Correlation

Covariance is an indicator of the magnitude and direction of the linear relationship between two variables, X and Y. However, the magnitude of covariance is influenced by the units of measurement. This can be taken care of by another measure called correlation coefficient. Correlation coefficient gets derived from covariance when working with standardized data. Mathematically, correlation coefficient, r_by, is

For purpose of computation of correlation coefficient, the following expression is recommended, where s_x and s_y are the standard deviations of X and Y:

Correlation coefficient, like covariance, indicates the strength and direction of a linear relationship between the two variables. If X and Y are perfectly related, then r_xy = 1 when the relationship is positive and -1 when the relationship is negative. If r_xy > 0 then X and Y are positively related, and closer the value is to +1, stronger is the relation. Similarly, if r_xy < 0 then X and Y are negatively related, and closer the value is to -1, stronger is the relation

See Also:

covariance

References:

Frank, H. and Althoen, S.C. "The correlation coefficient." §B.2 in Statistics: Concepts and Applications Cambridge, Great Britain: Cambridge University Press, pp. 110-117, 1995.

http://en.wikipedia.org/wiki/Correlation

http://mathworld.wolfram.com/CorrelationCoefficient.html

Cite This As:

Dogra, Shaillay K., "Correlation." From QSARWorld--A Strand Life Sciences Web Resource.
http://www.qsarworld.com/qsar-statistics-correlation.php