The dr package

The dr package for R for dimension reduction regression was first docu- mented in Weisberg (2002). This is a revision of that article, to correspond to version 3.0.0 of dr for R added to CRAN (cran.r-project.org) in Fall 2007. Regression is the study of the dependence of a response variable y on a collection of p predictors collected in x. In dimension reduction re- gression, we seek to find a few linearly independent linear combinations fl01x,...,fl 0 dx, such that all the information about the regression is con- tained in these d linear combinations. If d is very small, perhaps one or two, then the regression problem can be summarized using simple graph- ics; for example, for d = 1, the plot of y versus fl0 1x contains all the regression information. When d = 2, a 3D plot contains all the informa- tion. Formal estimation methods can additionally be used given the lower dimensional problem based on the few linear combinations. The primary goals of dimension reduction regression are determining the dimension d, and estimating fl1,...,fld, or more precisely the sub- space of

d0, without restriction on the subspaces involved other than their dimension. The first of these tests was proposed by Li (1991) in his paper on sir. Added to Version 3.0.0 are tests of coordinate hypotheses, proposed by Cook (2004), which eectively provides a test for elimination of predic- tors to reduce dimension, although the method is more general than this. These latter tests provide the basis for stepwise elimination of predictors. These tests are available in dr for methods sir, save, and ire.