- published: 22 Aug 2015
- views: 3123
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
can be written as
where Failed to parse (Missing texvc executable; please see math/README to configure.): \beta_1
, Failed to parse (Missing texvc executable; please see math/README to configure.): \beta_2