The Gauss-Markov theorem for multiple regression proves that
A)MX is an idempotent matrix.
B)the OLS estimator is BLUE.
C)the OLS residuals and predicted values are orthogonal.
D)the variance-covariance matrix of the OLS estimator is (
X)-1.

Question

The Gauss-Markov theorem for multiple regression proves that
A)MX is an idempotent matrix. 
B)the OLS estimator is BLUE. 
C)the OLS residuals and predicted values are orthogonal. 
D)the variance-covariance matrix of the OLS estimator is ( 
X)-1.

Quizplus · Accepted Answer

The Gauss-Markov theorem states that under certain assumptions (including the error term having zero conditional mean and constant variance, no perfect collinearity among predictors, and no correlation between the error term and any predictor), the OLS estimator in multiple regression is the Best Linear Unbiased Estimator (BLUE) for the population regression coefficients. Therefore, the answer is B, which states that the OLS estimator is BLUE. The other choices are either incorrect (A and C) or do not accurately describe the Gauss-Markov theorem (D).

The Gauss-Markov Theorem for Multiple Regression Proves That