A Note on the Geometric Representation of the Correlation Coefficients
A Note on the Geometric Representation of the Correlation Coefficients
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关于相关系数的几何表示的注记
DOI：
10.1080/00031305.1975.10477395
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发表时间：
1975
期刊：
影响因子：
--
通讯作者：
Kin Lam
中科院分区：
文献类型：
--
作者：
C. Leung;Kin Lam
给定具有有限方差0 - 1 2和0 - 22的两个随机变量X1和X2，我们有以下公式：其中0 - 1 + 2 2代表X1 + X2的方差。公式（1）为我们提供了随机变量的指导性和有用的几何表示的可能性（例如参见[1]）。根据数理统计中的许多基本文本，可以通过两个平面向量V1和V2来表示X1和X2之间的相关关系，这两个平面向量V1和V2的长度分别与0 - 1和0 - 2成比例，并且由角度θ（00~8~1800）分开，角度θ的余弦为P（X1，X2）（图1）。
Given two random variables Xl and X2 with finite variances 0" 1 2 and 0" 22, we have the following formula: where 0" 1+ 2 2 stands for the variance of Xl+ X2• Formula (1) provides us the possibility of an instructive and helpful geometric representation for random variables (see for example [lJ). According to many elementary texts in mathematical statistics, it is possible to represent the correlation relationship between Xl and X2 by two plane vectors Vl and V2 whose lengths are proportional to 0" 1 and 0" 2, respectively, and are separated by an angle 8 (00~ 8~ 1800) whose cosine is P (Xl, X2)(Fig. 1).