A researcher measures three variables X Y and Z for each ind

A researcher measures three variables, X, Y, and Z, for each individual in a sample of n = 25. The Pearson correlations for this sample are rXY = 0.8, rXZ = 0.6, and rYZ = 0.7. a. Find the partial correlation between X and Y, holding Z constant. b. Find the partial correlation between X and Z, holding Y constant.

Solution

a).

A researcher measures three variables, X, Y, and Z, for each individual in a sample of n = 25. The Pearson correlations for this sample are rXY = 0.8, rXZ = 0.6, and rYZ = 0.7.

a. Find the partial correlation between X and Y, holding Z constant.

r_xy.z = (r_xy-r_xzr_yz)/sqrt((1-r_xz²)(1-r_yz²))

r_xy.z = (0.8-0.6*0.7)/sqrt((1-0.6²)(1-0.7²))

=0.38/0.5713

=0.665

b. Find the partial correlation between X and Z, holding Y constant.

r_xz.y = (r_xz-r_xyr_yz)/sqrt((1-r_xy²)(1-r_yz²))

r_xy.z = (0.6-0.8*0.7)/sqrt((1-0.8²)(1-0.7²))

=0.04/0.4285

=0.093