Statistical Papers

, Volume 33, Issue 1, pp 21–29 | Cite as

A procedure for stepwise regression analysis

  • T. Johnsson


A procedure for stepwise regression analysis for the non-experimental case is suggested. Regarding the problem as a multiple inference one, the procedure picks out the relevant regressors and, based on a slightly new approach, estimates the structure of dependencies among the variables involved.


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  1. Butler, R.W. (1984): The significance Attained by the Best-Fitting Regressor Variable, JASA 79, 341–348.MATHMathSciNetGoogle Scholar
  2. Diehr, G. andHoflin, D.R. (1974): Approximating the Distribution of the Sample R2 in Best Subset Regressions, Technometrics 16, 317–320.MATHCrossRefGoogle Scholar
  3. Draper, N.R., Guttman, I. andKanemasu, H. (1971): The distribution of certain regression statistics, Biometrika 58, 295–298.MATHCrossRefMathSciNetGoogle Scholar
  4. Draper, N.R., Guttman, I. andLapczak, L. (1979): Actual Rejection Levels in a Certain Stepwise Test, Commun. in Statist. A8, 99–105.CrossRefGoogle Scholar
  5. Efroymson, M.A. (1960): “Multiple Regression Analysis” in Mathematical Methods for Digital Computers, eds. Rolston and H.S. Wilf, New York: John Wiley.Google Scholar
  6. Hocking, R.R. (1976): The Analysis and Selection of Variables in Linear Regression, Biometrics 32, 1–49.MATHCrossRefMathSciNetGoogle Scholar
  7. Hocking, R.R. (1983): Developments in linear regression methodology: 1959–1982, Technometrics 25, 219–230.MATHCrossRefMathSciNetGoogle Scholar
  8. Holm, S. (1977): Sequentially rejective multiple test procedures, Statistical Research Report 1977-1, University of Umeå, Institute of Mathematics & Statistics.Google Scholar
  9. Johnsson, T. (1989): A procedure for stepwise regressionanalysis, Research Report 1989:1, University of Göteborg, Department of Statistics.Google Scholar
  10. Marcus, R., Peritz, E. andGabriel, K.R. (1976): On closed testing procedures with special reference to ordered analysis of variance, Biometrika 63, 655–660.MATHCrossRefMathSciNetGoogle Scholar
  11. McIntyre, S.H., Montgomery, D.B., Srinivasan, V. andWeitz, B.A. (1983): Evaluating the Statistical Significance of Models Developed by Stepwise Regression, Journal of Marketing Research 20, 1–11.CrossRefGoogle Scholar
  12. Miller, A.J. (1984): Selection of Subsets of Regression Variables, JRSS-A 147, 389–425.MATHGoogle Scholar
  13. Miller, R.G. Jr (1980): Simultaneous Statistical Inference, 2nd ed., Springer Verlag, New York.Google Scholar
  14. Pinsker, I.S., Kipnis, V. and Grechanovsky, E. (1985): The Use of F-statistic in Forward Selection Regression Algorithm, Proc. Statist. Comput. Sec., ASA 419–423.Google Scholar
  15. Pope, P.T. andWebster, J.T. (1972): The use of An F-statistic in Stepwise Regression Procedures, Technometrics 14, 327–340.MATHCrossRefGoogle Scholar
  16. Rencher, A.C. andPun, F.C. (1980): Inflation of R2 in Best Subset Regression, Technometrics 22, 49–53.MATHCrossRefGoogle Scholar
  17. Thompson, M.L. (1978): Selection of Variables in Multiple Regression: Part I. A review and evaluation, Part II. Chosen procedures, computations and examples, Inst. Stat. Rev. 46, 1–19 and 129–146.MATHCrossRefGoogle Scholar
  18. Wilkinson, L. (1979): Tests of Significance in Stepwise Regression, Psychological Bulletin 86, 168–174.CrossRefGoogle Scholar
  19. Wilkinson, L. andDallal, G.E. (1981): Tests os Significance in Forward Selection Regression with an F-to-Enter Stopping Rule, Technometrics 23, 377–380.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • T. Johnsson
    • 1
  1. 1.Department of StatisticsUniversity of GöteborgGöteborgSweden

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