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Chapter 20

Non-Linear Regression

Sometimes we have a mechanistic model for the relationship between y and x, and we want to estimate the parameters and standard errors of the parameters of a specific non-linear equation from data. Some frequently used non-linear models are shown in Table 20.1. What we mean in this case by ‘non-linear’ is not that the relationship is curved (it was curved in the case of polynomial regressions, but these were linear models), but that the relationship cannot be linearized by transformation of the response variable or the explanatory variable (or both). Here is an example: it shows jaw bone length as a function of age in deer. Theory indicates that the relationship is an asymptotic exponential with three parameters:

Table 20.1 Useful non-linear functions.

 Name Equation Asymptotic functions Michaelis–Menten 2-parameter asymptotic exponential 3-parameter asymptotic exponential S-shaped functions 2-parameter logistic 3-parameter ...

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