{"term":{"id":"01347","doi":"10.1351\/goldbook.C01347","code":"C01347","status":"current","longtitle":"IUPAC Gold Book - correlation coefficient","title":"correlation coefficient","version":"2.3.3","lastupdated":"2014-02-24","definitions":[{"id":"1","text":"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(xi - x(bar))(i - y(bar))\/sqrt(∑i=1|n(xi - x(bar))^2.∑i=1|n(yi - y(bar))^2) 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: x(bar) = ∑i=1|n.xi\/n). 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.","links":[{"title":"coefficient","type":"goldify","url":"https:\/\/goldbook.iupac.org\/terms\/view\/C01124"}],"math":[{"meaning":null,"type":null,"alttext":"x","latex":"x"},{"meaning":null,"type":null,"alttext":"y","latex":"y"},{"meaning":null,"type":null,"alttext":"r","latex":"r"},{"meaning":null,"type":null,"alttext":"r = ∑i=1|n(xi - x(bar))(i - y(bar))\/sqrt(∑i=1|n(xi - x(bar))^2.∑i=1|n(yi - y(bar))^2)","latex":"r=\\frac{\\sum _{\\begin{array}{c}\ni=1\n\\end{array}}^{n}(x_{i}- \\overline{x})\\ (y_{i}- \\overline{y})}{\\sqrt{\\sum _{\\begin{array}{c}\ni=1\n\\end{array}}^{n}(x_{i}- \\overline{x})^{2}\\ \\sum _{\\begin{array}{c}\ni=1\n\\end{array}}^{n}(y_{i}- \\overline{y})^{2}}}"},{"meaning":null,"type":null,"alttext":"xi","latex":"x_{i}"},{"meaning":null,"type":null,"alttext":"yi","latex":"y_{i}"},{"meaning":null,"type":null,"alttext":"i","latex":"i"},{"meaning":null,"type":null,"alttext":"n","latex":"n"},{"meaning":null,"type":null,"alttext":"x ̄","latex":"\\overline{x}"},{"meaning":null,"type":null,"alttext":"y ̄","latex":"\\overline{y}"},{"meaning":null,"type":null,"alttext":"xi","latex":"x_{i}"},{"meaning":null,"type":null,"alttext":"yi","latex":"y_{i}"},{"meaning":null,"type":null,"alttext":"x(bar) = ∑i=1|n.xi\/n","latex":"\\overline{x}=\\frac{\\sum _{\\begin{array}{c}\ni=1\n\\end{array}}^{n}x_{i}}{n}"},{"meaning":null,"type":null,"alttext":"y ̄","latex":"\\overline{y}"},{"meaning":null,"type":null,"alttext":"x = a.y","latex":"x=a\\ y"},{"meaning":null,"type":null,"alttext":"r = 1","latex":"r=1"},{"meaning":null,"type":null,"alttext":"r","latex":"r"}],"sources":["PAC, 1990, 62, 2167. 'Glossary of atmospheric chemistry terms (Recommendations 1990)' on page 2182 (https:\/\/doi.org\/10.1351\/pac199062112167)"]}],"links":{"html":"https:\/\/goldbook.iupac.org\/terms\/view\/C01347\/html","json":"https:\/\/goldbook.iupac.org\/terms\/view\/C01347\/json","xml":"https:\/\/goldbook.iupac.org\/terms\/view\/C01347\/xml","plain":"https:\/\/goldbook.iupac.org\/terms\/view\/C01347\/plain","pdf":"https:\/\/goldbook.iupac.org\/terms\/view\/C01347\/pdf"},"citeas":"IUPAC. Compendium of Chemical Terminology, 2nd ed. (the \"Gold Book\"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). Online version (2019-) created by S. J. Chalk. ISBN 0-9678550-9-8. https:\/\/doi.org\/10.1351\/goldbook.","license":"Licensed under Creative Commons Attribution-NoDerivatives (CC BY-NC-ND) 4.0 International (https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/)","disclaimer":"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.","accessed":"2022-05-28T10:08:35+00:00"}}