Empirical Modeling: Choosing Models and Fitting Them to Data

Abstract

SummaryTreatments in mathematics books of how to select models and fit them to data have generally not been updated to account for improvements in knowledge and computing over the last 40 years. Here, we offer a derivation of the linear least squares formula that requires only precalculus and use it to develop a simple numerical method for fitting a broad class of nonlinear functions, with results that are far superior to methods in common practice. We also discuss the use of the Akaike information criterion (AIC) to choose among competing models that have been fit to a common data set.