IUPAC > Gold Book > alphabetical index > C > correlation coefficient
icon

IndexesDownload


correlation coefficient

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 ( x i − x ̄ ) ( y i − y ̄ ) ∑ i = 1 n ( x i − x ̄ ) 2 ∑ i = 1 n ( y i − y ̄ ) 2
where x i and y i are the measured values in the ith experiment of n total experiments, x ̄ and y ̄ are the arithmetic means of x i and y i:
x ̄ = ∑ i = 1 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
Interactive Link Maps
First LevelSecond LevelThird Level
GraphGraphGraph
Cite as:
IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8. doi:10.1351/goldbook.
Last update: 2014-02-24; version: 2.3.3.
DOI of this term: doi:10.1351/goldbook.C01347.
Original PDF version: http://www.iupac.org/goldbook/C01347.pdf. The PDF version is out of date and is provided for reference purposes only. For some entries, the PDF version may be unavailable.
Current PDF version | Version for print | History of this term
picture