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关于相关系数计算方程的一个极其奇怪的观察结果。

An extremely strange observation on the equations for calculation of correlation coefficient.

作者信息

Wu Guang

机构信息

Laboratoire de Toxicocinétique et Pharmacocinétique, Faculté de Pharmacie, Université de la Méditerraneé Aix-Marseille II, Marseilles, France.

出版信息

Eur J Drug Metab Pharmacokinet. 2003 Apr-Jun;28(2):85-92. doi: 10.1007/BF03190494.

DOI:10.1007/BF03190494
PMID:12877564
Abstract

Various equations are used to calculate the correlation coefficient, these equations are presumed equally. However we find the extraordinary results when using r = square root of ((sigma(ŷi - y)2) / (sigma(yi - y)2)) and r2 = (sigma(yi - y)2 - sigma(yi - ŷi)2) / (sigma(yi - y)2) to calculate the correlation coefficient, for example, a line within 95% confidence band of a regressed line. The results are so extraordinary that we do not know whether or not we can still call the results as correlation coefficient, however we are sure that these results need to be presented.

摘要

有多种方程用于计算相关系数,这些方程被认为是等效的。然而,当使用r = √(((σ(ŷi - y)²) / (σ(yi - y)²)) 以及r² = (σ(yi - y)² - σ(yi - ŷi)²) / (σ(yi - y)²))来计算相关系数时,我们得到了异常的结果,例如,一条位于回归线95%置信带内的直线。结果非常异常,以至于我们不知道是否还能将这些结果称为相关系数,但我们确定这些结果需要呈现出来。

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