A measure of the degree of linear association among a pair of variables.

The correlation between two random variables $X$ and $Y$ is defined as

$$ {\rm cor}(X,Y) = \frac{ E(XY) - E(X)E(Y) }{ \sqrt{ {\rm var}(X) {\rm var}(Y) } }$$

and is bounded between $-1$ (perfect negative linear relationship) and $1$ (perfect positive linear relationship). The numerator of ${\rm cor}(X,Y)$ is known as the covariance between $X$ and $Y$.

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