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Partial correlation

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In probability theory and statistics, partial correlation measures the degree of association between two variables, with the effect of a set of controlling variables removed.

Formal Definition

Formally, the partial correlation between X and Y given a set of n controlling variables Z = {Z1, Z2, …, Zn}, written ρXY·Z, is the correlation between the residuals RX and RY resulting from the linear regression of X with Z and of Y with Z, respectively.

Computation

By solving regression problem.

Recusively.

Using matrix inversion.

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