correlation coefficient

https://doi.org/10.1351/goldbook.C01347
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=1n(xix) (yiy)i=1n(xix)2 i=1n(yiy)2 where xi 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=i=1nxin (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 [Terms] [Paper]