Under the least squares assumptions for the multiple regression problem (zero conditional mean for the error term, all X_i and Y_i being i.i.d., all X_i and u_i having finite fourth moments, no perfect multicollinearity), the OLS estimators for the slopes and intercept A)have an exact normal distribution for n 25. B)are BLUE. C)have a normal distribution in small samples as long as the errors are homoskedastic. D)are unbiased and consistent.

Question

Under the least squares assumptions for the multiple regression problem (zero conditional mean for the error term, all X_i and Y_i being i.i.d., all X_i and u_i having finite fourth moments, no perfect multicollinearity), the OLS estimators for the slopes and intercept A)have an exact normal distribution for n > 25. B)are BLUE. C)have a normal distribution in small samples as long as the errors are homoskedastic. D)are unbiased and consistent.

Quizplus · Accepted Answer

The least squares assumptions ensure that OLS estimators for slopes and intercept are unbiased and consistent. They are not necessarily exactly normally distributed, but their distributions become increasingly normal as the sample size increases. They are also BLUE (Best Linear Unbiased Estimators) under these assumptions, but this is not the only correct statement, as options A and C are not necessarily true.

Under the Least Squares Assumptions for the Multiple Regression Problem