Non Linear Regression Calculator

Calculator

x values

Use commas, spaces, or new lines.

y values

Enter one y value for each x value.

Regression model

Try several models and compare fit scores.

Prediction x value

Leave blank if no prediction is needed.

Available outputs

Coefficients, fitted values, residuals, R squared, adjusted R squared, RMSE, MAE, MAPE, SSE, AIC, CSV, and PDF.

Model rules

Power needs positive x and y. Exponential needs positive y. Logarithmic and saturation need positive x values.

Example Data Table

x	y	Suggested model	Note
1	3.55	Exponential	Early growth point
2	5.03	Exponential	Curve rises smoothly
3	7.15	Exponential	Growth continues
4	10.14	Exponential	Higher fitted value expected
5	14.38	Exponential	Rate effect becomes visible
6	20.39	Exponential	Strong curve trend

Formula Used

The calculator uses least squares fitting. It minimizes the sum of squared residuals: SSE = sum(y - yhat)^2.

Exponential: y = a e^(bx), fitted with ln(y) = ln(a) + bx.
Power: y = a x^b, fitted with ln(y) = ln(a) + b ln(x).
Logarithmic: y = a + b ln(x).
Reciprocal: y = a + b/x.
Quadratic: y = a + bx + cx^2, fitted through normal equations.
Saturation: y = Vmax x / (Km + x), fitted with reciprocal transformation.

RMSE = sqrt(SSE / n). MAE is the average absolute residual. R squared = 1 - SSE / SST.

How to Use This Calculator

Enter x values in the first box.
Enter matching y values in the second box.
Select the nonlinear model that fits your situation.
Add a prediction x value if needed.
Press Calculate to view the result above the form.
Use CSV or PDF buttons to save the report.

Understanding Non Linear Regression

Non linear regression helps study data that bends, curves, levels off, or grows faster than a straight line. Many real processes behave this way. Population growth, cooling, enzyme activity, interest curves, and demand response often need curved models. This calculator gives a practical workspace for fitting common nonlinear patterns.

Why Curved Models Matter

A straight line is useful, but it can hide important behavior. A curve can show saturation, acceleration, decay, or diminishing returns. The selected model changes how each point is transformed before fitting. This keeps the tool simple while still giving strong estimates. You can test several equations and compare their fit scores.

How The Calculator Works

Enter paired x and y values in matching order. Choose a model from the list. The tool transforms the data when needed, solves the least squares equations, and rebuilds the fitted curve. It then shows coefficients, predicted values, residuals, and summary error measures. The prediction field estimates a new y value from any valid x value.

Interpreting The Results

The equation shows the model form and fitted constants. R squared describes how much variation is explained by the model. RMSE gives the typical prediction error in y units. MAE gives the average absolute error. SSE measures total squared error. A lower error usually means a closer fit, but the equation should also make sense for the subject.

Good Data Practices

Use enough data points for the chosen model. Avoid mixing units. Check that values meet model rules. For example, power and exponential models require positive y values. Power models also require positive x values. Outliers can strongly affect a curve. Review the residual table to spot unusual points. Document each chosen setting carefully.

Using Exports

CSV export is useful for spreadsheets and records. PDF export creates a quick text report for sharing. Both options preserve the main results, fitted values, and residuals. Keep exported reports with your project notes so calculations remain easy to review.

Final Notes

Non linear regression is not only about chasing the highest R squared. It is about choosing a curve that matches the process. Compare models, inspect residuals, and use domain knowledge. A clear curve can turn raw measurements into better decisions.

FAQs

What is non linear regression?

Non linear regression fits curved relationships between x and y. It estimates model constants so predicted values stay close to observed values.

Which model should I choose?

Choose the model that matches the process. Use exponential for growth or decay, power for scaling, logarithmic for slowing change, and saturation for leveling behavior.

Why do some models reject zero or negative values?

Some transformations use logarithms or reciprocals. Logarithms need positive values. Reciprocals cannot use zero because division by zero is undefined.

What does R squared mean?

R squared estimates how much variation the fitted curve explains. Higher values can be useful, but residuals and model meaning still matter.

What is RMSE?

RMSE is the square root of average squared error. It shows typical prediction error in the same unit as y.

Why is adjusted R squared included?

Adjusted R squared considers model size and data count. It helps compare models with different numbers of coefficients.

Can I export every fitted row?

Yes. The CSV export includes each x value, observed y value, fitted y value, and residual for spreadsheet review.

Can this replace statistical software?

It is useful for quick fitting and learning. For complex research, confidence intervals, and diagnostics, use dedicated statistical tools too.