Piecewise regression

For a relationship between a response variable (Y) and an explanatory variable (X), different linear relationships may apply for different ranges of X. A single linear model will not provide an adequate description of the relationship. Often a non-linear model will be most appropriate in this situation, but sometimes there is a clear break point demarcating two different linear relationships. Piecewise linear regression is a form of regression that allows multiple linear models to be fitted to the data for different ranges of X.

The regression function at the breakpoint may be discontinuous, but it is possible to specify the model such that the model is continuous at all points. For such a model the two equations for Y need to be equal at the breakpoint. Non-linear least squares regression techniques can be used to fit the model to the data.

A useful tutorial on piecewise linear regression is provided by Ryan & Porth (2007).