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# Curve Fitting: Fitting Functions to Agricultural and Biological Data

Published by the American Society of Agricultural and Biological Engineers, St. Joseph, Michigan www.asabe.org

Citation:  Computers in Agriculture and Natural Resources, 4th World Congress Conference, Proceedings of the 24-26 July 2006 (Orlando, Florida USA) Publication Date 24 July 2006  701P0606.(doi:10.13031/2013.21946)
Authors:   José Boaventura Cunha
Keywords:   Data fitting, Least squares algorithm, Linear regression, Nonlinear regression

Agricultural Engineers and Biologists often need to develop and use functions in order to explain observed events, perform predictions under different scenarios, find relevant characteristics of the data, such as growth rates, etc.. The purpose of curve fitting is to specify an appropriate function and adjust its parameters in a way that it matches, as close as possible, an experimental or historical data set. Fitting functions can be derived by applying regression techniques, interpolation, and spline curves. This paper deals with the development and application of linear and nonlinear regression techniques for fitting functions to agricultural and biological data sets. The application and utility of these fitting techniques are illustrated using experimental sets of data. The examples cover from simple linear curve fitting techniques, which use least squares algorithms, to complex real world problems, which must be described by functions that are nonlinear in the parameters and so needs the use of nonlinear regression techniques. In these illustrative examples, a particular attention is paid to the validation and adequacy of the fitting functions, using graphical inspection and numerical performance criterias, such as: statistical analysis of the residuals, the R-square, adjusted R-square, the RMSE-Root mean squared errors, confidence bounds for the estimated function parameters and prediction bounds for the fitted functions.