Three variables have population correlations x1x2 = 0.85, yx1 = 0.65, and yx2 = 0.65. For these,

Three variables have population correlations

ρx1x2

= 0.85, ρyx1

= 0.65, and ρyx2

= 0.65. For these, the partial correlations are ρyx1·x2

= ρyx2·x1

= 0.244. In a sample, rx1x2

= 0.90, ryx1

= 0.70, and ryx2

= 0.60, not far from the population values. For these, the sample partial correlations are ryx1·x2

= 0.46 and ryx2·x1

= −0.10. What does this large difference suggest about standard errors of partial correlationswhenmulticollinearity exists?(Anunwary observer might conclude that the partial effects of x1 and x2 have opposite signs and that the partial effect of x1 is much stronger, when they are identical in the population.)