Calculator Input
Enter one to three regression models. Sample size, predictor count, and RSS are required for every model you want to compare.
Example Data Table
Use these sample values to test the calculator or compare your own models.
| Model | n | Predictors | Intercept | RSS | TSS | Expected BIC | Note |
|---|---|---|---|---|---|---|---|
| Model A | 120 | 2 | Yes | 540 | 1200 | 194.8518 | Simple model with higher error. |
| Model B | 120 | 4 | Yes | 410 | 1200 | 171.3773 | Best balance of fit and complexity. |
| Model C | 120 | 6 | Yes | 395 | 1200 | 176.4797 | Better fit, but heavier complexity penalty. |
Formula Used
This calculator uses the common regression-based Bayesian Information Criterion:
BIC = n × ln(RSS / n) + k × ln(n)
Where:
- n = sample size
- RSS = residual sum of squares
- k = total estimated parameters
- k = predictors + 1 when an intercept is included
The calculator also reports:
AIC = n × ln(RSS / n) + 2k
RMSE = √(RSS / n)
R² = 1 − RSS / TSS, when TSS is supplied.
Lower BIC values indicate a more efficient regression model. BIC rewards better fit, but it penalizes extra parameters more strongly than AIC.
How to Use This Calculator
- Enter a label for each regression model.
- Type the sample size used in model estimation.
- Enter the number of predictors in each model.
- Provide the residual sum of squares for each model.
- Add total sum of squares if you want R² values.
- Check the intercept box when the model estimates one.
- Click Calculate BIC Regression to compare models.
- Review rank, BIC, delta BIC, and model weights.
- Use the graph to inspect relative model performance.
- Download CSV or PDF for reports and documentation.
Frequently Asked Questions
1) What does BIC measure in regression?
BIC measures how well a regression fits the data while penalizing unnecessary complexity. Lower values usually indicate a stronger balance between prediction quality and model simplicity.
2) Why is a lower BIC better?
A lower BIC means the model achieves a better fit after accounting for the number of estimated parameters. It discourages overfitting by raising the score when complexity grows too much.
3) Should the intercept count as a parameter?
Yes, the intercept usually counts as an estimated parameter. That is why this calculator includes a checkbox for it. If your formulation omits the intercept, uncheck the option.
4) Can I compare models with different predictor counts?
Yes. BIC is designed for exactly that purpose. It helps compare simple and complex regressions on the same response data, as long as the models use the same dataset.
5) What is delta BIC?
Delta BIC is the difference between a model’s BIC and the lowest BIC in the comparison. Smaller differences suggest stronger competition with the best model.
6) Why does this calculator ask for RSS?
RSS is directly used in the regression form of the BIC equation. It summarizes unexplained variation after fitting the model. Smaller RSS usually improves the BIC result.
7) Is BIC better than AIC?
Neither is always better. BIC penalizes complexity more strongly, especially with larger samples. AIC often favors predictive accuracy, while BIC is commonly preferred for model selection discipline.
8) Can I use this tool for one model only?
Yes. You can enter one regression and calculate its BIC. Still, BIC becomes most useful when you compare several candidate models built on the same observations.