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A procedure for stepwise regression analysis

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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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References

  • Butler, R.W. (1984): The significance Attained by the Best-Fitting Regressor Variable, JASA 79, 341–348.

    MATH  MathSciNet  Google Scholar 

  • Diehr, G. andHoflin, D.R. (1974): Approximating the Distribution of the Sample R2 in Best Subset Regressions, Technometrics 16, 317–320.

    Article  MATH  Google Scholar 

  • Draper, N.R., Guttman, I. andKanemasu, H. (1971): The distribution of certain regression statistics, Biometrika 58, 295–298.

    Article  MATH  MathSciNet  Google Scholar 

  • Draper, N.R., Guttman, I. andLapczak, L. (1979): Actual Rejection Levels in a Certain Stepwise Test, Commun. in Statist. A8, 99–105.

    Article  Google Scholar 

  • 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 

  • Hocking, R.R. (1976): The Analysis and Selection of Variables in Linear Regression, Biometrics 32, 1–49.

    Article  MATH  MathSciNet  Google Scholar 

  • Hocking, R.R. (1983): Developments in linear regression methodology: 1959–1982, Technometrics 25, 219–230.

    Article  MATH  MathSciNet  Google Scholar 

  • Holm, S. (1977): Sequentially rejective multiple test procedures, Statistical Research Report 1977-1, University of Umeå, Institute of Mathematics & Statistics.

  • Johnsson, T. (1989): A procedure for stepwise regressionanalysis, Research Report 1989:1, University of Göteborg, Department of Statistics.

  • Marcus, R., Peritz, E. andGabriel, K.R. (1976): On closed testing procedures with special reference to ordered analysis of variance, Biometrika 63, 655–660.

    Article  MATH  MathSciNet  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Miller, A.J. (1984): Selection of Subsets of Regression Variables, JRSS-A 147, 389–425.

    MATH  Google Scholar 

  • Miller, R.G. Jr (1980): Simultaneous Statistical Inference, 2nd ed., Springer Verlag, New York.

    Google Scholar 

  • 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.

  • Pope, P.T. andWebster, J.T. (1972): The use of An F-statistic in Stepwise Regression Procedures, Technometrics 14, 327–340.

    Article  MATH  Google Scholar 

  • Rencher, A.C. andPun, F.C. (1980): Inflation of R2 in Best Subset Regression, Technometrics 22, 49–53.

    Article  MATH  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • Wilkinson, L. (1979): Tests of Significance in Stepwise Regression, Psychological Bulletin 86, 168–174.

    Article  Google Scholar 

  • Wilkinson, L. andDallal, G.E. (1981): Tests os Significance in Forward Selection Regression with an F-to-Enter Stopping Rule, Technometrics 23, 377–380.

    Article  Google Scholar 

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Johnsson, T. A procedure for stepwise regression analysis. Statistical Papers 33, 21–29 (1992). https://doi.org/10.1007/BF02925308

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  • DOI: https://doi.org/10.1007/BF02925308

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