Partial correlation is a procedure that allows us to measure the region of three-way overlap precisely, and then to remove it from the picture in order to determine what the correlation between any two of the variables would be (hypothetically) if they were not each correlated with the third variable. Alternatively, you can say that partial correlation allows us to determine what the correlation between any two of the variables would be (hypothetically) if the third variable were held constant. The partial correlation of X and Y, with the effects of Z removed (or held constant), would be given by the formula
http://faculty.vassar.edu/lowry/ch3a.html
http://tolstoy.newcastle.edu.au/R/help/00a/0512.html
http://en.wikipedia.org/wiki/Partial_correlation
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