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

University of Wisconsin, Madison

This paper derives a formula for the square of the correlation coefficient r² in terms of its maximum possible value under rotation of the axes. The value of r² 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.

Key Words: scatterplot; SD-line

Journal of Educational and Behavioral Statistics, Vol. 12, No. 3, 235-239 (1987)
DOI: 10.3102/10769986012003235


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