## Nonlinear Regression |

Nonlinear regression is a statistical technique that helps describe nonlinear relationships in experimental data. Nonlinear regression models are generally assumed to be parametric, where the model is described as a nonlinear equation. Typically machine learning methods are used for non-parametric nonlinear regression.

Parametric nonlinear regression models the dependent variable (also called the response) as a function of a combination of nonlinear parameters and one or more independent variables (called predictors). The model can be univariate (single response variable) or multivariate (multiple response variables).

The parameters can take the form of an exponential, trigonometric, power, or any other nonlinear function. To determine the nonlinear parameter estimates, an iterative algorithm is typically used.

`y = f(X,β) + ε`

where, β represents nonlinear parameter estimates to be computed and ε represents the error terms.

Popular algorithms for fitting a nonlinear regression include:

- Gauss-Newton algorithm
- Gradient descent algorithm
- Levenberg-Marquardt algorithm

For these and other functions for parametric regression as well as for stepwise, robust, univariate, and multivariate regression, see Statistics Toolbox. It can be used to:

- Fit a nonlinear model to data and compare different models
- Generate predictions
- Evaluate parameter confidence intervals
- Evaluate goodness-of-fit

For nonparametric models using machine learning techniques such as neural networks, decision trees, and ensemble learning, see Neural Network Toolbox and Statistics Toolbox.

To create a model that fits curves, surfaces, and splines to data, see Curve Fitting Toolbox.

- Weighted Nonlinear Regression (Example)
- Data Driven Fitting with MATLAB 36:26 (Webinar)
- Nonparametric Fitting 4:07 (Video)
- Tips and Tricks: Data Analysis and Surface Fitting with MATLAB 42:33 (Webinar)
- Machine Learning with MATLAB 3:02 (Video)

- What Are Parametric Nonlinear Regression Models? (Documentation)
- Nonlinear Models (Documentation)
- Fitting a Nonlinear Model with MATLAB (Function)
- Interactive Modeling with MATLAB (Function)
- Predict or Simulate Responses to New Data (Documentation)

*See also*: *machine learning*, *linear regression*, *classification and ANOVA*, *data fitting*, *data analysis*, *mathematical modeling*