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

Wei-Yin Loh

Journal of Educational and Behavioral Statistics, 1987, vol. 12, issue 3, 235-239

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.

Keywords: scatterplot; SD-line (search for similar items in EconPapers)
Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:12:y:1987:i:3:p:235-239

DOI: 10.3102/10769986012003235

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