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