01347 IUPAC Gold Book - correlation coefficient 10.1351/goldbook.C01347 C01347 current 1 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 \(x_{i}\) 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 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. coefficient https://goldbook.iupac.org//terms/view/C01124 PAC, 1990, 62, 2167. 'Glossary of atmospheric chemistry terms (Recommendations 1990)' on page 2182 (https://doi.org/10.1351/pac199062112167) https://goldbook.iupac.org/terms/view/C01347/html https://goldbook.iupac.org/terms/view/C01347/json https://goldbook.iupac.org/terms/view/C01347/plain Citation: 'correlation coefficient' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.C01347 The IUPAC Gold Book is licensed under Creative Commons Attribution-ShareAlike CC BY-SA 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) for individual terms. If you are interested in licensing the Gold Book for commercial use, please contact the IUPAC Executive Director at executivedirector@iupac.org . The International Union of Pure and Applied Chemistry (IUPAC) is continuously reviewing and, where needed, updating terms in the Compendium of Chemical Terminology (the IUPAC Gold Book). Users of these terms are encouraged to include the version of a term with its use and to check regularly for updates to term definitions that you are using. 2026-05-09T03:35:45+00:00