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VincentShell · 2022年11月29日

Covariance是正的Correlation就一定也是正的吗？

  1. CFA I
  2. Quantitative

NO.PZ2021061603000034

问题如下：

Consider two variables, A and B. If variable A has a mean of-0.56, variable B has a mean of 0.23, and the covariance between the two variables is positive, the correlation between these two variables is:

选项：

A.negative. B.zero. C.positive.

解释：

C is correct.

The correlation coefficient is positive because the covariance is positive. The fact that one or both variables have a negative mean does not affect the sign of the correlation coefficient.

No.PZ2021061603000034 (选择题)

来源: 原版书

Consider two variables, A and B. If variable A has a mean of-0.56, variable B has a mean of 0.23, and the covariance between the two variables is positive, the correlation between these two variables is:

您的回答C, 正确答案是: C

A

negative.

B

zero.

C

positive.



求助老师

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已采纳答案

星星_品职助教 · 2022年11月29日

同学你好，

对的，Covariance和correlation一定同号。

从原理的角度解释，X和Y的correlation=covariance / σxσy，由于分母的两个σ都是正数，所以correlation和covariance的符号一定相同。

从记忆和考试的角度出发，covariance和correlation都表示的是两个变量的线性关系，相当于同一个东西的不同的表述方式，所以这两者一定是一致的。

VincentShell · 2022年12月08日

谢谢老师

ditto · 2023年09月09日

为什么分母的两个σ都是正数？

星星_品职助教 · 2023年09月13日

@ditto 标准差σ为方差开根号后取正值。

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