The multiple regression model for predicting Y from X₁, X₂, and X₃ is
Y_i = b₁X₁_i + b₂X₂_i + b₃X₃_i + a + e_i. If the bivariate correlation of Y and X₁ is positive (r_Y₁> 0) , the partial slope for X₁ (b₁) will be

Question

Quizplus · Accepted Answer

The partial slope (b) in a multiple regression model can be different from the bivariate correlation direction because it accounts for the unique contribution of a variable (X1) after removing the effects of other variables in the model. Thus, even if the bivariate correlation between Y and X1 is positive, the partial slope for X1 can be positive, negative, or zero depending on the relationships among all variables included in the model.

The Multiple Regression Model for Predicting Y from X1, X2

The Multiple Regression Model for Predicting Y from X₁, X₂