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

Question

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

Quizplus · Accepted Answer

A coefficient of +2.0 for an independent variable means that the estimated mean of Y increases by 2 units for each increase of 1 unit of that independent variable, holding all other independent variables constant. This is known as the partial effect of that variable on Y. Therefore, option B is the correct answer. Option A refers to the significance of the relationship, which cannot be determined solely based on the coefficient value. Option C wrongly suggests that other independent variables do not affect Y. Option D is also incorrect because the coefficient value does not provide information about the mean value of Y when the independent variable is zero. A regression coefficient (in this case, 2.0) represents the change in the dependent variable (Y) associated with a one-unit increase in the independent variable (in this case, 11ebc114_12a8_2cb0_8acb_2dd6db791f7a_TB8562_11), while holding all other independent variables constant (in this case, the other independent variable is not specified). Therefore, the estimated mean of Y increases by 2 units for each increase of 1 unit of 11ebc114_12a8_2cb0_8acb_2dd6db791f7a_TB8562_11, holding the other independent variable constant.

In a Multiple Regression Problem Involving Two Independent Variables, If