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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.
PAC, 1990, 62, 2167 (Glossary of atmospheric chemistry terms (Recommendations 1990)) on page 2182
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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: (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8.
Last update: 2014-02-24; version: 2.3.3.
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