Illustrating How Science Can Be Incorporated into a Nonlinear Regression Model

ABSTRACT We show the value of using available scientific knowledge in developing a data model for the simple example of drop heights of balls subject to drag. The science-based data model is a nonlinear regression model, where the mean is a solution to a differential equation. We contrast its analysis results with those from an empirical model. MATLAB code for fitting the science-based data model is also provided.