Use the data in ELEM94_95 to answer this question. See also Computer Exercise C4.10.
(i) Using all of the data, run the regression lavgsal on bs, lenrol, Istaff, and lunch. Report the coefficient on bs along with its usual and heteroskedasticity-robust standard errors. What do you conclude about the economic and statistical significance of bs?
(ii) Now drop the four observations with bs >.5, that is, where average benefits are (supposedly) more than 50% of average salary. What is the coefficient on bs? Is it statistically significant using the heteroskedasticity-robust standard error?
(iii) Verify that the four observations with bs >.5 are 68, 1,127, 1,508, and 1,670. Define four dummy variables for each of these observations. (You might call them d6S, d1127, d1508, and d1610.) Add these to the regression from part (i), and verify that the OLS coefficients and standard errors on the other variables are identical to those in part (ii). Which of the four dummies has a t statistic statistically different from zero at the 5% level?
(iv) Verify that, in this data set, the data point with the largest studentized residual (largest / statistic on the dummy variable) in part (iii) has a large influence on the OLS estimates. (That is, run OLS using all observations except the one with the large studentized residual.) Does dropping, in turn, each of the other observations with bs >.5 have important effects?
(v) What do you conclude about the sensitivity of OLS to a single observation, even with a large sample size?
(vi) Verify that the LAD estimator is not sensitive to the inclusion of the observation identified in part (iii).