Question

A two-variable model involving one quantitative explanatory variable and one categorical (binary) explanatory variable (and no interaction), results in two regression lines that are:

A.     Always parallel.

B.     Could be parallel but, depending on the data, may not.

C.      Never parallel.

D.     Always horizontal.

The two methods of including a binary categorical variable in a regression model are to use indicator coding or effect coding. For indicator coding in the two-variable model (with no interaction):

A.     The binary variable is coded (-1,1) and the coefficient for the binary variable in the corresponding regression equation is the difference between the two group means.

B.     The binary variable is coded (-1,1) and the coefficient for the binary variable in the corresponding regression equation is the difference between one of the group means and the least-squares mean (the overall mean).

C.      The binary variable is coded (0,1) and the coefficient coefficient for the binary variable in the corresponding regression equation is the difference between the two group means.

D.     The binary variable is coded (0,1) and the coefficient for the binary variable in the corresponding regression equation is the difference between one of the group means and the least-squares mean (the overall mean).

Answer 1

1) A two-variable model involving one quantitative explanatory variable and one categorical (binary) explanatory variable (and no interaction), results in two regression lines that are (A)always parallel because the coefficient of binary variable makes the difference in intercept not in slope. lines with two different intercepts would always be parallel to each other but with different positions.

2) C.      The binary variable is coded (0,1) and the coefficient for the binary variable in the corresponding regression equation is the difference between the two group means.

In regression, the binary variable is always coded as 0/1 with 1 means presence and 0 means absence of the reference category. In the regression equation with the binary variable, the coefficient of the binary variable represents the difference between two group means and this difference would be added to the overall mean to make any change in the intercept of the regression equation. So the intercepts differ for two groups keeping the slope constant which makes the two regression equation parallel.