The Gauss-Markov theorem for multiple regression states that the OLS estimator
A)has the smallest variance possible for any linear estimator.
B)is BLUE if the Gauss-Markov conditions for multiple regression hold.
C)is identical to the maximum likelihood estimator.
D)is the most commonly used estimator.

Question

Quizplus · Accepted Answer

The Gauss-Markov theorem for multiple regression states that if the Gauss-Markov conditions for multiple regression hold, then the Ordinary Least Squares (OLS) estimator is BLUE, i.e., it has the smallest variance possible for any linear unbiased estimator. Therefore, option B is the correct answer. Option A is incorrect because it only considers the variance minimization aspect of the theorem, and option C is incorrect because not all OLS estimators are maximum likelihood estimators. Option D is also incorrect since it is not necessarily the case that the OLS estimator is the most commonly used estimator.

The Gauss-Markov Theorem for Multiple Regression States That the OLS