In the file pubexp.dat there are data on public expenditure on education (EE), gross domestic product (GDP), and population (P) for 34 countries in the year 1980. It is hypothesized that per capita expenditure on education is linearly related to per capita GDP. That is, yi b1 b2xi ei where yi EEi Pi and xi GDPi Pi It is suspected that ei may be heteroskedastic with a variance related to xi.

(a) Why might the suspicion about heteroskedasticity be reasonable?

(b) Estimate the equation using least squares; plot the least squares function and the residuals. Is there any evidence of heteroskedasticity?

(c) Test for the existence of heteroskedasticity using a White test.

(d) Use Whites formula for least squares variance estimates to find some alternative standard errors for the least squares estimates obtained in part (b). Use these standard errors and those obtained in part (b) to construct two alternative 95% confidence intervals for b2. What can you say about the confidence interval that ignores the heteroskedasticity?

(e) Reestimate the equation under the assumption that var(ei)= alpha^2*xi. Report the results. Construct a 95% confidence interval for b2. Comment on its width relative to that of the confidence intervals found in part (d)