Given the multiple regression equation, ? = a + b1X1 + b2X2, and the bivariate equation ? = a + bX, why is the partial regression coefficient, b1, different from the regression coefficient, b, obtained by regressing Y on only X1?
What will be an ideal response?
This happens because X1 and X2 are usually correlated. In bivariate regression, X2 was not considered and any variation in Y that was shared by X1 and X2 was attributed to X1. However, in the case of multiple independent variables, this is no longer true.
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