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 [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.