Browse > Article
http://dx.doi.org/10.7468/jksmeb.2020.27.2.71

ILL-CONDITIONING IN LINEAR REGRESSION MODELS AND ITS DIAGNOSTICS  

Ghorbani, Hamid (Faculty of Mathematical Sciences, University of Kashan)
Publication Information
The Pure and Applied Mathematics / v.27, no.2, 2020 , pp. 71-81 More about this Journal
Abstract
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.
Keywords
diagnostic measures; ill-conditioned property; multicollinearity; regression analysis; singularity;
Citations & Related Records
연도 인용수 순위
  • Reference
1 S. Chatterjee & A. S. Hadi: Regression Analysis by Example (5th ed.). John Wiley & Sons, New York, 2012.
2 J.D. Curto & J.D. Pinto: The corrected VIF (CVIF). Journal of Applied Statistics 38 (2011), no. 7, 495-505.
3 D.E. Farrar & R.R. Glauber: Multicollinearity in regression analysis: the problem revisited. Review of Economics and Statistics 49 (1967), no. 1, 92107.
4 M. Friendly & E. Kwan: Where's Waldo? Visualizing Collinearity Diagnostics. The American Statistician 63 (2009), no. 1, 56-65.   DOI
5 R. Frisch: Statistical Con uence Analysis by Means of Complete Regression Systems. Universitetets Okonomiske Institutt., Oslo, 1934.
6 J. Gross: Linear Regression. Springer-Verlag, Berlin, Heidelberg, 2003.
7 Y. Haitovsky: Multicollinearity in Regression Analysis: Comment. The Review of Economics and Statistics 51 (2002), no. 4, 486-89.   DOI
8 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.   DOI
9 R. Klein: An Introduction to Econometrics. Prentic-Hall Pub., Englewood, Cliffs, N. J., 1962.
10 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.   DOI
11 D.C. Montgomery, E.A. Peck & G.G. Vining: Introduction to Linear Regression Analysis (5th ed.), John Wiley & Sons, (2012).
12 R.M. OBrien: A caution regarding rules of thumb for variance in ation factors. Quality & Quantity 41 (2007), no. 5, 673-679.   DOI
13 R Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, (2019), url=https://www.R-project.org.
14 G.W. Stewart: Collinearity and Least Squares Regression. Statist. Sci. 2 (1987), no. 1, 68-100.   DOI
15 E.C. Willis & D.R. Perlack: Multicollinearity: Effects, Symptoms, and Remedies. Journal of the Northeastern Agricultural Economics Council. 7 (1978), 55-61.   DOI
16 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.   DOI
17 D.A. Belsley, E. Kuh & R.E. Welsch: Regression Diagnostics: Identifying In uential Data and Sources of Collinearity. John Wiley & Sons, New York, 1980.
18 M.P. Allen: The problem of multicollinearity. In: Understanding Regression Analysis. Springer, Boston, (1997), 176-180.
19 D. Asteriou & S.G. Hall: Applied Econometrics: A Modern Approach Using Eviews and Microfit. Palgrave Macmillan Pub., New York, 2007.
20 D.A. Belsley: Conditioning Diagnostics: Collinearity and Weak Data Regression. John Wiley & Sons, New York, 1991.
21 N. Billington: The location of foreign direct investment: an empirical analysis. Applied Economics 31 (1999), no. 1, 65-76.   DOI