Enter Values
VIF Formula
VIFj = 1 / (1 − R²j)
R²j = R-squared from regressing Xj on all other X's (with intercept, same sample)
VIF Results
Overall Assessment
Max VIF
2.50
Mean VIF
1.70
Assessment based on max VIF
Per-Variable Diagnostics
| Variable | VIF | Tolerance | SE Multiplier | Status |
|---|
VIF Bar Chart
Correlation Heatmap
This heatmap visualizes pairwise correlations only. VIF is computed from auxiliary R² values, not pairwise correlations. For k ≥ 3, low pairwise correlations can coexist with high VIF.
Formula Breakdown
VIFj = 1 / (1 − R²j)
TOLj = 1 − R²j = 1 / VIFj | SE Multiplier = √VIFj
VIF Interpretation Guide
| VIF Range | Tolerance | Assessment |
|---|---|---|
| VIF < 5 | TOL > 0.20 | Low multicollinearity |
| 5 ≤ VIF ≤ 10 | 0.10 ≤ TOL ≤ 0.20 | Moderate multicollinearity |
| VIF > 10 | TOL < 0.10 | High multicollinearity |
Model Assumptions
- VIF measures linear association among regressors only — it does not detect nonlinear relationships.
- High VIF inflates standard errors but does NOT bias OLS coefficients (under standard assumptions, absent perfect multicollinearity).
- VIF thresholds (5, 10) are common rules of thumb, not formal statistical tests.
- R²j is from regressing Xj on all other regressors with intercept, using the same sample.
- Dropping variables to reduce VIF can introduce omitted variable bias.
- For educational purposes only. Not professional statistical advice.
Understanding Multicollinearity & VIF
What is Multicollinearity?
Multicollinearity occurs when independent variables in a multiple regression model are highly correlated with each other. While it does not bias OLS coefficient estimates, it inflates standard errors, making it harder to identify which variables are individually significant.
Variance Inflation Factor
VIFj = 1 / (1 − R²j)
Var(β̂j) = σ² / [SSTj × (1 − R²j)]
Where R²j is from the auxiliary regression of Xj on all other regressors
Var(β̂j) = σ² / [SSTj × (1 − R²j)]
Where R²j is from the auxiliary regression of Xj on all other regressors
Bias vs. Precision
A common misconception is that multicollinearity biases regression coefficients. In fact, under the standard Gauss-Markov assumptions, OLS remains the Best Linear Unbiased Estimator (BLUE) even with imperfect multicollinearity. The real issue is precision: as VIF increases, confidence intervals widen and t-statistics shrink, making it harder to reject null hypotheses.
When to Worry
- VIF > 10 is a common rule-of-thumb threshold, but context matters.
- If your coefficient estimates have acceptable precision (narrow enough confidence intervals), high VIF may not be a practical problem.
- Do not drop theoretically important variables just to reduce VIF — this can introduce omitted variable bias, which is worse than imprecise estimates.
- Increasing sample size is often the best remedy, as it reduces standard errors without risking bias.
Important: Perfect multicollinearity (R²j = 1, VIF = ∞) makes OLS estimation impossible. This typically arises from data construction errors such as the dummy variable trap.
Frequently Asked Questions
Multicollinearity occurs when independent variables in a regression model are highly correlated with each other. It matters because it inflates the standard errors of the regression coefficients, making it harder to determine whether individual variables are statistically significant. However, multicollinearity does not bias the OLS coefficient estimates themselves.
VIF for variable j is calculated as VIFj = 1/(1 − R²j), where R²j is the R-squared from regressing Xj on all other independent variables (the auxiliary regression, with intercept, using the same sample). A VIF of 1 means no collinearity. VIF below 5 is generally considered low multicollinearity. VIF between 5 and 10 indicates moderate multicollinearity. VIF above 10 suggests high multicollinearity that may warrant attention.
Perfect multicollinearity means one variable is an exact linear combination of others (R²j = 1, VIF = infinity). This makes OLS estimation impossible. Imperfect multicollinearity (high but less than perfect correlation) is much more common and merely inflates standard errors without preventing estimation. Perfect multicollinearity often arises from data construction errors like the dummy variable trap.
No. Under standard OLS assumptions and absent perfect multicollinearity, imperfect multicollinearity does not bias coefficients. OLS remains the Best Linear Unbiased Estimator (BLUE). The issue is precision, not bias: standard errors increase, confidence intervals widen, and t-statistics decrease, making it harder to reject null hypotheses.
Common remedies include: (a) increasing sample size to reduce standard errors, (b) dropping redundant variables if theoretically justified, (c) combining correlated variables into an index. However, dropping variables solely to reduce VIF can introduce omitted variable bias, which is a more serious problem than multicollinearity. If coefficients have acceptable precision for your purposes, no action is needed.
Tolerance is the reciprocal of VIF: TOLj = 1/VIFj = 1 − R²j. Tolerance ranges from 0 to 1, where values close to 0 indicate high multicollinearity and values close to 1 indicate no collinearity. Tolerance below 0.1 corresponds to VIF above 10 (high multicollinearity), and tolerance below 0.2 corresponds to VIF above 5 (moderate multicollinearity).
Yes. VIF captures the joint linear predictability of a variable by all other regressors, not just pairwise correlations. A variable may have low pairwise correlations with each other variable individually but still be highly predictable from the combination of all other variables. This is why VIF from auxiliary regressions is a more reliable diagnostic than pairwise correlation matrices alone.
Disclaimer
This calculator is for educational purposes only. VIF thresholds are rules of thumb and should be interpreted in context. Multicollinearity diagnostics are one part of regression analysis and should not be used in isolation. Not professional statistical advice.
