Consider the following multiple regression models (a)to (d)below.DFemme = 1 if the individual is a female,and is zero otherwise;DMale is a binary variable which takes on the value one if the individual is male,and is zero otherwise;DMarried is a binary variable which is unity for married individuals and is zero otherwise,and DSingle is (1-DMarried).Regressing weekly earnings (Earn)on a set of explanatory variables,you will experience perfect multicollinearity in the following cases unless:
A) i = + DFemme + Dmale + X3i
B) i = + DMarried + DSingle + X3i
C) i = + DFemme + X3i
D) i = DFemme + Dmale + DMarried + DSingle + X3i

Question

Consider the following multiple regression models (a)to (d)below.DFemme = 1 if the individual is a female,and is zero otherwise;DMale is a binary variable which takes on the value one if the individual is male,and is zero otherwise;DMarried is a binary variable which is unity for married individuals and is zero otherwise,and DSingle is (1-DMarried).Regressing weekly earnings (Earn)on a set of explanatory variables,you will experience perfect multicollinearity in the following cases unless:
A) i = + DFemme + Dmale + X3i 
B) i = + DMarried + DSingle + X3i 
C) i = + DFemme + X3i 
D) i = DFemme + Dmale + DMarried + DSingle + X3i

Quizplus · Accepted Answer

In Model C, there are only two explanatory variables: DFemme and X3i. There is no perfect multicollinearity in this model. In contrast, Model A includes both DFemme and Dmale, which are binary variables indicating gender, leading to perfect multicollinearity. Model B includes both DMarried and DSingle, which are also binary variables indicating marital status, resulting in perfect multicollinearity. Model D includes all four binary variables (DFemme, Dmale, DMarried, and DSingle), resulting in perfect multicollinearity. Thus, the only model without perfect multicollinearity is Model C.

Consider the Following Multiple Regression Models (A)to (D)below