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Use of R2 and Its Shortcomings
R. K. Borah1 , K. K. Singh Meitei2 , S. C. Kakaty3
  • Dept. of Statistics, Manipur University, Imphal-795003, India.
  • Dept. of Statistics, Manipur University, Imphal-795003, India.
  • Dept. of Statistics, Dibrugarh University, Dibrugarh-786004, India.
Correspondence should be addressed to: mr_raju06@rediffmail.com.
Section:Research Paper, Product Type: Isroset-Journal
Vol.4 , Issue.6 , pp.12-16, Dec-2017


CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v4i6.1216

Online published on Dec 31, 2017
Copyright © R. K. Borah, K. K. Singh Meitei, S. C. Kakaty . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 
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Citation :
IEEE Style Citation: R. K. Borah, K. K. Singh Meitei, S. C. Kakaty, “Use of R2 and Its Shortcomings”, International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.4, Issue.6, pp.12-16, 2017.

MLA Style Citation: R. K. Borah, K. K. Singh Meitei, S. C. Kakaty "Use of R2 and Its Shortcomings." International Journal of Scientific Research in Mathematical and Statistical Sciences 4.6 (2017): 12-16.

APA Style Citation: R. K. Borah, K. K. Singh Meitei, S. C. Kakaty, (2017). Use of R2 and Its Shortcomings. International Journal of Scientific Research in Mathematical and Statistical Sciences, 4(6), 12-16.
           
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Abstract :
The coefficient of determination R2 is a general measure of usefulness of the regression model. It shows the percentage of the total variation in the response variable which can be explained by the explanatory variable and is considered as the most commonly used measure of goodness of fit for regression models. It is demonstrated by many statisticians and practitioners that expression for the coefficient of determination is generally not equivalent. However it is widely misused. The primary source of the problem is that except for linear models with an intercept term, the several R2 statistics are not equivalent.
Key-Words / Index Term :
Coefficient of determination, Regression model, Regression analysis, Resistant or robust models
References :
[1] Draper, N. R., and Smith. H. (1981), Applied Regression Analysis (2nded.).New York: John Wiley.
[2] Hahn, G. J. (1973), ‟The Coefficient of Determination Exposed,” Chemtech, 3, 609-612.
[3] Hahn, G. J. (1977), “Fitting Regression Models With No Intercept Term.” Journal of Quality Technology, 9, 56-61.
[4] Hawkins, D. M. (1980), ‟ A Note on Fitting a Regression Without an Intercept Term,” The American Statistician, 34, 233.
[5] Healy, M. J. R. (1984), ‟The Use of R2 as a Measure of Goodness of Fit,” Journal of Royal Statistical Society ,Ser. A ,147 , 608-609.
[6] Kvalseth, T. O. (1985). ‟Cautionary Note about R2,”The American Statistician, Vol. 39, No.4, Part 1(Nov., 1985), pp. 279-285.
[7] Montgomery, D. C. and Peck, E. A. (2003), Introduction to Linear Regression Analysis(3rded.). New York :John Wiley.
[8] Marquardt, D. W., and Snee, R. D. (1974), “ Test Statistics for Mixture Models,” Technometrics, 16, 533-537.
[9] Scott, A. and Wild, C. (1991), “Transformations and R2” The American Statistician, Vol. 45, No. 2 (1991), pp. 127-129.
[10] Theil, H. (1971), Principles of Econometrics, New York: John Willy.
[11] Willet, J. B., and Singer, J. D. (1998), “Another Cautionary Note about R2: Its Use in Weighted Least-Squares Regression analysis,” The American Statistician, Vol. 42, No. 3 (1991), pp. 236-238.
 
 
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