Some Examples of Non-Linear Regression

by W. B. Meitei, PhD

Asymptotic functions

           a. Michaelis-Menten

\[y = \frac{ax}{1 + bx}\]

           b. 2-parametric asymptotic exponential

\[y = a\left( 1 - e^{- bx} \right)\]

           c. 3-parametric asymptotic exponential

\[y = a - be^{- cx}\]

S-shaped functions

           a. 2-parameter logistic

\[y = \frac{e^{a + bx}}{1 + e^{a + bx}}\]

           b. 3-parameter logistic

\[y = \frac{a}{1 + {be}^{- cx}}\]

           c. 4-parameter logistic

\[y = a + \frac{b - a}{1 + e^{(c - x)/d}}\]

           d. Weibull

\[y = a - be^{- cx^{d}}\]

           e. Gompertz

\[y = ae^{- be^{cx}}\]

Humped curves

           a. Ricker curve

\[y = axe^{- bx}\]

           b. First-order compartment

\[y = ke^{- e^{a}x} - e^{- e^{b}x}\]

           c. Bell-shaped

\[y = ae^{{- |bx|}^{2}}\]

           d. Biexponential

\[y = ae^{bx} - ce^{- dx}\] 

Suggested Citation: Meitei, W. B. (2025). Some Examples of Non-Linear Regression. WBM STATS.