A difficult regression parameter estimation problem is posed when the data sample is hypothesized to have been generated by more than a single regression model. To find the best-fitting number and location of underlying regression systems, the investigator must specify both the statistical criterion and the search-estimation procedure to be used. The approach outlined in this article is essentially a wedding of hierarchical clustering and standard regression theory. As the name suggests, piecewise regression may be described as a method of finding that piecewise continuous function which best describes the data sample. Computational procedures and a fully-worked example, together with possible extensions, are provided.