In multiple correlation equations we are often interested in finding out how much of the variation in the dependent variable is explained by one independent variable if all the other independent variables are kept constant.
For example in the equation Y = a + b1 X1 + b2 X2 we may want to find out how much variation in Y is explained by X1 if X2 is kept constant. This is given by the partial coefficient of determination. Using our simplified subscripts the partial correlation coefficient is given by R12.3.
is the partial correlation coefficient between Y and X1 when X2 is kept constant. Note that here there are two subscripts 1 and 2 before the dot unlike the single subscript before the dot in the multiple correlation coefficient discussed earlier. In fact if r13 and r23 are zero R12.3 reduces to r12, the simple correlation coefficient between Y and X1.