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 + b_{1 }X_{1} + b_{2} X_{2 }we may want to find out how much variation in Y is explained by X_{1} if X_{2} is kept constant. This is given by the partial coefficient of determination. Using our simplified subscripts the partial correlation coefficient is given by R_{12.3}.
is the partial correlation coefficient between Y and X_{1} when X_{2} 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 r_{13} and r_{23} are zero R_{12.3} reduces to r_{12}, the simple correlation coefficient between Y and X_{1}.