A Postscript to “A Note on a Geometric Interpretation of the Correlation Coefficientâ€

Philip H. Sorensen

Journal of Educational and Behavioral Statistics, 1983, vol. 8, issue 4, 311-314

Abstract: Essential dimensions for drawing an ellipse that bounds a constant probability area of a bivariate normal distribution may be computed from only knowledge of the correlation coefficient ( Ï ) or the standardized regression coefficient ( ß z x ). The length of the latus rectum of the ellipse is 2 (1 – Ï ) and the distance between focal points is 2 (1 + Ï ). Other values may be expressed in terms of Ï or derived from the foregoing. The geometry is illustrated and a set of curves for reading values directly from knowledge of Ï > 0 is provided.

Keywords: Geometric interpretation; regression line; constant probability ellipse (search for similar items in EconPapers)
Date: 1983
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Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:8:y:1983:i:4:p:311-314

DOI: 10.3102/10769986008004311

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