# Nonlinear Regression Common Models

The table below provides example model syntax for many published nonlinear regression models. A model selected at random is not likely to fit your data well. Appropriate starting values for the parameters are necessary, and some models require constraints in order to converge.

Table 1. Example model syntax
Name Model expression
Asymptotic Regression b1 + b2 * exp(b3 * x)
Asymptotic Regression b1 – (b2 * (b3 ** x))
Density (b1 + b2 * x) ** (–1 / b3)
Gauss b1 * (1 – b3 * exp(–b2 * x ** 2))
Gompertz b1 * exp(–b2 * exp(–b3 * x))
Johnson-Schumacher b1 * exp(–b2 / (x + b3))
Log-Modified (b1 + b3 * x) ** b2
Log-Logistic b1 – ln(1 + b2 * exp(–b3 * x))
Metcherlich Law of Diminishing Returns b1 + b2 * exp(–b3 * x)
Michaelis Menten b1 * x / (x + b2)
Morgan-Mercer-Florin (b1 * b2 + b3 * x ** b4) / (b2 + x ** b4)
Peal-Reed b1 / (1+ b2 * exp(–(b3 * x + b4 * x **2 + b5 * x ** 3)))
Ratio of Cubics (b1 + b2 * x + b3 * x ** 2 + b4 * x ** 3) / (b5 * x ** 3)
Ratio of Quadratics (b1 + b2 * x + b3 * x ** 2) / (b4 * x ** 2)
Richards b1 / ((1 + b3 * exp(–b2 * x)) ** (1 / b4))
Verhulst b1 / (1 + b3 * exp(–b2 * x))
Von Bertalanffy (b1 ** (1 – b4) – b2 * exp(–b3 * x)) ** (1 / (1 – b4))
Weibull b1 – b2 * exp(–b3 * x ** b4)
Yield Density (b1 + b2 * x + b3 * x ** 2) ** (–1)