1. Regression Analysis 4e Montgomery, Peck & Vining
Chapter 12
Introduction to Nonlinear Regression
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Nonlinear Regression Models
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If the derivatives of the expectation function for a regression model still contains the parameters, then the function is nonlinear.
For example,
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Text also contains a famous example of a nonlinear model, the Clausius-Clapeyron Equation
Regression Analysis 4e Montgomery, Peck & Vining

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12.2 Nonlinear Least Squares
Regression Analysis 4e Montgomery, Peck & Vining

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12.2 Nonlinear Least Squares
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Example 12.1
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12.2 Nonlinear Least Squares
Geometry of Linear and Nonlinear Least Squares
Regression Analysis 4e Montgomery, Peck & Vining

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12.3 Transformation to a Linear Model
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12.3 Transformation to a Linear Model
If a transformation can be applied to the function, and the result is a linear function, we say the original function is “intrinsically linear”.
Regression Analysis 4e Montgomery, Peck & Vining

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Example 12.2 The Puromycin Data
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Example 12.2 The Puromycin Data
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Example 12.2 The Puromycin Data
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Example 12.2 The Puromycin Data
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Linearizing the model expectation function to produce a linear regression model did not produce a satisfactory result
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Estimation of the variance and the covariance matrix:
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How linearization works:
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Problems
May converge very slowly
S may actually increase or fail to converge
Dependence on the starting values of 0
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Alternative Methods of Estimation
Method of Steepest Descent
Fractional Increments
Marquardt’s Compromise
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