Partial correlation: The partial correlation between X1 and Y ‘‘controlling for’’

X2 through Xk is defined as the simple correlation between the residuals EYj2 ... k and E1j2 ... k , given in the previous exercise. The partial correlation is denoted rY1j2...k .

(a) Using the Canadian occupational prestige data, calculate the partial correlation between prestige and education, controlling for income and percentage women (see the previous exercise).

(b) In light of the interpretation of a partial regression coefficient developed in the previous exercise, why is rY1j2 ... k ¼ 0 if and only if B1 (from the multiple regression of Y on X1 through Xk ) is 0?