Using Figure 9.2 (on page 223), show how the confidence interval–generating ellipse can be used to derive a confidence interval for the difference of the parameters β 1 - β 2 . Compare the confidence...

Using Figure 9.2 (on page 223), show how the confidence interval–generating ellipse can be used to derive a confidence interval for the difference of the parameters β₁
- β₂. Compare the confidence interval for this linear combination with that for β₁
= β₂. Which combination of parameters is estimated more precisely? Why? What would happen if the regressors X1 and X₂
were negatively correlated?