Skip to main content

Information-Theoretic Measures of Fit for Univariate and Multivariate Linear Regressions

  • Chapter
Henri Theil’s Contributions to Economics and Econometrics

Part of the book series: Advanced Studies in Theoretical and Applied Econometrics ((ASTA,volume 25))

  • 121 Accesses

Abstract

For the purpose of measuring the relative importance of independent variables in a multiple regression, Kruskal (1987) proposed an averaging procedure over all possible orderings of these variables. The present article uses this suggestion, but it is based on a different measure, from statistical information theory, and it extends the result to systems of equations.

This article first appeared in The American Statistician, 42 (November 1988), 249–252. Reprinted with the permission of The American Statistical Association.

Henri Theil is McKethan-Matherly Eminent Scholar and Ching-Fan Chung is McKethan-Matherly Post-Doctoral Fellow, Graduate School of Business Administration, University of Florida, Gainesville, Florida 32611.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover 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

  • Anderson, T.W.: 1984, An Introduction to Multivariate Statistical Analysis, 2nd ed., John Wiley, New York.

    Google Scholar 

  • Chung, C.-F.: 1987, “On Calculating the Information-Theoretic Measure of Fit for Multivariate Linear Regressions,” McKethan-Matherly Discussion Paper 28, University of Florida, College of Business Administration.

    Google Scholar 

  • Hotelling, H.: 1936, “Relations Between Two Sets of Variates,” Biometrika, 28, 321–377.

    Google Scholar 

  • Kruskal, W.: 1987, “Relative Importance by Averaging Over Orderings,” The American Statistician, 41, 6–10.

    Google Scholar 

  • Lawley, D.N.: 1956, “Tests of Significance of the Latent Roots of Covariance and Correlation Matrices,” Biometrika, 43, 128–136.

    Google Scholar 

  • Lawley, D.N.: 1959, “Tests of Significance in Canonical Analysis,” Biometrika, 46, 59–66.

    Google Scholar 

  • Theil, H.: 1958, Economic Forecasts and Policy, North-Holland, Amsterdam.

    Google Scholar 

  • Theil, H.: 1971, Principles of Econometrics, John Wiley, New York.

    Google Scholar 

  • Theil, H.: 1987, “How Many Bits of Information Does an Independent Variable Yield in a Multiple Regression?” Statistics and Probability Letters, 6, 107–108.

    Article  Google Scholar 

  • Theil, H., and Chung, C.-F.: 1988, “Relations Between Two Sets of Variable: The Bits of Information Provided by Each Variate in Each Set,” Statistics and Probability Letters, 6, 137–139.

    Article  Google Scholar 

  • Theil, H., and Fiebig, D.G.: 1984, “Exploiting Continuity: Maximum Entropy Estimation of Continuous Distributions,” Ballinger, Cambridge, Massachusetts.

    Google Scholar 

  • Tinsley, P.A., Spindt, P.A., and Friar, M.E.: 1980, “Indicator and Filter Attributes of Monetary Aggregates: A Nit-Picking Case for Disaggregation,” Journal of Econometrics, 14, 61–91.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Theil, H., Chung, CF. (1992). Information-Theoretic Measures of Fit for Univariate and Multivariate Linear Regressions. In: Raj, B., Koerts, J. (eds) Henri Theil’s Contributions to Economics and Econometrics. Advanced Studies in Theoretical and Applied Econometrics, vol 25. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2408-9_22

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-2408-9_22

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5062-3

  • Online ISBN: 978-94-011-2408-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics