Variance Inflation Factor (VIF = 1/(1−R²_j)), Tolerance & Standard Error Inflation Calculator

Diagnose regression multicollinearity via VIF = 1/(1 − R²_j) (<5 low, 5–10 moderate, >10 severe).

Variance Inflation Factor (VIF)
6.25 VIF
Tolerance (1 − R²_j) 0.16 tolerance
Standard Error Inflation Factor (√VIF) 2.5 × SE
Unique Variance Share 16 %
Inputs
⚡ Scenarios:
R²_j
Auxiliary R²_j when regressing predictor X_j on all other predictors (0.00 to 0.99).
Results & Graph
Variance Inflation Factor (VIF)
6.25 VIF
Tolerance (1 − R²_j)
0.16 tolerance
Standard Error Inflation Factor (√VIF)
2.5 × SE
Unique Variance Share
16 %

Variance Inflation Factor (VIF)

Graph 1 • VIF Multicollinearity • Domain Architecture & Live Telemetry Maps Auxiliary R Squared through VIF Multicollinearity Formula.
Variance Inflation Factor (VIF: 6.25 VIF VIF Multicollinearity • Invariants & Metrics Variance Inflation Factor (V 6.25 VIF Tolerance (1 − R²_j) 0.16 tolerance Standard Error Inflation Fac 2.5 × SE Unique Variance Share 16 %
Graph 2 • Variance Inflation Factor (VIF) Across Auxiliary R Squared Sweep (40% → 160%) Evaluates Tolerance = 1 − R²_j; VIF = 1 / (1 − R²_j); SE_Multiplier = √VIF across 7 operating points (current input highlighted).
0 VIF 550 VIF 1.1k VIF 1.51 0.336R²_j 2.02 0.504R²_j 3.05 0.672R²_j 6.25 0.840R²_j 1.0k 1.01R²_j 1.0k 1.18R²_j 1.0k 1.34R²_j
Graph 3 • VIF Multicollinearity Multi-Scenario Envelope Shows how Variance Inflation Factor (VIF) responds across ±30% scenario shifts.
0 VIF 550 VIF 1.1k VIF 2.43 -30% 3.50 -15% 6.25 +0% 29.41 +15% 1.0k +30%
Summary: At auxiliary R²_j = 0.84, Tolerance is 0.16 and VIF is 6.25 (Moderate Collinearity (5–10)), inflating the regression coefficient’s standard error by 2.5×.
Summary: At auxiliary R²_j = 0.84, Tolerance is 0.16 and VIF is 6.25 (Moderate Collinearity (5–10)), inflating the regression coefficient’s standard error by 2.5×.
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Formula & Mathematical Methodology: VIF Multicollinearity Formula

Tolerance = 1 − R²j
VIF = 1 / (1 − R²j)
SEMultiplier = √VIF
Tolerance = 1 − R²_j; VIF = 1 / (1 − R²_j); SE_Multiplier = √VIF
  • auxiliaryRSquared: Auxiliary R Squared (R²_j)

Rounding: Internal floating-point calculations run in 64-bit IEEE-754 double precision; display values round to 2–4 decimal places.

Worked Example: Worked Mathematical Example: VIF Multicollinearity

Diagnose regression multicollinearity via VIF = 1/(1 − R²_j) (<5 low, 5–10 moderate, >10 severe).

  1. Specify the function parameters, matrix entries, or confusion matrix counts.
  2. Apply the closed-form or iterative formula: Tolerance = 1 − R²_j; VIF = 1 / (1 − R²_j); SE_Multiplier = √VIF.
  3. Examine the primary result, error bounds, and 3 interactive SVG plots.
Result: Computes VIF Multicollinearity via Tolerance = 1 − R²_j; VIF = 1 / (1 − R²_j); SE_Multiplier = √VIF.

Frequently Asked Questions

How does the Variance Inflation Factor (VIF = 1/(1−R²_j)), Tolerance & Standard Error Inflation Calculator compute the solution?

It evaluates Tolerance = 1 − R²_j; VIF = 1 / (1 − R²_j); SE_Multiplier = √VIF directly in your browser and updates three custom SVG visualizations in real time.

Can I solve backwards for an input parameter using Goal Seek?

Yes. Click "🎯 Goal Seek" in the results toolbar to solve backwards for any numeric input field.

Does this calculator run locally offline?

Yes. All calculations run 100% locally in your browser and work offline via the CalculatorGraph PWA.

Mathematics & Statistics · Econometrics & Regression

Variance Inflation Factor (VIF = 1/(1−R²_j)), Tolerance & Standard Error Inflation Calculator: inputs, method, and how to read the result

Diagnose regression multicollinearity via VIF = 1/(1 − R²_j) (<5 low, 5–10 moderate, >10 severe).

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Auxiliary R Squared: Auxiliary R²_j when regressing predictor X_j on all other predictors (0.00 to 0.99).

What the calculation includes

With the default values shown, Variance Inflation Factor (VIF) is 6.25 VIF. The calculation follows VIF Multicollinearity Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Auxiliary R Squared from 0.84 R²_j to 0.92 R²_j changes Variance Inflation Factor (VIF) from 6.25 VIF to 12.5 VIF. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses exact analytical or standard numerical analysis formulations from NIST DLMF.
  • Double-precision floating-point arithmetic has ~15–17 significant decimal digits of precision.

Scope: Global Mathematical & Statistical Standard Check the assumptions and limitations against your situation before relying on the estimate.

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