On the Detection of Influential Outliers in Linear Regression Analysis

Arimiyaw Zakaria; Nathaniel Kwamina Howard; Bismark Kwao Nkansah

doi:doi:10.11648/j.ajtas.20140304.14

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On the Detection of Influential Outliers in Linear Regression Analysis

Arimiyaw Zakaria, Nathaniel Kwamina Howard, Bismark Kwao Nkansah

Published in American Journal of Theoretical and Applied Statistics (Volume 3, Issue 4)

Received: 11 July 2014 Accepted: 21 July 2014 Published: 30 July 2014

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Abstract

In this paper, we propose a measure for detecting influential outliers in linear regression analysis. The performance of the proposed method, called the Coefficient of Determination Ratio (CDR), is then compared with some standard measures of influence, namely: Cook’s distance, studentised deleted residuals, leverage values, covariance ratio, and difference in fits standardized. Two existing datasets, one artificial and one real, are employed for the comparison and to illustrate the efficiency of the proposed measure. It is observed that the proposed measure appears more responsive to detecting influential outliers in both simple and multiple linear regression analyses. The CDR thus provides a useful alternative to existing methods for detecting outliers in structured datasets.

Published in	American Journal of Theoretical and Applied Statistics (Volume 3, Issue 4)
DOI	10.11648/j.ajtas.20140304.14
Page(s)	100-106
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Coefficient of Determination Ratio, Cook’s Distance, DFFITS, CVR, Studentised Deleted Residuals, Leverage Values

References

[1]	Barnett, V., & Lewis, T. (1994). Outliers in statistical data (3rd ed.). New York, NY: John Wiley and Sons.
[2]	Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed.). London, England: Lawrence Erlbaum Associates.
[3]	Weisberg, S. (2005). Applied linear regression (3rd ed.). New York, NY: John Wiley and Sons.
[4]	Nurunnabi, A. A. M., Imon, A. H. M. R., Ali, A. B. M. S., & Nasser, M. (2011). Outlier detection in linear regression. Retrieved June 9, 2011 from http://irma-international.org/chapter/outlier-detection-linear-regression/53318/
[5]	Chatterjee, S., & Hadi, A. S. (1988). Sensitivity analysis in linear regression. New York, NY: John Wiley & Sons.
[6]	Cook, R. D. & Weisberg, S. (1982). Residuals and Influence in Regression. New York, NY: Chapman and Hall.
[7]	Rencher, A. C. & Schaalje, G. B. (2008). Linear models in statistics (2nd ed.). New Jersey, NJ: John Wiley & Sons.
[8]	Siniksaran, E. & Satman, M. H. (2011). PURO: A package for unmasking regression outliers. Gazi University Journal of Science, 24 (1), 59-68.
[9]	Moore, J. (1975): Total biochemical oxygen demand of dairy manures. Ph. D. Thesis, Univ. of Minnesota, Dept. Agricultural Engineering.
[10]	Chatterjee, S. & Hadi, A. S. (1986). Influential observations, high leverage points, and outliers in linear regression. Statistical Science, 1 (3), 379-393.

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APA Style

Arimiyaw Zakaria, Nathaniel Kwamina Howard, Bismark Kwao Nkansah. (2014). On the Detection of Influential Outliers in Linear Regression Analysis. American Journal of Theoretical and Applied Statistics, 3(4), 100-106. https://doi.org/10.11648/j.ajtas.20140304.14

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ACS Style

Arimiyaw Zakaria; Nathaniel Kwamina Howard; Bismark Kwao Nkansah. On the Detection of Influential Outliers in Linear Regression Analysis. Am. J. Theor. Appl. Stat. 2014, 3(4), 100-106. doi: 10.11648/j.ajtas.20140304.14

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AMA Style

Arimiyaw Zakaria, Nathaniel Kwamina Howard, Bismark Kwao Nkansah. On the Detection of Influential Outliers in Linear Regression Analysis. Am J Theor Appl Stat. 2014;3(4):100-106. doi: 10.11648/j.ajtas.20140304.14

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@article{10.11648/j.ajtas.20140304.14,
  author = {Arimiyaw Zakaria and Nathaniel Kwamina Howard and Bismark Kwao Nkansah},
  title = {On the Detection of Influential Outliers in Linear Regression Analysis},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {3},
  number = {4},
  pages = {100-106},
  doi = {10.11648/j.ajtas.20140304.14},
  url = {https://doi.org/10.11648/j.ajtas.20140304.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20140304.14},
  abstract = {In this paper, we propose a measure for detecting influential outliers in linear regression analysis. The performance of the proposed method, called the Coefficient of Determination Ratio (CDR), is then compared with some standard measures of influence, namely: Cook’s distance, studentised deleted residuals, leverage values, covariance ratio, and difference in fits standardized. Two existing datasets, one artificial and one real, are employed for the comparison and to illustrate the efficiency of the proposed measure. It is observed that the proposed measure appears more responsive to detecting influential outliers in both simple and multiple linear regression analyses. The CDR thus provides a useful alternative to existing methods for detecting outliers in structured datasets.},
 year = {2014}
}

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TY  - JOUR
T1  - On the Detection of Influential Outliers in Linear Regression Analysis
AU  - Arimiyaw Zakaria
AU  - Nathaniel Kwamina Howard
AU  - Bismark Kwao Nkansah
Y1  - 2014/07/30
PY  - 2014
N1  - https://doi.org/10.11648/j.ajtas.20140304.14
DO  - 10.11648/j.ajtas.20140304.14
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 100
EP  - 106
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20140304.14
AB  - In this paper, we propose a measure for detecting influential outliers in linear regression analysis. The performance of the proposed method, called the Coefficient of Determination Ratio (CDR), is then compared with some standard measures of influence, namely: Cook’s distance, studentised deleted residuals, leverage values, covariance ratio, and difference in fits standardized. Two existing datasets, one artificial and one real, are employed for the comparison and to illustrate the efficiency of the proposed measure. It is observed that the proposed measure appears more responsive to detecting influential outliers in both simple and multiple linear regression analyses. The CDR thus provides a useful alternative to existing methods for detecting outliers in structured datasets.
VL  - 3
IS  - 4
ER  -

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Author Information

Arimiyaw Zakaria

Department of Mathematics and Statistics, University of Cape Coast, Cape Coast, Ghana
Nathaniel Kwamina Howard

Department of Mathematics and Statistics, University of Cape Coast, Cape Coast, Ghana
Bismark Kwao Nkansah

Department of Mathematics and Statistics, University of Cape Coast, Cape Coast, Ghana

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APA Style

Arimiyaw Zakaria, Nathaniel Kwamina Howard, Bismark Kwao Nkansah. (2014). On the Detection of Influential Outliers in Linear Regression Analysis. American Journal of Theoretical and Applied Statistics, 3(4), 100-106. https://doi.org/10.11648/j.ajtas.20140304.14

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ACS Style

Arimiyaw Zakaria; Nathaniel Kwamina Howard; Bismark Kwao Nkansah. On the Detection of Influential Outliers in Linear Regression Analysis. Am. J. Theor. Appl. Stat. 2014, 3(4), 100-106. doi: 10.11648/j.ajtas.20140304.14

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AMA Style

Arimiyaw Zakaria, Nathaniel Kwamina Howard, Bismark Kwao Nkansah. On the Detection of Influential Outliers in Linear Regression Analysis. Am J Theor Appl Stat. 2014;3(4):100-106. doi: 10.11648/j.ajtas.20140304.14

Copy | Download

@article{10.11648/j.ajtas.20140304.14,
  author = {Arimiyaw Zakaria and Nathaniel Kwamina Howard and Bismark Kwao Nkansah},
  title = {On the Detection of Influential Outliers in Linear Regression Analysis},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {3},
  number = {4},
  pages = {100-106},
  doi = {10.11648/j.ajtas.20140304.14},
  url = {https://doi.org/10.11648/j.ajtas.20140304.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20140304.14},
  abstract = {In this paper, we propose a measure for detecting influential outliers in linear regression analysis. The performance of the proposed method, called the Coefficient of Determination Ratio (CDR), is then compared with some standard measures of influence, namely: Cook’s distance, studentised deleted residuals, leverage values, covariance ratio, and difference in fits standardized. Two existing datasets, one artificial and one real, are employed for the comparison and to illustrate the efficiency of the proposed measure. It is observed that the proposed measure appears more responsive to detecting influential outliers in both simple and multiple linear regression analyses. The CDR thus provides a useful alternative to existing methods for detecting outliers in structured datasets.},
 year = {2014}
}

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TY  - JOUR
T1  - On the Detection of Influential Outliers in Linear Regression Analysis
AU  - Arimiyaw Zakaria
AU  - Nathaniel Kwamina Howard
AU  - Bismark Kwao Nkansah
Y1  - 2014/07/30
PY  - 2014
N1  - https://doi.org/10.11648/j.ajtas.20140304.14
DO  - 10.11648/j.ajtas.20140304.14
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 100
EP  - 106
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20140304.14
AB  - In this paper, we propose a measure for detecting influential outliers in linear regression analysis. The performance of the proposed method, called the Coefficient of Determination Ratio (CDR), is then compared with some standard measures of influence, namely: Cook’s distance, studentised deleted residuals, leverage values, covariance ratio, and difference in fits standardized. Two existing datasets, one artificial and one real, are employed for the comparison and to illustrate the efficiency of the proposed measure. It is observed that the proposed measure appears more responsive to detecting influential outliers in both simple and multiple linear regression analyses. The CDR thus provides a useful alternative to existing methods for detecting outliers in structured datasets.
VL  - 3
IS  - 4
ER  -

Copy | Download