TY - JOUR

T1 - The inequality between the coefficient of determination and the sum of squared simple correlation coefficients

AU - Shieh, Gwowen

PY - 2001/5

Y1 - 2001/5

N2 - The inequality between the coefficient of determination and the sum of two squared simple correlation coefficients in a two-variable regression model is reexamined through two relative measures. They are the relative coefficient of determination and the relative simple correlation, which are the ratio of the coefficient of determination to the sum of squares of the two simple correlations and the ratio of two simple correlations, respectively. This approach not only permits new insights into their relationship but also allows clear and informative visual representations of various aspects of the counterintuitive condition. We consider the occurrence and corresponding magnitude, probability, and expected magnitude of the enhancement-synergism situation. Numerical examples are presented to illustrate these phenomena.

AB - The inequality between the coefficient of determination and the sum of two squared simple correlation coefficients in a two-variable regression model is reexamined through two relative measures. They are the relative coefficient of determination and the relative simple correlation, which are the ratio of the coefficient of determination to the sum of squares of the two simple correlations and the ratio of two simple correlations, respectively. This approach not only permits new insights into their relationship but also allows clear and informative visual representations of various aspects of the counterintuitive condition. We consider the occurrence and corresponding magnitude, probability, and expected magnitude of the enhancement-synergism situation. Numerical examples are presented to illustrate these phenomena.

KW - Coefficient of determination

KW - Multiple regression

KW - Simple correlation coefficient

UR - http://www.scopus.com/inward/record.url?scp=0035587910&partnerID=8YFLogxK

U2 - 10.1198/000313001750358437

DO - 10.1198/000313001750358437

M3 - Article

AN - SCOPUS:0035587910

VL - 55

SP - 121

EP - 124

JO - American Statistician

JF - American Statistician

SN - 0003-1305

IS - 2

ER -