한국수학교육학회지시리즈B:순수및응용수학 (The Pure and Applied Mathematics)

  • 제27권2호
  • /
  • Pages.71-81
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  • 2020
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  • 1226-0657(pISSN)
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  • 2287-6081(eISSN)
한국수학교육학회 (Korean Society of Mathematical Education)
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ILL-CONDITIONING IN LINEAR REGRESSION MODELS AND ITS DIAGNOSTICS

  • 투고 : 2019.07.22
  • 심사 : 2019.11.04
  • 발행 : 2020.05.31
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초록

Multicollinearity is a common problem in linear regression models when two or more regressors are highly correlated, which yields some serious problems for the ordinary least square estimates of the parameters as well as model validation and interpretation. In this paper, first the problem of multicollinearity and its subsequent effects on the linear regression along with some important measures for detecting multicollinearity is reviewed, then the role of eigenvalues and eigenvectors in detecting multicollinearity are bolded. At the end a real data set is evaluated for which the fitted linear regression models is investigated for multicollinearity diagnostics.

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참고문헌

  1. M.P. Allen: The problem of multicollinearity. In: Understanding Regression Analysis. Springer, Boston, (1997), 176-180.
  2. D. Asteriou & S.G. Hall: Applied Econometrics: A Modern Approach Using Eviews and Microfit. Palgrave Macmillan Pub., New York, 2007.
  3. D.A. Belsley: Conditioning Diagnostics: Collinearity and Weak Data Regression. John Wiley & Sons, New York, 1991.
  4. D.A. Belsley, E. Kuh & R.E. Welsch: Regression Diagnostics: Identifying In uential Data and Sources of Collinearity. John Wiley & Sons, New York, 1980.
  5. N. Billington: The location of foreign direct investment: an empirical analysis. Applied Economics 31 (1999), no. 1, 65-76. https://doi.org/10.1080/00036846.2019.12067087
  6. S. Chatterjee & A. S. Hadi: Regression Analysis by Example (5th ed.). John Wiley & Sons, New York, 2012.
  7. J.D. Curto & J.D. Pinto: The corrected VIF (CVIF). Journal of Applied Statistics 38 (2011), no. 7, 495-505.
  8. D.E. Farrar & R.R. Glauber: Multicollinearity in regression analysis: the problem revisited. Review of Economics and Statistics 49 (1967), no. 1, 92107.
  9. M. Friendly & E. Kwan: Where's Waldo? Visualizing Collinearity Diagnostics. The American Statistician 63 (2009), no. 1, 56-65. https://doi.org/10.1198/tast.2009.0012
  10. R. Frisch: Statistical Con uence Analysis by Means of Complete Regression Systems. Universitetets Okonomiske Institutt., Oslo, 1934.
  11. J. Gross: Linear Regression. Springer-Verlag, Berlin, Heidelberg, 2003.
  12. Y. Haitovsky: Multicollinearity in Regression Analysis: Comment. The Review of Economics and Statistics 51 (2002), no. 4, 486-89. https://doi.org/10.2307/1926450
  13. M. Imdadullah, M. Aslam & S. Altaf: mctest: an R package for detection of collinearity among regressors. The R Journal 8 (2016), no. 2, 495-505. https://doi.org/10.32614/RJ-2016-062
  14. R. Klein: An Introduction to Econometrics. Prentic-Hall Pub., Englewood, Cliffs, N. J., 1962.
  15. C. Mela & P. Kopalle: The Impact of Collinearity on Regression Analysis: The Asymmetric Effect of Negative and Positive Correlations. Applied Economics 34 (2002), 667-77. https://doi.org/10.1080/00036840110058482
  16. D.C. Montgomery, E.A. Peck & G.G. Vining: Introduction to Linear Regression Analysis (5th ed.), John Wiley & Sons, (2012).
  17. R.M. OBrien: A caution regarding rules of thumb for variance in ation factors. Quality & Quantity 41 (2007), no. 5, 673-679. https://doi.org/10.1007/s11135-006-9018-6
  18. R Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, (2019), url=https://www.R-project.org.
  19. G.W. Stewart: Collinearity and Least Squares Regression. Statist. Sci. 2 (1987), no. 1, 68-100. https://doi.org/10.1214/ss/1177013439
  20. E.C. Willis & D.R. Perlack: Multicollinearity: Effects, Symptoms, and Remedies. Journal of the Northeastern Agricultural Economics Council. 7 (1978), 55-61. https://doi.org/10.1017/S0163548400001989
  21. H. Woods, H. Steinour & H.R. Starke: Effect of Composition of Portland Cement on Heat Evolved during hardening. Industrial & Engineering Chemistry 24 (1932), no. 11, 1207-1214. https://doi.org/10.1021/ie50275a002