Retro-Regression – A Way to Resolve Multivariate Regression Ambiguities

Milan Randić^a,* and Matevž Pompe^b
a National Institute of Chemistry, Ljubljana, Slovenia & 3225 Kingman Rd. Ames, IA 50014, USA. E-mail: mrandic@msn.com
^b Faculty of Chemistry and Chemical Technology, University of Ljubljana, Aškerčeva 5, 1000 Ljubljana, Slovenia

Abstract
Stepwise multivariate regression analysis (MRA) is one of the oldest data reduction techniques. When optimal descriptors are selected at each step in a stepwise regression in MRA descriptors that have appeared in earlier steps may disappear and novel combinations of new descriptors may arise. This introduces difficulties in interpretation of the regression equations, because it is not possible to construct orthgonalized descriptors using stepwise regression. We outline a procedure to resolve the difficulties arising in selection of optimal descriptors in multivariate regression analysis which allows construction of orthogonal descriptors to accompany the regression obtained in the final step.

Key words: retro-regression, OSAR, boiling points