Nonlinear Regression Shapes

Curve fitting, empirical modeling, and an appreciation of shape

The art of fitting a nonlinear regression model often starts with choosing a model form. This submission is an attempt to teach the reader a simple but general paradigm for their models as a sum of fundamental shapes that are then shifted and scaled to fit the data.

I've included a bestiary of fundamental forms, each of which has been plotted. Each form also has a description of some fundamental characteristics, such as limits and other special values.

Who might wish to read this submission? Anyone who is interested in fitting an empirical model to their (1-d) data, although many of the ideas in here are applicable to problems in higher dimensions too.

Please e-mail me of any errors I've made, as well as any interesting functional forms that I've failed to include in the bestiary.