A regressor that is 95 percent explained by the others

Question

You regress candidate signal x3 on the other four signals in your model and find R3^2 = 0.95. Compute the VIF for x3, the standard-error inflation, and say whether it crosses the usual warning line.

Accepted Answer

Compute the VIF. 	ext{VIF}3 = \frac{1}{1 - R3^2} = \frac{1}{1 - 0.95} = \frac{1}{0.05} = 20. Standard-error inflation. The standard error is multiplied by \sqrt{20} \approx 4.47, so the confidence interval on \hat\beta3 is nearly four and a half times wider than it would be with an independent regressor. Should you worry? Yes. The common thresholds are VIF above 5, or the stricter VIF above 10, as cause for concern. A VIF of 20 blows past both. Only 1 - 0.95 = 5\% of this signal's variation is unique; the coefficient rests on that sliver and will be unstable. Consider dropping or combining x…

A regressor that is 95 percent explained by the others

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