# Non-Linear Regression Algorithm

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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.

## References

### 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.

### 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 $f$(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 $v = \frac{V_\max[\mbox{S}]}{K_m + [\mbox{S}]}$ can be written as $f(x,\boldsymbol\beta)= \frac{\beta_1 x}{\beta_2 + x}$ where $\beta_1$ is the parameter $V_\max$, $\beta_2$ is the parameter $K_m$ and [S] is the independent variable, x. This function is nonlinear because it cannot be expressed as a linear combination of the $\beta$s.