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On direction of dependence

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Abstract

Under the assumption of the existence of linear relationship between two random variables, new formulas are introduced to express the coefficient of correlation. One of these formulas, the fourth power of the correlation coefficient is used to determine the direction of dependency between two random variables. Also an interpretation of the correlation coefficient as an asymmetric function of kurtosis coefficient and skewness coefficient of dependent variable and independent variable is provided. In the absent of the intercept in linear regression, the correlation coefficient is also expressed as a ratio of coefficients of variation between independent and dependent variables.

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Authors and Affiliations

  1. Institute of Statistics, University of Neuchâtel, Neuchâtel, Switzerland

    Yadolah Dodge

  2. Department of Statistics, Tarbiat Modares University, Tehran, Iran

    Iraj Yadegari

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  1. Yadolah Dodge
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  2. Iraj Yadegari
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Correspondence to Yadolah Dodge.

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Dodge, Y., Yadegari, I. On direction of dependence. Metrika 72, 139–150 (2010). https://doi.org/10.1007/s00184-009-0273-0

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  • DOI: https://doi.org/10.1007/s00184-009-0273-0

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