VIF Calculator

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Multicollinearity Diagnostic

What Is Variance Inflation Factor (VIF)?

The Variance Inflation Factor (VIF) measures the degree of multicollinearity in a multiple linear regression model. It quantifies how much the variance (and standard error) of an estimated regression coefficient is inflated due to linear correlation with other predictors.

A VIF of 1 indicates no correlation among predictors. Values exceeding 5 or 10 signal severe multicollinearity, which inflates standard errors, destabilizes coefficient estimates ($\beta_j$), and reduces statistical power.

When to Use It

Multiple Linear Regression: Validating the non-multicollinearity Gauss-Markov assumption before interpreting coefficient significance.
Feature Selection & Engineering: Pinpointing redundant or collinear features to eliminate from predictive models.
Econometric & Survey Modeling: Detecting interrelated demographic or financial predictors that distort slope estimates.
Evaluating Tolerance ($1 - R^2$): Examining the proportion of variance in a predictor not explained by other predictors in the model.

The Mathematical Formulas

$$\text{Tolerance}_j = 1 - R_j^2$$ $$\text{VIF}_j = \frac{1}{\text{Tolerance}_j} = \frac{1}{1 - R_j^2}$$ $$\text{Standard Error Inflation Factor} = \sqrt{\text{VIF}_j} = \frac{1}{\sqrt{1 - R_j^2}}$$

Where $R_j^2$ is the coefficient of determination from an auxiliary regression of predictor $X_j$ on all other remaining independent variables.

Worked Example

Scenario: Regressing predictor $X_1$ against predictors $X_2$ and $X_3$ yields an auxiliary $R_1^2 = 0.80$.

Step 1: Calculate Tolerance:
$\text{Tolerance}_1 = 1 - R_1^2 = 1 - 0.80 = 0.20$.

Step 2: Calculate VIF:
$\text{VIF}_1 = \frac{1}{\text{Tolerance}_1} = \frac{1}{0.20} = 5.0000$.

Step 3: Calculate Standard Error Inflation:
$\sqrt{\text{VIF}_1} = \sqrt{5.0000} \approx 2.2361$.

Conclusion: The variance of $\hat{\beta}_1$ is 5 times larger and its standard error is 2.24 times wider than if $X_1$ were completely uncorrelated with $X_2$ and $X_3$.

Computation Complete

VIF & Collinearity Results

Maximum Variance Inflation Factor

VIF = 5.0000

Moderate Multicollinearity (Threshold: 5 ≤ VIF < 10)

Max VIF 5.0000

Mean VIF 5.0000

Min Tolerance 0.2000

Max SE Inflation 2.2361x

Analyzed Predictors 1

Step-by-Step Calculation

Predictor Collinearity Diagnostics Table

Predictor	Auxiliary R²	Tolerance (1 - R²)	VIF	SE Inflation (√VIF)	Collinearity Severity

VIF Calculator

VIF Calculator

VIF & Collinearity Results

Step-by-Step Calculation

Predictor Collinearity Diagnostics Table

Interpretation

VIF Threshold & Severity Plot

Perfect for students, researchers, and professionals looking to build real statistical skills.