correlation coefficient

A measure of the degree of interrelationship which exists between two measured quantities, $x$ and $y$ ; the correlation coefficient ( $r$ ) is defined by the following relation:

$r = ∑ i = 1 n ( x i − x ̄ ) ( y i − y ̄ ) ∑ i = 1 n ( x i − x ̄ ) 2 ∑ i = 1 n ( y i − y ̄ ) 2$

where $x i$ and $y i$ are the measured values in the $i$ th experiment of $n$ total experiments, $x ̄$ and $y ̄$ are the arithmetic means of $x i$ and $y i$ :

$x ̄ = ∑ i = 1 n x i n$

(similar expression for $y ̄$ ). The linear correlation coefficient indicates the degree to which two quantities are linearly related. If $x = a y$ is followed then $r = 1$ , and departures from this relationship decrease $r$ ; if interpretations of data based on the linear correlation coefficient are to be made, one should consult a book on statistics.

Source:

PAC, 1990, 62, 2167 (Glossary of atmospheric chemistry terms (Recommendations 1990)) on page 2182