In a multiple regression problem involving two independent variables, if b₁ is computed to be +2.0, it means that
A) the relationship between X₁ and Y is significant.
B) the estimated mean of Y increases by 2 units for each increase of 1 unit of X₁, holding X₂ constant.
C) the estimated mean of Y increases by 2 units for each increase of 1 unit of X₁, without regard to X₂.
D) the estimated mean of Y is 2 when X₁ equals zero.

Question

Quizplus · Accepted Answer

The coefficient b₁ represents the change in Y (dependent variable) associated with a one-unit increase in X₁ (independent variable), holding all other variables constant. Therefore, if b₁ is computed to be +2.0, it means that the estimated mean of Y increases by 2 units for each increase of 1 unit of X₁, holding X₂ constant. Option A is incorrect because the significance of the relationship between X₁ and Y cannot be determined from the regression coefficient alone. Option C is incorrect because it ignores the effect of X₂ on Y. Option D is incorrect because it assumes that Y is 2 when X₁ is zero, which may not be true in most cases.

In a Multiple Regression Problem Involving Two Independent Variables, If