# Non-Linear Regression Algorithm

A Non-Linear Regression Algorithm is a parametric regression algorithm that can be applied by a non-linear regression system (that can solve a non-linear regression task by producing a regressed nonlinear function.

**Context:**- It can (typically) minimize a Non-Linear Least Squares (to produce a least squares regression line).
- It can range from being a Univariate Non-Linear Regression Algorithm to being a Multivariate Non-Linear Regression Algorithm.
- It can range from being a Simple Non-Linear Regression Algorithm to being a Robust Non-Linear Regression Algorithm.
- It can range from being a Continuous Non-Linear Regression Algorithm to being a Segmented Non-Linear Regression Algorithm.
- It can range from being an Ordinary Non-Linear Regression Algorithm (such as ordinary nonlinear least squares) to being a Regularized Non-Linear Regression Algorithm.
- It can often be based on a Nonlinear Function Approximation Algorithm.

**Example(s):****Counter-Example(s):****See:**Logistic Regression Algorithm, Hyperbolic Regression Algorithm, Non-Linear Least Squares.

## References

- http://onlineregression.sdsu.edu/onlineregression12.php
- http://onlineregression.sdsu.edu/onlineregression14.php

### 2015

- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/nonlinear_regression Retrieved:2015-4-30.
- In statistics,
**nonlinear regression**is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables. The data are fitted by a method of successive approximations.

- In statistics,

### 2011

- http://en.wikipedia.org/wiki/Nonlinear_regression
- In statistics,
**nonlinear regression**is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables. The data are fitted by a method of successive approximations.The data consist of error-free independent variables (explanatory variables),

*x*, and their associated observed dependent variables (response variables),*y*. Each*y*is modeled as a random variable with a mean given by a nonlinear function [math]f[/math](*x*,β). Systematic error may be present but its treatment is outside the scope of regression analysis. If the independent variables are not error-free, this is an errors-in-variables model, also outside this scope.For example, the Michaelis–Menten model for enzyme kinetics [math] v = \frac{V_\max[\mbox{S}]}{K_m + [\mbox{S}]} [/math] can be written as [math] f(x,\boldsymbol\beta)= \frac{\beta_1 x}{\beta_2 + x} [/math] where [math]\beta_1[/math] is the parameter [math]V_\max[/math], [math]\beta_2[/math] is the parameter [math]K_m[/math] and [

*S*] is the independent variable,*x*. This function is nonlinear because it cannot be expressed as a linear combination of the*[math]\beta[/math]*s.

- In statistics,