Nonlinear Regression

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Describe nonlinear relationships and make predictions from experimental data


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).


y = f(X,β) + ε


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.

Examples and How To

Software Reference

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