4.4 In the three-variable model, Y and regressors X2 and X3, we can compute three partial correlation coeffi cients. For example, the partial correlation between Y and X2, holding X3 constant, denoted as r12.3, is as follows: r r rr r r 12 3 12 13 23 13 2 23 2 1 1 . ( )( ) where the subscripts 1, 2, and 3 denote the variables Y, X2, and X3, respectively and r12, r13 and r23 are simple correlation coeffi cients between the variables.

(a) When will r12.3 be equal to r12? What does that mean?

(b) Is r12.3 less than, equal to or greater than r12? Explain.