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Multivariate Approach to Partial Correlation Analysis

Received: 13 May 2015     Accepted: 29 May 2015     Published: 11 June 2015
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Abstract

Multivariate approach to generate variance covariance and partial correlation coefficients of one or more independent variables has been the concern of advanced statisticians and users of statistical tools. This work tackled the problem by keeping one or some variables constant and partitioned the variance covariance matrices to find multivariate partial correlations. Due to the challenges that faced the analysis and computation of complex variables, this research used matrix to ascertain the level of relationship that exist among these variables and obtained correlation coefficients from variance covariance matrices. It was proved that partial correlation coefficients are diagonal matrices that are normally distributed. (Work count = 101).

Published in Science Journal of Applied Mathematics and Statistics (Volume 3, Issue 3)
DOI 10.11648/j.sjams.20150303.20
Page(s) 165-170
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), 2015. Published by Science Publishing Group

Keywords

Multivariate, Correlation, Partial, Normality, Coefficients, Variables, Matrices

References
[1] Anderson, T. W., (2003); An Introduction to Multivariate Statistical Analysis 3rd Edition. Wiley-Interscience, New York
[2] Francois Husson, Sebastien Le and Jerome Pages (2010); Exploratory Multivariate Analysis. Chapman & Hall Books, retrieved from CRC Press www.crcpress.com
[3] Kendall, M. G., and Stuart, A. (1973). The Advanced Theory of Statistics (Inference and Relationship). Vol. 2 (Third ed.). Hafner Publishing Co., New York.
[4] Morison D. F., (2007); Multivariate statistical Methods. McGraw-Hill Book Company, New York. Retrieved from onlinelibrary.wiley.com.
[5] Neter, John, Michael H. Kutner, Christopher Nachtsheim, and William Wasserman (1996). Applied Linear Statistical Models. McGraw Hill, Boston.
[6] Partial Correlation Analysis retrieved from https://explorable.com/partial-correlation-analysis
[7] Rao, C. R., (2008); Linear Statistical Inference and its Application: Second Edition. John Wiley & Sons Inc. Retrieved from onlinelibrary.wiley.com.
[8] Regression Tutorial Menu Dictionary, STATS @ MTSU retrieved from http://mtweb.mtsu.edu/stats/regression/level3/multicorrel/multicorrcoef.htm
[9] Steiger, J. H., and Browne, M. W. (1984). The Comparison of Interdependent Correlations between Optimal Linear composites. Psychometrika, 49, 11-24.
[10] Stockwell Ian (2008); Introduction to Correlation and Regression. SAS Global Forum, Batimore.
[11] Tabachnick, B., and Fidell L. (1989); Using Multivariate Statistics. Harper & Row Publishers, New York.
Cite This Article
  • APA Style

    Onyeneke Casmir Chidiebere. (2015). Multivariate Approach to Partial Correlation Analysis. Science Journal of Applied Mathematics and Statistics, 3(3), 165-170. https://doi.org/10.11648/j.sjams.20150303.20

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    ACS Style

    Onyeneke Casmir Chidiebere. Multivariate Approach to Partial Correlation Analysis. Sci. J. Appl. Math. Stat. 2015, 3(3), 165-170. doi: 10.11648/j.sjams.20150303.20

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    AMA Style

    Onyeneke Casmir Chidiebere. Multivariate Approach to Partial Correlation Analysis. Sci J Appl Math Stat. 2015;3(3):165-170. doi: 10.11648/j.sjams.20150303.20

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  • @article{10.11648/j.sjams.20150303.20,
      author = {Onyeneke Casmir Chidiebere},
      title = {Multivariate Approach to Partial Correlation Analysis},
      journal = {Science Journal of Applied Mathematics and Statistics},
      volume = {3},
      number = {3},
      pages = {165-170},
      doi = {10.11648/j.sjams.20150303.20},
      url = {https://doi.org/10.11648/j.sjams.20150303.20},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20150303.20},
      abstract = {Multivariate approach to generate variance covariance and partial correlation coefficients of one or more independent variables has been the concern of advanced statisticians and users of statistical tools. This work tackled the problem by keeping one or some variables constant and partitioned the variance covariance matrices to find multivariate partial correlations. Due to the challenges that faced the analysis and computation of complex variables, this research used matrix to ascertain the level of relationship that exist among these variables and obtained correlation coefficients from variance covariance matrices. It was proved that partial correlation coefficients are diagonal matrices that are normally distributed. (Work count = 101).},
     year = {2015}
    }
    

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    JF  - Science Journal of Applied Mathematics and Statistics
    JO  - Science Journal of Applied Mathematics and Statistics
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    AB  - Multivariate approach to generate variance covariance and partial correlation coefficients of one or more independent variables has been the concern of advanced statisticians and users of statistical tools. This work tackled the problem by keeping one or some variables constant and partitioned the variance covariance matrices to find multivariate partial correlations. Due to the challenges that faced the analysis and computation of complex variables, this research used matrix to ascertain the level of relationship that exist among these variables and obtained correlation coefficients from variance covariance matrices. It was proved that partial correlation coefficients are diagonal matrices that are normally distributed. (Work count = 101).
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Author Information
  • Mathematics and Statistics Department, University of Calabar, Calabar, Nigeria

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