Comment: Fisher Lecture: Dimension Reduction in Regression.

The author comments on the paper "Fisher Lecture: Dimension Reduction in Regression," by R. D. Cook. The paper develops a theoretical foundation for exploring principal components and other dimension reduction methods in a regression context. It reports to a model, via the inverse regression of predictors, to analyze reduction in a forward regression problem. It also allows extension to mixtures of predictors. The role of predictor screening and a connection with the supervised principal components method are explored.