Significant F, weak t-stats, but the VIFs are all near 1

Question

A five-regressor model has a significant overall F, but no individual t-statistic is significant, the usual multicollinearity signature. This time, though, the variance inflation factors are all close to 1.

Is multicollinearity the culprit here? If not, what is?

Accepted Answer

No, this is not multicollinearity. VIFs near 1 mean the regressors are essentially uncorrelated with one another, so there is no inflation of standard errors from overlap. The multicollinearity story requires high VIFs; low VIFs rule it out. This is the instructive negative case: the F-versus-t pattern is suggestive of collinearity but not proof, always check the VIFs. What is actually happening. With uncorrelated regressors, the significant-F-but-insignificant-t pattern usually means each predictor has a small, individually underpowered effect, while the F pools all five pieces of evidence t…

Significant F, weak t-stats, but the VIFs are all near 1

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