多个随机变量样本统计相关性的另一种度量指标

Another Measure Indication of Multivariable Related Coefficient

已有的多变量相关性指标（如复相关、偏相关、广义相关系数、多向列联表分析、和谐系数等），都是从代数的角度进行定义的。文中用数性积的几何意义解释了Ｐｅａｒｓｏｎ相关系数ｒ，得到了一个与ｒ等价的度量两个变量之间相关关系密切程度指标———平行四边形的面积。在此基础上，逐步推广到ｐ维情况，并且得到了衡量ｐ个随机变量之间相关性指标———ｐ维平行２ｐ面体的体积。最后举例说明了其应用。

The existing measures of multivariable correlativity,for example,complex related coefficient,partial related coefficient and gener alized related coefficient are all defined from the algebraic angel.This paper attempts to explain Pearson related coefficient `r' from the geometrical meaning of dot conduct,and qives a new measure equivalent to `r' the area of parallelogram.On this base,we progressively extend it to the p-dimensional case and obtain the index of measuring correlation for p-dimens onal random variable.Finaly we cite an example to explain its application.