A Postscript to “A Note on a Geometric Interpretation of the Correlation Coefficient”

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 (ρ) or the standardized regression coefficient (ß_zx ). The length of the latus rectum of the ellipse is $$\sqrt{2}$$ (1 –ρ) and the distance between focal points is $$\sqrt{2}$$ (1 +ρ). Other values may be expressed in terms ofρ or derived from the foregoing. The geometry is illustrated and a set of curves for reading values directly from knowledge ofρ> 0 is provided.