VIF from a pairwise correlation between two regressors

Question

Your model has exactly two regressors, x1 and x2, and their sample correlation is 0.80. Compute the variance inflation factor for x1, and by how much its standard error is inflated.

Accepted Answer

Two regressors is the easy case. When there are only two regressors, the auxiliary regression of x1 on the others is just a regression of x1 on x2, so its R^2 equals the squared correlation: R1^2 = 	ext{corr}(x1, x2)^2 = 0.80^2 = 0.64. Apply the VIF formula. 	ext{VIF}1 = \frac{1}{1 - R1^2} = \frac{1}{1 - 0.64} = \frac{1}{0.36} \approx 2.78. Standard-error inflation. The standard error grows by \sqrt{2.78} \approx 1.67, so about a 67 percent widening of the confidence interval. That is meaningful but well under the usual VIF-of-5 alarm threshold, so a correlation of 0.80 is uncomfortable but…

VIF from a pairwise correlation between two regressors

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