Mathematics/Statistics/Correlation Coefficients

Tip: This is often represented as r.

The Correlation Coefficient is a value that describes "how well can a straight line fit this data". It is similar to covariance except that a correlation coefficient will always be between [-1, 1].

A value of exactly 1 indicates that there is a strong positive correlation between x and y. That is, as x increases, so does y. And as y increases, so does x.

A value of exactly -1 indicates that there is a strong negative correlation between x and y. That is, as x increases, y decreases. And as y increases, x decreases.

As values approach 0, it indicates a weaker and weaker correlation, with 0 indicating that there is absolutely no correlation between x and y.

There are a few ways to calculate a correlation coefficient.

Sample Correlation Coefficient

The equation to calculate the Sample Correlation Coefficient is the following.

$r={\frac {1}{n-1}}\sum _{i=1}{n}({\frac {x_{i}-{\bar {x}}}{S_{x}}})({\frac {y_{i}-{\bar {y}}}{S_{y}}})$

For further explanation, see this Khan Academy video.