Question

Suppose you have four classifications: freshmen (f), sophomore (so), junior (j), and senior (se). You construct a dummy variable, one for each classification that takes on the value of (1) should that classification be true for that observation and 0 otherwise. Further assume that you estimate the following model: E[GPA]= .5*ACT+1*So+-0.97*J+{c}*Se How much higher/lower is a Junior's GPA, after controlling for ACT, than for the omitted category?

Answer 1

Background:

For 4 classifications (i.e. 4 number of qualitative variables), we need only have three dummy variables. In the given equation, E[GPA]= .5*ACT+1*So+-0.97*J+{c}*Se the three dummy variables are defined as follows:

So = 1 if a sophomore is being considered and 0 otherwise

J = 1 if a junior is being considered and 0 otherwise

Se = 1 if a senior is being considered and 0 otherwise

If all the variables So, J and Se = 0 then the Freshman (f), the omitted category, is being considered.

Solution:

Considering only the omitted category, Freshman (f), the equation becomes

E(GPA/f) = .5*ACT -------------------------------------------(1)

Considering only the junior (J), its GPA will be given by the following equation

E(GPA/J) = .5*ACT + 0.97 --------------------------------(2)

Controlling the ACT means, we keep the value of ACT constant for comparing the expected GPA of (f) and (J) categories.

From (1) and (2), we can say that the expected GPA for a junior will be 0.97 higher than the expected GPA of freshman, after controlling for ACT.