Partial correlation

From Glossary of Meteorology

partial correlation

The correlation between the residuals of two random variables (variates) with respect to common regressors.

Denoting the regression function of two variates y and z with respect to a common set of regressors x1, x2, · · · xn by Y and Z, the coefficient of partial correlation between y and z is defined as the coefficient of simple linear correlation between (y - Y) and (z - Z). To estimate the partial correlation, it is usually necessary to resort to sample approximations Y′ and Z′ of Y and Z. In that case, the estimate of the partial correlation is the sample value of the coefficient of simple, linear correlation between (y - Y′) and (z - Z′). In the simplest case in which Y′ and Z′ are taken as linear functions of a single variable x, the sample estimate ryz.x of the partial correlation coefficient is given by the formula
where the symbol ruv denotes the sample coefficient of linear correlation between any pair of variates u, v.
See regression.

Copyright 2022 American Meteorological Society (AMS). For permission to reuse any portion of this work, please contact Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act (17 U.S. Code § 107) or that satisfies the conditions specified in Section 108 of the U.S.Copyright Act (17 USC § 108) does not require AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a website or in a searchable database, or other uses of this material, except as exempted by the above statement, require written permission or a license from AMS. Additional details are provided in the AMS Copyright Policy statement.