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Exploring regression structure with graphics

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Summary

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 asgraphical 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.

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Authors and Affiliations

  1. Department of Applied Statistics, University of Minnesota, 55108, St. Paul, Minnesota, USA

    R. Dennis Cook

  2. SUNY-Binghamton, Department of Mathematical Sciences, 13902, Binghamton, NY, USA

    Nate Wetzel

  3. University of Valencia, Spain

    José D. Bermúdez

  4. Universidad Autónoma de Madrid, Spain

    J. De La Horra

  5. University of Birmingham, UK

    Frank Critchley

  6. Duke University, USA

    Michael Lavine

  7. UCLA, USA

    Ker-Chau Li

  8. University of Chicago, USA

    R. E. McCulloch

  9. RAND, USA

    Sally C. Morton

  10. The Ohio State University, USA

    X. Shen

  11. University of Minnesota, USA

    Sanford Weisberg

  12. Binghamton University, USA

    S. Zacks

Authors
  1. R. Dennis Cook
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  2. Nate Wetzel
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  3. José D. Bermúdez
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  4. J. De La Horra
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  5. Frank Critchley
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  6. Michael Lavine
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  7. Ker-Chau Li
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  8. R. E. McCulloch
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  9. Sally C. Morton
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  10. X. Shen
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  11. Sanford Weisberg
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  12. S. Zacks
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Additional information

Read before the Spanish Statistical Society at a meeting organized by the Carlos III University of Madrid on Wednesday, April 21, 1993

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Cook, R.D., Wetzel, N., Bermúdez, J.D. et al. Exploring regression structure with graphics. Test 2, 33–100 (1993). https://doi.org/10.1007/BF02562669

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  • DOI: https://doi.org/10.1007/BF02562669

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