Question: Let $K = 2$ and $Xbeta = X_1 + X_2$. Suppose $X_1'X_2 = X_2'X_1$ and compare $Var[hatbeta_1 | X]$, $Var[hatbeta_1 + hatbeta_2 | X]$, and

Let $K = 2$ and $X\beta = X_1 + X_2$. Suppose $X_1'X_2 = X_2'X_1$ and compare $Var[\hat\beta_1 | X]$, $Var[\hat\beta_1 + \hat\beta_2 | X]$, and $Var[\hat\beta_1 - \hat\beta_2 | X]$ as $X_1'X_2 \to X_1'X_1$. Construct a graphic illustration along the lines of Figure 9.5.

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