Covariance

Covariance, in the field of Applied Probability, represents the joint variability of two random variables. It indicates the direction of the linear relationship between the variables. A positive covariance means that as one variable increases, the other tends to increase as well, while a negative covariance indicates that as one variable increases, the other tends to decrease.

We can honestly just think of this as the proportion operator $\propto$ associated with two variables.

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General Form

$$Co{v}_{x,y}=\frac{\sum (x_i-\bar{x})(y_i-\bar{y})}{N-1}$$

Where:

• $Co{v}_{x,y}$ is the covariance between variables $x$ and $y$
• $x_i$ and $y_i$ are the respective values $x$ and $y$ at data point $i$
• $\bar{x}$ and $\bar{y}$ are the respective means of $x$ and $y$
• $N$ is the number of data values we are iterating over