Curve Fitting & Nonlinear Regression (Statistical Associates

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Curve Fitting & Nonlinear Regression (Statistical Associates Blue Book Series 25)

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. Coverage: SPSS.

The full content is now available from Statistical Associates Publishers. http://www.statisticalassociates.com.

Below is the unformatted table of contents.

CURVE FITTING AND NONLINEAR REGRESSION

Table of Contents

Overview5
Curve Fitting5
Key Concepts and Terms5
Curve Estimation dialog in SPSS5
Models6
Statistical output for the SPSS curve estimation module19
Comparative fit plots19
Regression coefficients20
R-square21
Analysis of variance table21
Saved variables23
Curve Estimation Assumptions23
Data dimensions23
Data level24
Randomly distributed residuals24
Independence24
Normality24
Curve Fitting: Frequently Asked Questions24
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 Regression32
Overview32
Key Concepts and Terms33
Linearization33
Nonlinear regression example36
Entering a model36
Parameters37
Other input options38
Statistical Output41
Parameter Estimates Table42
Correlation of Parameter Estimates Table43
ANOVA Table and R244
Modeling multiple individuals44
Overview44
Data setup44
Segmented models46
Conditional logic statements46
Alternative models as multiple conditions46
Nonlinear regression assumptions47
Data level47
Proper specification47
Nonlinear regression: Frequently asked questions48
Bibliography51
Pagecount: 53
Country USA
Manufacturer Statistical Associates Publishers
Binding Kindle Edition
ReleaseDate 2012-08-29
Format Kindle eBook

Country	USA
Manufacturer	Statistical Associates Publishers
Binding	Kindle Edition
ReleaseDate	2012-08-29
Format	Kindle eBook

Curve Fitting & Nonlinear Regression (Statistical Associates Blue Book Series 25)

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