A review and computer code for assessing the structural dimension of a regression model: uncorrelated 2D views

The general goal of a regression analysis is to understand how the conditional cdf F(y|x) of a response variable y varies as a set of predictors varies. The process of knowledge may gain advantage from the use of graphical data representations. Unfortunately, the so-called “curse of dimensionality” can make the use of graphics difficult. Nevertheless, many regression problems may have a relatively simple structural dimension, thus, it is possible to draw a plot in lower dimensions that contains all the essential information. Several graphical and non-graphical methodologies have been proposed in order to reduce the dimensionality of a regression problem. In this article we review a graphical method based on dynamic graphics, and present a computer implementation in the Xlisp-Stat programming language. Examples and a case study are given as an outline for performing a regression analysis.