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Does the Correlation Coefficient Really Measure the Degree of Clustering Around a Line?

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  • Wei-Yin Loh

Abstract

This paper derives a formula for the square of the correlation coefficient r 2 in terms of its maximum possible value under rotation of the axes. The value of r 2 is minimized at 0 when the principal components of the scatterplot coincide with the axes, and is maximized when the principal components are at ±45° to the axes. An application of the formula to quick visual estimation of r is indicated.

Suggested Citation

  • Wei-Yin Loh, 1987. "Does the Correlation Coefficient Really Measure the Degree of Clustering Around a Line?," Journal of Educational and Behavioral Statistics, , vol. 12(3), pages 235-239, September.
    • Handle: RePEc:sae:jedbes:v:12:y:1987:i:3:p:235-239
    DOI: 10.3102/10769986012003235
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    Cited by:

    1. Elena Shakina & Angel Barajas, 2014. "The Changing Role Of Intellectual Resources During The Economic Crisis Of 2008-2009," HSE Working papers WP BRP 17/MAN/2014, National Research University Higher School of Economics.

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    Keywords

    scatterplot; SD-line;

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