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Visualizing 1D Regression

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Theory and Applications of Recent Robust Methods

Part of the book series: Statistics for Industry and Technology ((SIT))

Abstract

Regression is the study of the conditional distribution of the response y given the predictors x. In a 1D regression, y is independent of x given a single linear combination βT x of the predictors. Special cases of 1D regression include multiple linear regression, binary regression and generalized linear models. If a good estimate b of some non-zero multiple cβ of β can be constructed, then the 1D regression can be visualized with a scatterplot of b T x versus y. A resistant method for estimating cβ is presented along with applications.

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References

  1. G. E. P. Box and D. R. Cox, An Analysis of Transformations. J. Roy. Statist. Soc. Ser. B Stat. Methodol. 26 (1964), 211–246.

    MathSciNet  MATH  Google Scholar 

  2. D. R. Brillinger, The Identification of a Particular Nonlinear Time Series. Biometrika 64 (1977), 509–515.

    Article  MathSciNet  MATH  Google Scholar 

  3. D. R. Brillinger, A Generalized Linear Model with “Gaussian” Regressor Variables. In P. J. Bickel, K. A. Doksum, and J. L. Hodges, editors, A Festschrift for Erich L. Lehmann, pages 97–114. Wadsworth, Pacific Grove, CA, 1983.

    Google Scholar 

  4. J. M. Chambers, W. S. Cleveland, B. Kleiner, and P. Tukey. Graphical Methods for Data Analysis. Duxbury Press, Boston, 1983.

    MATH  Google Scholar 

  5. R. D. Cook, Deletion of Influential Observations in Linear Regression. Technometrics 19 (1977), 15–18.

    Article  MathSciNet  MATH  Google Scholar 

  6. R. D. Cook, Regression Graphics: Ideas for Studying Regression Through Graphics. John Wiley and Sons, New York, 1998.

    MATH  Google Scholar 

  7. R. D. Cook, Principal Hessian Directions Revisited. J. Amer. Statist. Assoc. 93 (1998), 84–100.

    Article  MathSciNet  MATH  Google Scholar 

  8. R. D. Cook, SAVE: A Method for Dimension Reduction and Graphics in Regression. Comm. Statist. Theory Methods 29 (2000), 2109–2121.

    Article  MATH  Google Scholar 

  9. R. D. Cook, D. M. Hawkins, and S. Weisberg, Comparison of Model Misspecification Diagnostics Using Residuals from Least Mean of Squares and Least Median of Squares. J. Amer. Statist. Assoc. 87 (1992), 419–424.

    Article  MathSciNet  Google Scholar 

  10. R. D. Cook and B. Li, Dimension Reduction for Conditional Mean in Regression. Ann. Statist. 30 (2002), 455–474.

    Article  MathSciNet  MATH  Google Scholar 

  11. R. D. Cook and C. J. Nachtsheim, Reweighting to Achieve Elliptically Contoured Co-variates in Regression. J. Amer. Statist. Assoc. 89 (1994), 592–599.

    Article  MATH  Google Scholar 

  12. R. D. Cook and D. J. Olive, A Note on Visualizing Response Transformations in Regression. Technometrics 43 (2001), 443–449.

    Article  MathSciNet  Google Scholar 

  13. R. D. Cook and S. Weisberg, Transforming a Response Variable for Linearity. Biometrika 81 (1994), 731–737.

    Article  MATH  Google Scholar 

  14. R. D. Cook and S. Weisberg, Applied Regression Including Computing and Graphics. John Wiley and Sons, New York, 1999.

    Book  MATH  Google Scholar 

  15. R. D. Cook and S. Weisberg, Graphs in Statistical Analysis: Is the Medium the Message? Amer. Statist. 53 (1999), 29–37.

    Google Scholar 

  16. W. K. Fung, X. He, L. Liu, and P. D. Shi, Dimension Reduction Based on Canonical Correlation. Statist. Sinica 12 (2002), 1093–1114.

    MathSciNet  MATH  Google Scholar 

  17. U. Gather, T. Hilker, and C. Becker, A Note on Outlier Sensitivity of Sliced Inverse Regression. Statistics 36 (2002), 271–281.

    Article  MathSciNet  MATH  Google Scholar 

  18. D. M. Hawkins, D. Bradu, and G. V. Kass, Location of Several Outliers in Multiple Regression Data Using Elemental Sets. Technometrics 26 (1984), 197–208.

    Article  MathSciNet  Google Scholar 

  19. K. C. Li, Sliced Inverse Regression for Dimension Reduction. J. Amer. Statist. Assoc. 86 (1991), 316–342.

    Article  MathSciNet  MATH  Google Scholar 

  20. K. C. Li and N. Duan, Regression Analysis Under Link Violation. Ann. Statist. 17 (1989), 1009–1052.

    Article  MathSciNet  MATH  Google Scholar 

  21. D. J. Olive, Applications of Robust Distances for Regression. Technometrics 44 (2002), 64–71.

    Article  MathSciNet  Google Scholar 

  22. P. J. Rousseeuw and A. M. Leroy, Robust Regression and Outlier Detection. John Wiley and Sons, New York, 1987.

    Book  MATH  Google Scholar 

  23. P. J. Rousseeuw and K. Van Driessen, A Fast Algorithm for the Minimum Covariance Determinant Estimator. Technometrics 41 (1999), 212–223.

    Article  Google Scholar 

  24. T. M. Stoker, Consistent Estimation of Scaled Coefficients. Econometrica 54 (1986), 1461–1481.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Southern Illinois University, Mailcode 4408, Carbondale, IL, 62901-4408, USA

    D. J. Olive

Authors
  1. D. J. Olive
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Katholieke Universiteit Leuven, W. de Croylaan 54, 3001, Leuven, Belgium

    Mia Hubert

  2. Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 S9, 9000, Gent, Belgium

    Greet Pison  & Stefan Van Aelst  & 

  3. Department of Mathematics and Computer Science, University of Antwerp, Middelheimlaan 1, 2020, Antwerp, Belgium

    Anja Struyf

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© 2004 Springer Basel AG

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Olive, D.J. (2004). Visualizing 1D Regression. In: Hubert, M., Pison, G., Struyf, A., Van Aelst, S. (eds) Theory and Applications of Recent Robust Methods. Statistics for Industry and Technology. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7958-3_20

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  • DOI: https://doi.org/10.1007/978-3-0348-7958-3_20

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9636-8

  • Online ISBN: 978-3-0348-7958-3

  • eBook Packages: Springer Book Archive

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