correlation coefficient
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.
PAC, 1990, 62, 2167. (Glossary of atmospheric chemistry terms (Recommendations 1990)) on page 2182 [Terms] [Paper]