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

doi:10.1007/BF02562669

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

Statistics (Twin Cities)

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	33-100
Number of pages	68
Journal	Test
Volume	2
Issue number	1-2
DOIs	https://doi.org/10.1007/BF02562669
State	Published - Dec 1993

Keywords

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

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10.1007/BF02562669

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title = "Exploring regression structure with graphics",

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.",

keywords = "Added variable plots, Dimension reduction subspaces, Graphical regression, Three-dimensional scatterplots, conditional independence",

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year = "1993",

month = dec,

doi = "10.1007/BF02562669",

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T1 - Exploring regression structure with graphics

AU - Cook, R. Dennis

AU - Wetzel, Nate

AU - Bermúdez, José D.

AU - De La Horra, J.

AU - Critchley, Frank

AU - Lavine, Michael

AU - Li, Ker Chau

AU - McCulloch, R. E.

AU - Morton, Sally C.

AU - Shen, X.

AU - Weisberg, Sanford

AU - Zacks, S.

PY - 1993/12

Y1 - 1993/12

N2 - 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.

AB - 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.

KW - Added variable plots

KW - Dimension reduction subspaces

KW - Graphical regression

KW - Three-dimensional scatterplots

KW - conditional independence

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Exploring regression structure with graphics

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