The Gauss-Markov Theorem for Multiple Regression Proves That A $\boldsymbol { M } _ { \boldsymbol { X } }$

Short Answer

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