08. Correlation Coefficients

Correlation Coefficients

Correlation coefficients provide a measure of the strength and direction of a linear relationship.

We can tell the direction based on whether the correlation is positive or negative.

A rule of thumb for judging the strength:

Strong                              
Moderate                              
Weak
$0.7 \leq |r| \leq 1.0$              $0.3 \leq |r| < 0.7$                     $0.0 \leq |r| < 0.3$

Calculation of the Correlation Coefficient

$r = \frac{\sum\limits_{i=1}^n(x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum(x_i - \bar{x})^2}\sqrt{\sum(y_i - \bar{y})^2}}$

It can also be calculated in Excel and other spreadsheet applications using CORREL(col1, col2), where col1 and col2 are the two columns you are looking to compare to one another.