It is known that two-group linear discriminant function can be constructed via binary regression. In this article, it is shown that the opposite relation is also relevant – it is possible to present multiple regression as a linear combination of a main part, based on the pooled variance, and Fisher discriminators by data segments. Presenting regression as an aggregate of the discriminators allows one to decompose coefficients of the model into sum of several vectors related to segments. Using this technique provides an understanding of how the total regression model is composed of the regressions by the segments with possible opposite directions of the dependency on the predictors.
Lipovetsky, Stan and Conklin, Michael
"Regression By Data Segments Via Discriminant Analysis,"
Journal of Modern Applied Statistical Methods: Vol. 4
, Article 7.
Available at: http://digitalcommons.wayne.edu/jmasm/vol4/iss1/7