CURVE FITTING & NONLINEAR REGRESSION

Overview

Both curve fitting and nonlinear regression are methods of finding a best-fit line to a set of data points even when the best-fit line is nonlinear.

Below, curve-fitting is discussed with respect to the SPSS curve estimation module, obtained by selecting Analyze > Regression > Curve Estimation. This module can compare linear, logarithmic, inverse, quadratic, cubic, power, compound, S-curve, logistic, growth, and exponential models based on their relative goodness of fit where a single dependent variable is predicted by a single independent variable or by a time variable. As such it is a useful exploratory tool preliminary to selecting multivariate models in generalized linear modeling, which supports nonlinear link functions. (Generalized linear modeling is treated in a separate Statistical Associates "Blue Book" volume).

The province of nonlinear regression is fitting curves to data which cannot be fitted using nonlinear transforms of the independent variables or by nonlinear link functions which transform the dependent variable. This type of data is "intrinsically nonlinear" and requires approaches treated in a second section of this e-book, which covers nonlinear regression in SPSS, obtained by selecting Analyze > Regression > Nonlinear.

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Below is the unformatted table of contents.

CURVE FITTING AND NONLINEAR REGRESSION

Table of Contents

Overview	5
Curve Fitting	5
Key Concepts and Terms	5
Curve Estimation dialog in SPSS	5
Models	6
Statistical output for the SPSS curve estimation module	19
Comparative fit plots	19
Regression coefficients	20
R-square	21
Analysis of variance table	21
Saved variables	23
Curve Estimation Assumptions	23
Data dimensions	23
Data level	24
Randomly distributed residuals	24
Independence	24
Normality	24
Curve Fitting: Frequently Asked Questions	24
Can the SPSS Curve Estimation module tell me what type of model I need (ex., linear, logarithmic, exponential)?	24
I want to use, from the Curve Estimation module, the two best functions of my independent in a regression equation, but will this introduce multicollinearity?	30
What software other than SPSS is available for curve fitting?	30
Nonlinear Regression	32
Overview	32
Key Concepts and Terms	33
Linearization	33
Nonlinear regression example	36
Entering a model	36
Parameters	37
Other input options	38
Statistical Output	41
Parameter Estimates Table	42
Correlation of Parameter Estimates Table	43
ANOVA Table and R2	44
Modeling multiple individuals	44
Overview	44
Data setup	44
Segmented models	46
Conditional logic statements	46
Alternative models as multiple conditions	46
Nonlinear regression assumptions	47
Data level	47
Proper specification	47
Nonlinear regression: Frequently asked questions	48
Bibliography	51