Question: (Partitioned Regression) Let $X_2'X_1 = 0$. We have already seen that such orthogonality implies that algebraically $hatbeta_1$ is not affected by the presence of $X_2$

(Partitioned Regression) Let $X_2'X_1 = 0$. We have already seen that such orthogonality implies that algebraically $\hat\beta_1$ is not affected by the presence of $X_2$ in the OLS regression (Example 3.3, Exercise 3.13). Show that in addition $Cov[\hat\beta_1, \hat\beta_2 | X] = 0$, as might be expected.

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