相关性的定义

Defining Correlation

专题: Statistics / 统计
难度: L2
来源: OpenQuant

题目详情

$X$ 和 $Y$ 的相关系数为 0.56。问 $8X$ 与 $Y+7$ 的相关系数是多少？

The correlation between $X$ and $Y$ is 0.56. What is the correlation between $8X$ and $Y+7$ ?"

解析

相关系数定义为协方差与标准差乘积之比，而这三者都不会因为乘上常数或加上常数而改变相关系数的数值。因此，相关系数仍然是 $0.56$ 。

Original Explanation

The correlation between $X$ and $Y$ is defined as the ratio of their covariance to the product of their standard deviations, none of which are affected by multiplication or addition of constants. The correlation is thus still $0.56$ .