Examine whether the following statements are true, false, or uncertain. Give a short explanation. If a statement is not true in general but is true under some conditions, state the conditions.

(a) Since the least squares residuals are heteroskedastic and autocorre lated, even when the true errors are independent and homoskedastic, tests for homoskedasticity and serial independence based on least squares residuals are useless.

(b) There is a better chance of detecting outliers with predicted residuals or studentized residuals than with least squares residuals.

(c) In tests of significance we should not use a constant level of signifi- cance. The significance level should be a decreasing function of the sample size.

(d) To test for omitted variables, all we have to do is get some proxies for them, regress the least squares residual , on the proxies, and test whether the coefficients of these proxies are zero.

(e) The procedure of estimating the regression equation?