Work backward from a reported VIF to the auxiliary R-squared

Question

Your regression output reports a variance inflation factor of $5$ for one regressor, but it does not print the auxiliary $R^2$ .

Recover the auxiliary $R^2$ : what fraction of that regressor's variation is explained by the other regressors?

Accepted Answer

Invert the VIF formula. Starting from 	ext{VIF} = \frac{1}{1 - R^2}, solve for R^2: 1 - R^2 = \frac{1}{	ext{VIF}}, \qquad R^2 = 1 - \frac{1}{	ext{VIF}}. Plug in VIF = 5. R^2 = 1 - \frac{1}{5} = 1 - 0.20 = 0.80. So 80 percent of this regressor's variation is explained by the others, and only 20 percent is unique. As a sanity check, the standard error is inflated by \sqrt{5} \approx 2.24. Why this is handy. VIF and auxiliary R^2 carry the same information; being able to flip between them lets you translate a rule of thumb (VIF above 5) into a plain statement (the regressor is at least 80 per…

Work backward from a reported VIF to the auxiliary R-squared

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