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.
| 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) |