Prove That Under the Extended Least Squares Assumptions the OLS $\hat { \boldsymbol { \beta } }$

question 35

Essay

Prove that under the extended least squares assumptions the OLS estimator $\hat { \boldsymbol { \beta } }$ is unbiased and that its variance-covariance matrix is $\sigma _ { u } ^ { 2 } \left( \boldsymbol { X } ^ { \prime } \boldsymbol { X } \right) ^ { - 1 }$

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