A sociologist is looking at the relationship between consumption expenditures y of families in the United States, family income x, and w h ether or not the family lives in an urban or rural com m unity (Urban = 1 if urban, 0 otherwise). She collects data on 50 families across the United States, a portion of which is shown in the accompanying table. The full data set can be found on the text website, labeled Urban.
|
Consumption ($)
|
Income ($)
|
Urban
|
|
62336
|
87534
|
0
|
|
60076
|
94796
|
1
|
|
.....
|
.....
|
.....
|
|
59055
|
100908
|
1
|
a. Estimate a linear model without a dummy, y = β0 + β1x + ε. Compute the predicted consumption expenditures of a family with income of $75,000.
b. Include a dummy d to predict consumption for Income = $75,000 in urban and rural com m unities.
c. Include a dummy d and an interaction xd variable to predict consumption for Income = $75,000 in urban and rural com m unities.
d. Which of the above models is most suitable for the data? Explain.