Nonlinear Regression Calculator

Free nonlinear regression calculator. Fit logarithmic, inverse, square-root, and Michaelis-Menten curves with step-by-step solutions, R², and graphs. Browser-based privacy.

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Nonlinear Regression Calculator

Free nonlinear regression calculator. Fit logarithmic, inverse, square-root, and Michaelis-Menten curves with step-by-step solutions, R², and graphs. Browser-based privacy.

Model

Enter your data points

#	X	Y

Results

Equation

R²

Predicted Y

For X = —

Statistics

Statistic	Value
Standard Error
Sample Size (n)
Degrees of Freedom

Chart

Step-by-Step Solution

Como usar isto Nonlinear Regression Calculator

Crescimento e decaimento

Fit logarithmic, inverse, square-root, and Michaelis-Menten curves with automatic linearization.

Dados de entrada

Enter paired X and Y values. Minimum 2 points required. Watch model constraints (e.g., x > 0 for log).

Saída estatística

Get model parameters, R², standard error, predictions, and step-by-step transformations.

Choose the simplest model that captures your data. Overly complex models overfit noise.

What Is Nonlinear Regression?

📐 Nonlinear regression fits relationships where the effect of the predictor on the response follows a curved, bounded, or saturating pattern that a straight line cannot capture. Unlike polynomial regression — which bends freely — nonlinear models are chosen because they express known scientific laws.

📊 This calculator supports four common nonlinear models:

Logarithmic — growth slows continuously (e.g., diminishing returns in marketing)
Inverse — response decays with reciprocal distance (e.g., gravity, electrostatic force)
Square Root — effect grows but at a decelerating rate (e.g., resource allocation)
Michaelis-Menten — enzyme kinetics and saturating processes (e.g., reaction rates plateau as substrate concentration rises)

📐 Each model is linearized mathematically so ordinary least squares can be applied, then parameters are transformed back to the original scale.

How Nonlinear Regression Works

1
Select a model: Choose logarithmic, inverse, square-root, or Michaelis-Menten based on the expected shape of your data.
2
Transform the data: Apply a mathematical transformation that converts the nonlinear equation into a straight line. For example, logarithmic regression transforms X to ln(x) and then fits y = a + b·ln(x).
3
Fit ordinary least squares (OLS): Apply linear regression to the transformed variables. The slope and intercept give the parameters of the original nonlinear model.
4
Back-transform parameters: Convert regression coefficients into the natural parameters of the chosen model (e.g., Vmax and Km for Michaelis-Menten).
5
Evaluate on the original scale: Compute predicted values using the original (non-transformed) equation, then calculate R², standard error, and residuals to assess real-world fit.

When to Use Nonlinear Regression

The relationship follows a known physical, biological, or economic law (e.g., enzyme kinetics, inverse-square laws)
Polynomial curves wiggle unrealistically while a simpler nonlinear form captures the trend smoothly
The response naturally saturates, decays, or grows at a decelerating rate
You need parameters with direct scientific meaning (e.g., Vmax, Km, carrying capacity)

When to Avoid Nonlinear Regression

When a simple straight line or low-degree polynomial already explains the data well
When the chosen model’s constraints are violated (e.g., x ≤ 0 for logarithmic, x = 0 for inverse)
When data is sparse — nonlinear models can be unstable with few points
When the true relationship is periodic, oscillatory, or has multiple inflection points not covered by these models

Nonlinear Regression Calculator