申論題

4. A researcher is investigating determinants of academic performance among high
school students. Suppose that academic performance (measured by GPA) depends
on gender (male or female) and whether the student lives in urban areas (urban or
rural). The model can be specified as:

where female: is a dummy variable that indicates if the student is female, that
is, female: = 1 if student i is female and female: = O if student i is not female
(meaning that student i is male). urban, is a dummy variable indicating if student
i lives in urban areas, that is, urban: = 1 if student i lives in urban areas; and
urban: = O if student i does not live in urban areas (meaning that the student lives
in rural areas). female: X urban, is an interaction term of these two variables. Gi
is a random error term.

(c) What is the difference between the expected GPA of female students living in urban areas and the expected GPA of male students living in urban areas? What is the difference between male students living in urban areas and male students living in rural areas? Express in terms of B's and show your work. that