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On the Investigation of Alternative Regressions by Principal Component Analysis

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  • Douglas M. Hawkins

Abstract

In a multiple regression problem, let the p × 1 vector x consist of the dependent variable and p – 1 predictor variables. The correlation matrix of x is reduced to principal components. The components corresponding to low eigenvalues may be useful in suggesting possible alternative subregressions. This possibility is analysed, and formulae derived for the derivation of subregressions from the principal components.

Suggested Citation

  • Douglas M. Hawkins, 1973. "On the Investigation of Alternative Regressions by Principal Component Analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 22(3), pages 275-286, November.
    • Handle: RePEc:bla:jorssc:v:22:y:1973:i:3:p:275-286
    DOI: 10.2307/2346776
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    Cited by:

    1. Claudia García-García & Catalina B. García-García & Román Salmerón, 2021. "Confronting collinearity in environmental regression models: evidence from world data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 895-926, September.
    2. Norman Fickel, 2000. "Sequential Regression: A Neodescriptive Approach to Multicollinearity," Econometrics 0004009, University Library of Munich, Germany.
    3. Norman Fickel, 2001. "Sequential Regression: A Neodescriptive Approach to Multicollinearity," EERI Research Paper Series EERI_RP_2001_09, Economics and Econometrics Research Institute (EERI), Brussels.
    4. Fickel, Norman, 2000. "Sequential regression: a neodescriptive approach to multicollinearity," Discussion Papers 33/2000, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    5. Enache, Daniel & Weihs, Claus, 2004. "Importance Assessment of Correlated Predictors in Business Cycles Classification," Technical Reports 2004,66, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    6. Gene Golub & Virginia Klema & G. W. Stewart, 1977. "Rosetak Document 4: Rank Degeneracies and Least Square Problems," NBER Working Papers 0165, National Bureau of Economic Research, Inc.
    7. David A. Belsley, 1976. "Multicollinearity: Diagnosing its Presence and Assessing the Potential Damage It Causes Least Squares Estimation," NBER Working Papers 0154, National Bureau of Economic Research, Inc.
    8. Bauer, Jan O. & Drabant, Bernhard, 2023. "Regression based thresholds in principal loading analysis," Journal of Multivariate Analysis, Elsevier, vol. 193(C).

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