Partial correlation

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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
ams2001glos-Pe4
where the symbol ruv denotes the sample coefficient of linear correlation between any pair of variates u, v.
See regression.

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