Enter regression inputs
Example data table
| X | Y | Interpretation |
|---|---|---|
| 1 | 3.2 | Starting response value |
| 2 | 5.1 | Moderate upward curvature begins |
| 3 | 7.8 | Growth accelerates further |
| 4 | 11.4 | Nonlinear trend becomes visible |
| 5 | 16.1 | Higher-order fit may help |
| 6 | 22.3 | Curve rises strongly at larger x |
Formula used
The tool minimizes the sum of squared errors:
SSE = Σ(yi - ŷi)².
The best fit is the model with the highest useful explanatory power and lower error.
Supported equations
Quadratic: y = a + bx + cx²Cubic: y = a + bx + cx² + dx³Exponential: y = ae^(bx)Power: y = ax^bLogarithmic: y = a + b ln(x)Inverse: y = a + b/x
The page also reports R², Adjusted R², RMSE,
MAE, MAPE, AIC, and BIC for easier comparison.
How to use this calculator
- Enter one x,y pair per line in the data area.
- Name the dataset and label each axis clearly.
- Choose Auto to compare all supported curve families.
- Pick a manual model when theory suggests one pattern.
- Optionally enter a future x value for prediction.
- Submit the form to view results above the inputs.
- Review coefficients, diagnostics, residuals, and the fitted chart.
- Export the summary and prediction table as CSV or PDF.
Frequently asked questions
1. What does nonlinear regression do?
It finds a curve that best explains how one variable changes with another when a straight line is not suitable. The goal is to reduce squared prediction errors while keeping the model interpretable.
2. Which model should I choose first?
Start with Auto when you are exploring patterns. Use a manual model only when domain knowledge already suggests exponential growth, logarithmic response, inverse decay, or polynomial curvature.
3. Why can some models fail to fit?
Some equations need valid domains. Power and logarithmic models require positive x values, exponential and power need positive y values, and inverse models cannot use x equal to zero.
4. What is the difference between RMSE and MAE?
RMSE penalizes large mistakes more heavily because residuals are squared before averaging. MAE treats every absolute error equally, so it is often easier to interpret in original units.
5. Is the highest R² always the best choice?
Not always. A model can score a high R² yet overfit. That is why the tool also reports adjusted R², error measures, residuals, and information criteria for balance.
6. Can I use this tool for forecasting?
Yes, but predictions are only as reliable as the underlying relationship and data range. Forecasts far outside observed x values should be checked carefully against theory and real-world limits.
7. What does the residual table tell me?
Residuals show the gap between observed and predicted values. Random, small residuals usually indicate a better fit, while obvious patterns may suggest that another curve family is more appropriate.
8. Why export CSV or PDF results?
CSV makes it easy to continue analysis in spreadsheet tools. PDF helps share a fixed report containing the chosen model, diagnostics, coefficients, and point-by-point prediction results.