Skip to main content

Independent Variable Selection in Multiple Regression

  • Chapter
Prescriptions for Working Statisticians

Part of the book series: Springer Texts in Statistics ((STS))

Abstract

The data analyst confronted with a large number of variables from which he must select a parsimonious subset, as independent variables in a multiple regression, is faced with a number of technical issues. What criterion should he use to judge the adequacy of his selection? What procedure should he use to select the subset of independent variables? How should he check for/guard against/correct for possible multicollinearity in his chosen set of independent variables?

“Stepwise regression can lead to confusing results...”

Daniel and Wood ([1980], p. 85)

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Abt, K. 1967. On the identification of the significant independent variables in linear models. Metrika 12: 2–15.

    MathSciNet  Google Scholar 

  • Akaike, H. 1972. Information theory and an extension of the maximum likelihood principle. Proceedings, Second International Symposium on Information. Theory, 267–81.

    Google Scholar 

  • Allen, D. M. 1971. The prediction sum of squares as a criterion for selecting prediction variables. Technical Report 23. Department of Statistics. University of Kentucky.

    Google Scholar 

  • Allen, D. M. 1974. The relationship between variable selection and data augmentation and a method for prediction. Technometrics 16 (February): 125–27.

    Article  MathSciNet  MATH  Google Scholar 

  • Amemiya, T. 1976. Selection of regressors. Technical Report 225. Institute for Mathematical Studies in the Social Sciences. Stanford University.

    Google Scholar 

  • Beaton, A. E. 1964. The use of special matrix operators in statistical calculus. Research Bulletin RB 64 51 (October). Princeton: Educational Testing Service.

    Google Scholar 

  • Bendel, R. B. and Afifi, A. A. 1977. Comparison of stopping rules in forward “Stepwise” regression. Journal of the American Statistical Association 72 (March): 46–53.

    Article  MATH  Google Scholar 

  • Daniel, C. and Wood, F. S. 1980. Fitting Equations to Data. New York: Wiley.

    MATH  Google Scholar 

  • Draper, N. R. and Smith, H. 1966. Applied Regression Analysis. New York: Wiley.

    Google Scholar 

  • Dunnett, C. W. and Sobel, M. 1954. A bivariate generalization of Student’s distribution, with tables for certain special cases. Biometrika 41 (April): 153–69.

    MathSciNet  MATH  Google Scholar 

  • Efroymson, M. A. 1962. Multiple regression analysis. In Mathematical Methods for Digital Computers, ed. A. Ralston, and H. S. Wilf. New York: Wiley.

    Google Scholar 

  • Fisher, R. A. 1934. Statistical Methods for Research Workers. New York: Hafner.

    Google Scholar 

  • Goldstein, M. and Smith, A. F. M. 1974. Ridge type estimators for regression analysis. Journal of the Royal Statistical Society, Series B 36 (December): 284–91.

    MathSciNet  MATH  Google Scholar 

  • Goodnight, J. H. 1979. A tutorial on the SWEEP operator. American Statistician 33 (August): 149–58.

    Article  MATH  Google Scholar 

  • Gorman, J. W. and Toman, R. J. 1966. Selection of variables for fitting equations to data. Technometrics 8 (February): 27–51.

    Article  Google Scholar 

  • Hocking, R. R. 1972. Criteria for selection of a subset regression: Which one should be used? Technometrics 14 (November): 967–70.

    Article  Google Scholar 

  • Hocking, R. R. 1976. The analysis and selection of variables in linear regression. Biometrics 32 (March): 1–49.

    Article  MathSciNet  MATH  Google Scholar 

  • Hoerl, A. E. and Kennard, R. W. 1970. Ridge regression: Biased estimation of non-orthogonal problems. Technometrics 12 (February): 55–67.

    Article  MATH  Google Scholar 

  • Krishnaiah, P. R. and Armitage, J. V. 1. 1965. Probability Integrals of the Multivariate F Distribution, with Tables and Applications, ARL 65-236. Ohio: Wright-Patterson AFB.

    Google Scholar 

  • Kullback, S. and Leibler, R. A. 1951. On information and sufficiency. Annals of Mathematical Statistics 22 (March): 79–66.

    Article  MathSciNet  MATH  Google Scholar 

  • Madansky, A. 1976. Foundations of Econometrics. Amsterdam: North-Holland.

    MATH  Google Scholar 

  • Malinvaud, E. 1966. Statistical Methods of Econometrics. Chicago: Rand-McNally.

    MATH  Google Scholar 

  • Mallows, C. L. 1967. Choosing a subset regression. Bell Telephone Laboratories, unpublished report.

    Google Scholar 

  • Pope, P. T. 1969. On the stepwise construction of a prediction equation. Tech. Report 37. THEMIS, Statistics Department, Southern Methodist University, Dallas, Texas.

    Google Scholar 

  • Pope, P. T. and Webster, J. T. 1972. The use of an F-statistic n stepwise regression procedures. Technometrics 14 (May): 327–40.

    Article  MATH  Google Scholar 

  • Roberts, H. V. and Ling, R. F. 1982. Conversational Statistics with IDA. New York: Scientific Press and McGraw-Hill.

    Google Scholar 

  • Theil, H. 1961. Economic Forecasts and Policy. Amsterdam: North-Holland.

    Google Scholar 

  • Thompson, M. L. 1978a. Selection of variables in multiple regression: Part I. A review and evaluation. International Statistical Review 46 (April): 1–19.

    MathSciNet  MATH  Google Scholar 

  • Thompson, M. L. 1978b. Selection of variables in multiple regression: Part II. Chosen procedures, computations, and examples. International Statistical Review 46 (April): 129–46.

    MathSciNet  MATH  Google Scholar 

  • Vinod, H. D. 1976. Application of new ridge regression methods to a study of Bell system scale economies. Journal of the American Statistical Association 71 (December): 929–33.

    Article  MATH  Google Scholar 

  • Vinod, H. D. and Ullah, A. 1981. Recent Advances in Regression Analysis. New York: Marcel Dekker.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag New York Inc.

About this chapter

Cite this chapter

Madansky, A. (1988). Independent Variable Selection in Multiple Regression. In: Prescriptions for Working Statisticians. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3794-5_7

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-3794-5_7

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-8354-6

  • Online ISBN: 978-1-4612-3794-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics