Coefficient of Linear Correlation

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PAS

Cegep/2

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72 words

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1 minute

Measure of intensity of linear relationship between two variables
Ratio of covariance to the product of standard deviations
Syn. Pearson's correlation coefficient

Sample coefficient of linear correlation:

$$r(X,Y)=\frac{Cov(X,Y)}{s_X,s_Y}$$

Population coefficient of linear correlation:

$$\rho (X,Y)=\frac{Cov(X,Y)}{{\sigma }_X,{\sigma }_Y}$$

Properties

• $-1\le \rho (X,Y)\le 1$
• If $Y=aX+b$, then $\rho (X,Y)=\mathrm{sign}(a)$

Contributors

Ajitani Hifumi

Changelog

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