DEFINITION of 'Nonlinear Regression'
A form of regression analysis in which data is fit to a model expressed as a mathematical function. Simple linear regression relates two variables (X and Y) with a straight line (y = mx + b), while nonlinear regression must generate a line (typically a curve) as if every value of Y was a random variable. The goal of the model is to make the sum of the squares as small as possible. Nonlinear regression uses logarithmic functions, trigonometric functions and exponential functions, among other fitting methods.
INVESTOPEDIA EXPLAINS 'Nonlinear Regression'
Nonlinear regression modeling is similar to linear regression modeling in that both seek to graphically track a particular response from a set of variables. Nonlinear models are more complicated than linear models to develop because the function is created through a series of approximations (iterations) that may stem from trialanderror. Mathematicians use several established methods, such as the GaussNewton method and the LevenbergMarquardt method.

Nonlinearity
A relationship which cannot be explained as a linear combination ... 
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Regression
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