## correlation coefficient

https://doi.org/10.1351/goldbook.C01347
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: $r=\frac{\sum _{\begin{array}{c} i=1 \end{array}}^{n}(x_{i}- \overline{x})\ (y_{i}- \overline{y})}{\sqrt{\sum _{\begin{array}{c} i=1 \end{array}}^{n}(x_{i}- \overline{x})^{2}\ \sum _{\begin{array}{c} i=1 \end{array}}^{n}(y_{i}- \overline{y})^{2}}}$ where xi and yi are the measured values in the ith experiment of n total experiments, x ̄ and y ̄ are the arithmetic means of xi and yi: $\overline{x}=\frac{\sum _{\begin{array}{c} i=1 \end{array}}^{n}x_{i}}{n}$ (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 (https://doi.org/10.1351/pac199062112167)