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.

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