Under the least squares assumptions for the multiple regression problem (zero conditional mean for the error term,all Xi and Yi being i.i.d. ,all Xi and ui 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 Xi and Yi being i.i.d. ,all Xi and ui 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 OLS estimators for the slopes and intercept are unbiased and consistent under the given least squares assumptions. However, there is no guarantee that their distribution will be exactly normal, especially for small sample sizes, and homoscedasticity is not a sufficient condition for normality. Also, while the OLS estimators are efficient in the class of linear unbiased estimators, they may not necessarily be best linear unbiased estimators (BLUE) in certain cases, such as when the errors are heteroscedastic.

Under the Least Squares Assumptions for the Multiple Regression Problem