Abstract
This handbook is a collection of linear and nonlinear models for fitting experimental data.
It is intended to help researchers fit appropriate curves to their data. Curve fitting, also known as regression analysis, is a common technique for modelling data. The simplest use of a regression model is to summarize the observed relationships in a particular set of data. More importantly, regression models are developed to describe the physical, chemical and biological processes in a system (Rawlings 1988).
This handbook is organized in the following manner:  Section 2 defines the terminology and briefly describes the general idea of regression.  Section 3 discusses the use of the SAS procedures PROC REG and PROC NLIN for linear and nonlinear curve fitting.  Section 4 presents eight classes of curves frequently used for modelling data. Each class contains several curves which are described in detail. For each curve, the equation, the derivatives, and the linearized form of the equation are provided, as well as sample plots and SAS programs for fitting the curve.  Section 5 explains how to use this handbook for curve fitting. Some strategies for selecting starting values and the concept of convergence are also discussed. Two examples are given to illustrate the curvefitting procedures.  Section 6 provides a brief introduction to various basic attributes of curves. Also included are the corresponding algebra and calculus for identifying these attributes. A strong statistical or calculus background is not required to use this handbook. Although the discussions and examples are based on SAS programs and assume some knowledge of programming, they should be of general interest for anyone fitting curves.
This handbook does not provide an indepth discussion of regression analysis. Rather, it should be used in conjunction with a reliable text on linear and nonlinear regression such as Ratkowsky (1983) or Rawlings (1988).
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Updated October 16, 2008
