Sample Covariance between X and Y
Let $(x_i, y_i), i=1,2, \cdots , n$ be $n$ pairs of observations.
Covariance measures the simultaneous variability between the two variables. It indicates how the two variables are related. A positive value of covariance indicate that the two variables moves in the same direction, whereas a negative value of covariance indicate that the two variables moves on opposite direction.
Formula
The sample covariance between $x$ and $y$ is denoted by $Cov(x,y)$ or $s_{xy}$ and is defined as
$Cov(x,y) =s_{xy}=\dfrac{1}{n-1}\sum_{i=1}^{n} (x_i-\overline{x})(y_i-\overline{y})$
OR
$s_{xy} = \dfrac{1}{n-1}\bigg(\sum xy - \dfrac{(\sum x)(\sum y)}{n}\bigg)$
where,
$\overline{x} =\dfrac{1}{n}\sum_{i=1}^{n}x_i$sample mean of $x$,$\overline{y}=\dfrac{1}{n}\sum_{i=1}^{n}y_i$sample mean of $y$
Related Resources
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