Compute the variance inflation factor for a correlated regressor

Question

In a three-factor return regression you check regressor $x_1$ for collinearity by regressing it on the other two regressors. That auxiliary regression has $R^2 = 0.90$ .

Compute the variance inflation factor (VIF) for $x_1$ , and state by how much its standard error is inflated compared with the no-collinearity case.

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The formula. The variance inflation factor for regressor j is 	ext{VIF}j = \frac{1}{1 - Rj^2}, where Rj^2 is the R^2 from regressing xj on all the other regressors. It measures how much the sampling variance of \hat\betaj is multiplied because that regressor overlaps with the rest. Plug in. With R1^2 = 0.90, 	ext{VIF}1 = \frac{1}{1 - 0.90} = \frac{1}{0.10} = 10. From variance to standard error. The VIF multiplies the variance of the coefficient. Standard error is the square root of variance, so the standard error is inflated by \sqrt{	ext{VIF}} = \sqrt{10} \approx 3.16. Your confidence int…

Compute the variance inflation factor for a correlated regressor

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