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\rho_P(x,y) = \frac{{\rm cov}(x,y)}{\sigma(x) \sigma(y)} |
where
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| body | x=\{ x_1, \, x_2, \, ... x_n \} |
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and | LaTeX Math Inline |
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| body | y=\{ y_1, \, y_2, \, ... y_n \} |
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| finite arrays of -variable and -variable values |
| covariance between -variable and -variable |
| standard deviation of -variable and -variable |
Pearson correlation coefficient ranges between -1 and 1 and indicates how accurately the two variables can be approximated by a linear correlation:
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- Maximum value relates to perfect linear correlation with (see also Fig. 1)
- Zero value relates to absence of correlation between and (see also Fig. 2)
- Minimum value relates to perfect linear correlation with (also called anti-correlation) (see also Fig. 3)
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| Fig. 1. Highly correlated variables | Fig. 2. Poorly correlated variables | Fig. 3. Highly anti-correlated variables |
See also
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Formal science / Mathematics / Statistics / Statistical correlation
[ Statistical correlation metrics @ review ]
