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

Gwowen Shieh*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)121-124
Number of pages4
JournalAmerican Statistician
Volume55
Issue number2
DOIs
StatePublished - May 2001

Keywords

  • Coefficient of determination
  • Multiple regression
  • Simple correlation coefficient

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