Exploring regression structure with graphics

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

Research output: Contribution to journalArticle

12 Citations (Scopus)

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 1993
Externally publishedYes

Fingerprint

Regression
Predictors
Dimension-reduction Subspaces
Marginal Distribution
Conditional Distribution
Regression Analysis
Methodology
Graphics
Conditional distribution
Regression analysis
Dimension reduction

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

Cook, R. D., Wetzel, N., Bermúdez, J. D., De La Horra, J., Critchley, F., Lavine, M., ... Zacks, S. (1993). Exploring regression structure with graphics. Test, 2(1-2), 33-100. https://doi.org/10.1007/BF02562669

Exploring regression structure with graphics. / Cook, R. Dennis; Wetzel, Nate; Bermúdez, José D.; De La Horra, J.; Critchley, Frank; Lavine, Michael; Li, Ker Chau; McCulloch, Robert; Morton, Sally C.; Shen, X.; Weisberg, Sanford; Zacks, S.

In: Test, Vol. 2, No. 1-2, 12.1993, p. 33-100.

Research output: Contribution to journalArticle

Cook, RD, Wetzel, N, Bermúdez, JD, De La Horra, J, Critchley, F, Lavine, M, Li, KC, McCulloch, R, Morton, SC, Shen, X, Weisberg, S & Zacks, S 1993, 'Exploring regression structure with graphics', Test, vol. 2, no. 1-2, pp. 33-100. https://doi.org/10.1007/BF02562669
Cook RD, Wetzel N, Bermúdez JD, De La Horra J, Critchley F, Lavine M et al. Exploring regression structure with graphics. Test. 1993 Dec;2(1-2):33-100. https://doi.org/10.1007/BF02562669
Cook, R. Dennis ; Wetzel, Nate ; Bermúdez, José D. ; De La Horra, J. ; Critchley, Frank ; Lavine, Michael ; Li, Ker Chau ; McCulloch, Robert ; Morton, Sally C. ; Shen, X. ; Weisberg, Sanford ; Zacks, S. / Exploring regression structure with graphics. In: Test. 1993 ; Vol. 2, No. 1-2. pp. 33-100.
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