As a project for his business statistics class, a student examined the factors that determined parking meter rates throughout the campus area. Data were collected for the price per hour of parking, blocks to the quadrangle, and one of the three jurisdictions: on campus, in downtown and off campus, or outside of downtown and off campus. The population regression model hypothesized is Yᵢ = β₀ + β₁X₁ᵢ + β₂X₂ᵢ + β₃X₃ᵢ + ε where
Y is the meter price
X₁ is the number of blocks to the quad
X₂ is a dummy variable that takes the value 1 if the meter is located in downtown and off campus and the value 0 otherwise
X₃ is a dummy variable that takes the value 1 if the meter is located outside of downtown and off campus, and the value 0 otherwise
Suppose that whether the meter is located on campus is an important explanatory factor. Why should the variable that depicts this attribute not be included in the model?
A) Its inclusion will introduce autocorrelation.
B) Its inclusion will introduce collinearity.
C) Its inclusion will inflate the standard errors of the estimated coefficients.
D) Both B and C.

Question

Quizplus · Accepted Answer

The inclusion of a dummy variable for whether the meter is located on campus will introduce collinearity because the three jurisdictions are mutually exclusive and exhaustive. This means that if we know the values of the dummy variables for downtown and off campus and outside of downtown and off campus, we can perfectly predict the value of the dummy variable for on campus. As a result, the inclusion of the dummy variable for on campus will not provide any additional information to the model and will only serve to inflate the standard errors of the estimated coefficients.

As a Project for His Business Statistics Class, a Student