## 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 @C01124@ ($$r$$) 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 $$x_{i}$$ and $$y_{i}$$ are the measured values in the $$i$$th experiment of $$n$$ total experiments, $$\overline{x}$$ and $$\overline{y}$$ are the arithmetic means of $$x_{i}$$ and $$y_{i}$$: $\overline{x}=\frac{\sum _{\begin{array}{c} i=1 \end{array}}^{n}x_{i}}{n}$ (similar expression for $$\overline{y}$$). The linear correlation @C01124@ 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 @C01124@ 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 [Terms] [Paper]