Adjusted R², F-Statistic, Akaike (AIC) & Bayesian (BIC) Regression Model Calculator

Penalize R² for excess predictors via Adjusted R², overall F-test, AIC, and BIC.

Adjusted R-Squared (Adj R²)
0.71 Adj R²
Overall Model F-Statistic F(4, 115) 73.929 F-stat
Akaike Information Criterion (AIC) -31.381 AIC
Bayesian Information Criterion (BIC) -17.443 BIC
Inputs
⚡ Scenarios:
R²
Multiple coefficient of determination R² (0 to 0.999).
n
Total observations n in the regression.
predictors k
Number of independent explanatory variables k.
RSS
Residual Sum of Squares (RSS / SSE) for AIC/BIC.
Results & Graph
Adjusted R-Squared (Adj R²)
0.71 Adj R²
Overall Model F-Statistic F(4, 115)
73.929 F-stat
Akaike Information Criterion (AIC)
-31.381 AIC
Bayesian Information Criterion (BIC)
-17.443 BIC

Adjusted R-Squared (Adj R²)

Graph 1 • Adjusted R², F-Stat & AIC/BIC • Domain Architecture & Live Telemetry Maps Unadjusted R Squared, Sample Size N, Predictor Count K through Adjusted R², F-Stat & AIC/BIC Formula.
Adjusted R-Squared (Adj R²): 0.71 Adj R² Adjusted R², F-Stat & AIC/BIC • Invariants & Metrics Adjusted R-Squared (Adj R²) 0.71 Adj R² Overall Model F-Statistic F( 73.929 F-stat Akaike Information Criterion -31.381 AIC Bayesian Information Criteri -17.443 BIC
Graph 2 • Adjusted R-Squared (Adj R²) Across Unadjusted R Squared Sweep (40% → 160%) Evaluates Adj_R² = 1 − [ (1 − R²)(n − 1) / (n − k − 1) ]; F = [ R² / k ] / [ (1 across 7 operating points (current input highlighted).
0 Adj R² 0.550 Adj R² 1.10 Adj R² 0.263 0.288R² 0.412 0.432R² 0.561 0.576R² 0.710 0.720R² 0.859 0.864R² 0.999 1.01R² 0.999 1.15R²
Graph 3 • Joint Sensitivity: Unadjusted R Squared × Sample Size N Compares Adjusted R-Squared (Adj R²) when Sample Size N is shifted +25% (solid) vs. −25% (dashed).
0 Adj R² 0.550 Adj R² 1.10 Adj R² --- Sample Size N @ 75% 0.490 -30% 0.601 -15% 0.712 +0% 0.823 +15% 0.934 +30%
Summary: With R² = 0.72, n = 120, and k = 4 predictors, Adjusted R² is 0.7103, overall F(4, 115) = 73.93, AIC = -31.38, and BIC = -17.44.
Summary: With R² = 0.72, n = 120, and k = 4 predictors, Adjusted R² is 0.7103, overall F(4, 115) = 73.93, AIC = -31.38, and BIC = -17.44.
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Formula & Mathematical Methodology: Adjusted R², F-Stat & AIC/BIC Formula

AdjR² = 1 − [ (1 − R²)n − 1n − k − 1 ]
F = R² / k1 − R²n − k − 1
Adj_R² = 1 − [ (1 − R²)(n − 1) / (n − k − 1) ]; F = [ R² / k ] / [ (1 − R²) / (n − k − 1) ]
  • unadjustedRSquared: Unadjusted R Squared (R²)
  • sampleSizeN: Sample Size N (n)
  • predictorCountK: Predictor Count K (predictors k)
  • residualSumOfSquaresRss: Residual Sum Of Squares Rss (RSS)

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: Adjusted R², F-Stat & AIC/BIC

Penalize R² for excess predictors via Adjusted R², overall F-test, AIC, and BIC.

  1. Specify the function parameters, matrix entries, or confusion matrix counts.
  2. Apply the closed-form or iterative formula: Adj_R² = 1 − [ (1 − R²)(n − 1) / (n − k − 1) ]; F = [ R² / k ] / [ (1 − R²) / (n − k − 1) ].
  3. Examine the primary result, error bounds, and 3 interactive SVG plots.
Result: Computes Adjusted R², F-Stat & AIC/BIC via Adj_R² = 1 − [ (1 − R²)(n − 1) / (n − k − 1) ]; F = [ R² / k ] / [ (1 − R²) / (n − k − 1) ].

Frequently Asked Questions

How does the Adjusted R², F-Statistic, Akaike (AIC) & Bayesian (BIC) Regression Model Calculator compute the solution?

It evaluates Adj_R² = 1 − [ (1 − R²)(n − 1) / (n − k − 1) ]; F = [ R² / k ] / [ (1 − R²) / (n − k − 1) ] 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

Adjusted R², F-Statistic, Akaike (AIC) & Bayesian (BIC) Regression Model Calculator: inputs, method, and how to read the result

Penalize R² for excess predictors via Adjusted R², overall F-test, AIC, and BIC.

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.

  • Unadjusted R Squared: Multiple coefficient of determination R² (0 to 0.999).
  • Sample Size N: Total observations n in the regression.
  • Predictor Count K: Number of independent explanatory variables k.
  • Residual Sum Of Squares Rss: Residual Sum of Squares (RSS / SSE) for AIC/BIC.

What the calculation includes

With the default values shown, Adjusted R-Squared (Adj R²) is 0.71 Adj R². The calculation follows Adjusted R², F-Stat & AIC/BIC Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Unadjusted R Squared from 0.72 R² to 0.79 R² changes Adjusted R-Squared (Adj R²) from 0.71 Adj R² to 0.783 Adj R². 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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