Question

The following regression model has been proposed to predict sales at a fast food outlet. y=18−2x₁+7x₂+15x₃

Where
x₁= number of competitors
x₂= population within one mile
x₃=1 if a drive-up window otherwise
Y= sales in (1000s)

What is the interpretation of 15 (the coefficient of X₃ ) in the regression equation?
a) none of the stated answers is correct
b) Sales of stores with drive-up windows are $15,000 higher than those without drive-up windows
c) Sales of stores with drive-up windows are never higher than those without drive-up windows
d) Sales of stores with drive-up windows are $15,000 lower than those without drive-up windows

Answer 1

The coefficient 15 in the regression model indicates that sales at fast food outlets with a drive-up window are $15,000 higher than those without, holding other factors constant.

Step-by-step explanation:

The interpretation of the coefficient 15 for the variable x3 in the regression equation y=18-2x1+7x2+15x3 is that, holding all other factors constant, having a drive-up window at a fast food outlet is associated with an increase in sales by $15,000. Here's why: the variable x3 is a binary variable that takes on a value of 1 if the outlet has a drive-up window, and 0 if it does not.

The coefficient 15 then refers to the increment in the dependent variable y, which represents sales in (1000s), when a drive-up window is present. Therefore, the correct answer is (b) Sales of stores with drive-up windows are $15,000 higher than those without drive-up windows.