Variance inflation factor

The variance inflation factor (VIF) quantifies how much a regression coefficient's variance is inflated by multicollinearity. VIF above 10 signals unreliable individual coefficient estimates, even when the overall model fits well.

ByHoang TruongUpdated July 2, 2026

FrameworkClassical linear regression model

See it move

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Regressing predictor j on all the other predictors gives an auxiliary R² of 90%, meaning the other predictors explain 90% of j's variation. The variance inflation factor is 1 ÷ (1 − 0.90) = 10, the conventional danger threshold. j's coefficient standard error is therefore ten times larger than it would be without multicollinearity, even though the main regression's overall R² is untouched.

Where it fits

SubjectData Analysis & StatisticsAdvancedTopicMultiple Regression & InterpretationAdvancedTopicRegression Diagnostics & ProblemsAdvanced

The formula

LaTeX

\text{VIF}_j = \frac{1}{1 - R^2_j}

Variables

$V I F_{j}$: Variance inflation factor for predictor j
$R_{j}^{2}$: R-squared from regressing predictor j on all other predictors in the model

VIF = 1 means no multicollinearity for that predictor. Values above 10 (or 5 in stricter practice) signal that individual coefficient estimates are unreliable.