High R-squared, wide intervals, and VIFs of 25

Question

A three-regressor model has R^2 = 0.55 and a highly significant F, but each coefficient's 95 percent confidence interval comfortably includes zero. The reported variance inflation factors are all around 25. Diagnose the situation and recommend a fix.

Accepted Answer

The diagnosis is explicit here: multicollinearity. A VIF of 25 means each regressor is heavily explained by the others (since 	ext{VIF} = 1/(1 - Rj^2), a VIF of 25 implies Rj^2 = 1 - 1/25 = 0.96). The regressors overlap so much that only about 4 percent of each one's variation is unique. That inflates every standard error by \sqrt{25} = 5, which is exactly why the confidence intervals are so wide that they all straddle zero, even though the model as a whole fits well. Reconciling the F and the intervals. The F-test and R^2 reflect the regressors' strong joint explanatory power. The wide indi…

High R-squared, wide intervals, and VIFs of 25

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