Calculator
Paste numeric data. Select response and predictors. Submit to compute BIC and diagnostics.
Example data table
The example below uses two predictors (X1, X2) and one response (Y).
| X1 | X2 | Y |
|---|---|---|
| 1 | 2 | 3 |
| 2 | 1 | 4 |
| 3 | 3 | 7 |
| 4 | 5 | 10 |
| 5 | 8 | 16 |
| 6 | 13 | 25 |
| 7 | 21 | 40 |
| 8 | 34 | 66 |
| 9 | 55 | 108 |
| 10 | 89 | 175 |
Formula used
This calculator fits an ordinary least squares regression and then computes a relative Bayesian Information Criterion score.
- RSS = Σ(y − ŷ)², where ŷ are model predictions.
- n = number of usable rows after cleaning.
- k = number of estimated parameters (and optionally +1 for variance).
- BIC (relative) = n ln(RSS/n) + k ln(n).
Constants that do not change between models are omitted, since BIC is primarily used to compare models fit on the same data.
How to use this calculator
- Paste your dataset in the textbox using a consistent delimiter.
- Click Parse Columns to populate the column selectors.
- Select your response (Y) and one or more predictors (X).
- Choose whether to include an intercept and whether k includes variance.
- Press Submit to see results above the form.
- Use CSV or PDF export buttons to save your output.
BIC selection
Bayesian Information Criterion helps rank regression models by trading off fit and complexity. This calculator reports a relative BIC score so you can compare different predictor sets on the same cleaned rows. Lower values generally indicate a better balance, especially as sample size increases. Because the penalty grows with ln(n), adding extra predictors must deliver meaningful error reduction to improve the ranking. Try several predictor subsets and keep the response column fixed. Compare results after removing weak predictors one by one.
Fit diagnostics
The output includes metrics that translate model performance into interpretable quantities. RSS measures total squared error, RMSE returns error in the original units, and MAE provides a robust average absolute deviation. R² summarizes explained variance, while adjusted R² corrects for additional predictors. Use these together to confirm that a lower BIC also aligns with practical predictive accuracy. Check residual size and sign to spot systematic underprediction. Also note leverage points.
Parameter count
BIC relies on k, the number of estimated parameters, as the complexity counter. In ordinary least squares, k equals the number of coefficients, including the intercept when enabled. Some conventions also count the error variance as an extra parameter; this tool includes an option for that choice. When models are close, small differences in k can change which specification is preferred. Keep the same k rule across all runs for fairness.
Data and sample size
Rows containing missing or non-numeric values are skipped to keep matrix calculations stable. The resulting n directly influences both the penalty term and the reliability of coefficient estimates. If many rows are removed, check delimiters, decimals, and empty cells. For credible comparisons, keep n comfortably larger than k and avoid selecting more predictors than the dataset can support without collinearity. Aim for at least ten times more rows than parameters.
Exports and reporting
Results are designed for documentation: coefficient estimates, standard errors, and a compact actual-versus-predicted preview help validate plausibility. Exporting CSV supports versioning in spreadsheets, and the PDF snapshot is useful for reviews and reports. When comparing models, export each run and record the predictor list and intercept choice so the BIC ranking remains traceable and reproducible over time. Save exports per model to support peer review and audits.
FAQs
1) What does a lower BIC mean?
Lower BIC usually means a better balance of fit and simplicity for models trained on the same rows and response. Use it to rank alternative predictor sets under consistent settings.
2) Can I compare BIC across different datasets?
It’s not recommended. BIC comparisons are most reliable when models share the same n, the same response, and the same cleaned dataset. Different scales and samples can distort interpretation.
3) Why are some rows skipped?
A row is skipped if any selected column is missing or not numeric. This prevents invalid matrix operations and ensures the reported n matches the data actually used for estimation.
4) What triggers a singular matrix error?
Singularity often occurs when predictors are redundant or highly collinear, or when k is too large for n. Remove overlapping predictors, reduce the model size, or use more data.
5) Should I include the intercept?
Include it in most cases. Excluding the intercept forces the line through zero, which can bias coefficients and inflate residuals if the true baseline is not zero.
6) What does “Count variance in k” do?
Some BIC definitions treat the error variance as an estimated parameter. Turning this on adds one to k. It can influence rankings when models are closely matched, especially with smaller samples.