Exploring regression structure with graphics

R. Dennis Cook, Nate Wetzel, José D. Bermúdez, J. De La Horra, Frank Critchley, Michael Lavine, Ker Chau Li, R. E. McCulloch, Sally C. Morton, X. Shen, Sanford Weisberg, S. Zacks

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

We investigate the extent to which it may be possible to carry out a regression analysis using graphics alone, an idea that we refer to as graphical regression. The limitations of this idea are explored. It is shown that graphical regression is theoretically possible with essentially no constraints on the conditional distribution of the response given the predictors, but with some conditions on marginal distribution of the predictors. Dimension reduction subspaces and added variable plots play a central role in the development. The possibility of useful methodology is explored through two examples.

Original languageEnglish (US)
Pages (from-to)33-100
Number of pages68
JournalTest
Volume2
Issue number1-2
DOIs
StatePublished - Dec 1 1993
Externally publishedYes

Keywords

  • Added variable plots
  • Dimension reduction subspaces
  • Graphical regression
  • Three-dimensional scatterplots
  • conditional independence

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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  • Cite this

    Cook, R. D., Wetzel, N., Bermúdez, J. D., De La Horra, J., Critchley, F., Lavine, M., Li, K. C., McCulloch, R. E., Morton, S. C., Shen, X., Weisberg, S., & Zacks, S. (1993). Exploring regression structure with graphics. Test, 2(1-2), 33-100. https://doi.org/10.1007/BF02562669