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One of the Properties of the OLS Estimator Is A \boldsymbol

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Short Answer

One of the properties of the OLS estimator is a. Xβ^=0k+1\boldsymbol { X } \hat { \boldsymbol { \beta } } = \mathbf { 0 } _ { k + 1 } .
b. that the coefficient vector β^\hat { \beta } has full rank.
c. X(YXβ^)=0k+1\boldsymbol { X } ^ { \prime } ( \boldsymbol { Y } - \boldsymbol { X } \hat { \boldsymbol { \beta } } ) = \mathbf { 0 } _ { k + 1 } .
d. (XX)1=XY\left( \boldsymbol { X } ^ { \prime } \boldsymbol { X } \right) ^ { - 1 } = \boldsymbol { X } ^ { \boldsymbol {} } \boldsymbol { Y }

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