Recent advances in dimension reduction and visualization can greatly facilitate the exploratory and diagnostic stages of a regression analysis. This paper contains an expository discussion of selected methodology that came from these advances. Various applications are described, including new results on survival regressions with censoring. All of the methodology described in this paper is available in Arc, a recently released computer program that integrates many standard regression methods with recent developments in regression graphics. Arc implementations are indicated throughout the discussion.
- Central subspace
- Principal Hessian directions
- Sliced average variance estimation
- Sliced inverse regression