Variance Inflation Factor (VIF) Calculator

Understanding the variance inflation factor (VIF) calculator — concept and principle

The variance inflation factor measures how much multicollinearity, the overlap between one predictor and the other predictors in a regression, inflates the uncertainty of that predictor's coefficient. Use it when checking a linear or logistic regression model before interpreting individual coefficients.

How it is calculated

• Regress predictor j on all the other predictors (not on the outcome) and take the R² of that auxiliary regression, written R²ⱼ.
• VIF = 1 ÷ (1 − R²ⱼ).
• Tolerance = 1 − R²ⱼ = 1 ÷ VIF.
• Concern level shown here: VIF above 10 is "serious multicollinearity", above 5 is "moderate", otherwise "low".

R²ⱼ is between 0 and 1 and has no unit. Each predictor in a model has its own VIF.

The principle

The sampling variance of an ordinary least squares coefficient can be written as σ² ÷ [(n − 1) × Var(xⱼ)] × 1 ÷ (1 − R²ⱼ). The last factor is the VIF. If xⱼ is unrelated to the other predictors (R²ⱼ = 0), VIF = 1 and there is no inflation. As xⱼ becomes predictable from the others, only the small part of its variation that is unique can be used to estimate its effect, so the estimate becomes unstable and its variance rises. The standard error grows with the square root of VIF: a VIF of 4 doubles it.

Worked example

1. Input: R² of the predictor on the others = 0.8.
2. Tolerance = 1 − 0.8 = 0.2.
3. VIF = 1 ÷ 0.2 = 5.
4. Label: moderate. The rule is "VIF > 5"; 5 is the boundary, and in floating point 1 ÷ 0.2 evaluates a hair above 5, so it is flagged.
5. Meaning: the coefficient's variance is 5 times what it would be with uncorrelated predictors, and its standard error is about √5 ≈ 2.24 times larger.

How to read the result

VIF = 1 means no collinearity. Rules of thumb flag values above 5 or above 10, but these are conventions, not tests. A high VIF does not bias coefficients and does not hurt prediction accuracy; it makes individual coefficients imprecise and sensitive to small data changes. Whether to act depends on your goal: for prediction you may ignore it, for explaining effects you may combine, drop or regularise correlated variables.

Common mistakes

• Using the R² of the main model (outcome on predictors) instead of the auxiliary regression.
• Worrying about high VIFs for polynomial or interaction terms and dummy variables of one category, which are expected and often harmless (centering helps).

Frequently asked questions

What VIF is too high?

Many texts use 10; more cautious analysts use 5. Consider the sample size and how precise each coefficient needs to be.

Can VIF be less than 1?

No. Since 0 ≤ R²ⱼ < 1, VIF is always at least 1.

How do I fix multicollinearity?

Collect more data, combine related variables into an index, drop a redundant one, center variables for interaction terms, or use ridge regression.

Sources: D. A. Belsley, E. Kuh and R. E. Welsch, Regression Diagnostics, Wiley, 1980 · M. H. Kutner, C. J. Nachtsheim, J. Neter and W. Li, Applied Linear Statistical Models, 5th ed., McGraw-Hill, 2005, Chapter 10