A sociologist is studying the relationship between consumption expenditures y of families in the United States, family income x, and whether or not the family lives in an urban or rural community. She collects data on 50 families, a portion of which is shown in the accompanying table. The entire data set, labeled Urban_Rural, can be found on the text website.

a. Estimate y = β₀ + β₁x + β₂d + ε where the dummy variable d equals 1 for urban families. Use the estimated model to predict the consumption expenditure of urban families with an income of $80,000. What is the corresponding consumption expenditure of rural families?

b. Estimate y = β₀ + β₁x + β₂d + ε where the dummy variable d equals 1 for rural families. Use the estimated model to predict the consumption expenditure of urban families with an income of $80,000. What is the corresponding consumption expenditure of rural families?

c. Interpret the results of the above two models.

Consumption ()Income ($) 62,336 60,076 87,534 94,796 Community Rural Urban 59,055 100,908 Urban