A chain restaurant that specializes in selling hamburgers wants to analyze how y = sales

QUESTION:

A chain restaurant that specializes in selling hamburgers wants to analyze how y = sales for a customer (the total amount spent by a customer on food and drinks, in dollars) depends on the location of the restaurant, which is classified as inner city, suburbia, or at an interstate exit.

a. Construct indicator variables x1 for inner-city and x2 for suburbia so you can include location in a regression equation for predicting the sales.

b. For part a, suppose ŷ = 5.8 – 0.7x1 + 1.2x2. Find the difference between the estimated mean sales in suburbia and at interstate exits.


ANSWER:

a. x1 = 1 if inner city; 0 if other; x2 = 1 if suburbia; 0 if other

b. Suburbia: ŷ = 5.8 – 0.7(0) + 1.2(1) = 7.0; interstate exits: ŷ = 5.8 – 0.7(0) + 1.2(0) = 5.8 Interstate exit restaurants have predicted sales of $1.20 less than suburban restaurants.

 

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