The Gauss-Markov theorem for multiple regression proves that A)M_X 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 $\sigma _ { u } ^ { 2 }$ ( $X ^ { \prime }$ X)^-¹.

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The Gauss-Markov theorem states that in a linear regression model where the errors have expectation zero, are uncorrelated, and have equal variances, the ordinary least squares (OLS) estimator is the best linear unbiased estimator (BLUE) of the coefficients. This means it has the smallest variance among all linear unbiased estimators.

The Gauss-Markov Theorem for Multiple Regression Proves That A)MX Is σu2\sigma _ { u } ^ { 2 }σu2​

The Gauss-Markov Theorem for Multiple Regression Proves That
A)M_X Is $\sigma _ { u } ^ { 2 }$