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. In fact, the first-order partial correlation (i.e. when n=1) is nothing else than a difference between a correlation and the product of the removable correlations divided by the product of the coefficients of alienation of the removable correlations. The coefficient of alienation, and its relation with joint variance through correlation are available in Guilford (1973, pp. 344–345).
Read more about this topic: Partial Correlation
Famous quotes containing the words formal and/or definition:
“The formal Washington dinner party has all the spontaneity of a Japanese imperial funeral.”
—Simon Hoggart (b. 1946)
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (1772–1834)