to travel when they take a vacation. Consider the model

MILES is miles driven per year, INCOME is measured in \(\$ 1000\) units, \(A G E\) is the average age of the adult members of the household, and KIDS is the number of children.

a. Use the data file vacation to estimate the model by OLS. Construct a \(95 \%\) interval estimate for the effect of one more child on miles traveled, holding the two other variables constant.

b. Plot the OLS residuals versus INCOME and AGE. Do you observe any patterns suggesting that heteroskedasticity is present?

c. Sort the data according to increasing magnitude of income. Estimate the model using the first 90 observations and again using the last 90 observations. Carry out the Goldfeld-Quandt test for heteroskedastic errors at the \(5 \%\) level. State the null and alternative hypotheses.

d. Estimate the model by OLS using heteroskedasticity robust standard errors. Construct a \(95 \%\) interval estimate for the effect of one more child on miles traveled, holding the two other variables constant. How does this interval estimate compare to the one in (a)?

e. Obtain GLS estimates assuming \(\sigma_{i}^{2}=\sigma^{2}\) INCOME \({ }_{i}^{2}\). Using both conventional GLS and robust GLS standard errors, construct a 95\% interval estimate for the effect of one more child on miles traveled, holding the two other variables constant. How do these interval estimates compare to the ones in (a) and (d)?

Transcribed Image Text:

MILES = B+BINCOME + B3AGE + B+ KIDS+ e