Using Figure 9 2 (on page 223), show how the confidence intervalgenerating ellipse can be used to derive a confidence interval for the difference of the parameters 1 ( 2 Compare the confidence interval for this linear combination with that for 1 2 Which combination of parameters is estimated more p...

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Using Figure 9.2 (on page 223), show how the confidence intervalgenerating ellipse can be used to derive

Question:

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 þ β2. Which combination of parameters is estimated more precisely? Why? What would happen if the regressors X1 and X2 were negatively correlated?

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