Management proposed the following regression model to predic

Management proposed the following regression model to predict sales at a fast food outlet

Y=b_o + b₁X₁ + b₂X₂ + b₃X₃

Where X₁=number of competitors within one mile

X₂= population within one mile (1000s)

X₃=1 if drive up window present

X₃=0 if no drive up window

Y=sales ($1000)

The following estimated regression equation was developed after 20 outlets were surveyed.

Y=10.1 -4.2X₁ + 6.8X₂ + 15.3X₃

Interpret the coefficient on X₃ [3]

Predict sales for a store with 2 competitors, a population of 8000 within one mile and no drive up window [3]

Solution

a. If we increase X3 by 1 and hold the other two independent variables constant, we expect the sales for a store to increase by 15.

b.

Y=10.1 -4.2X1 + 6.8X2 + 15.3X3

Where X1=2, X2= 8000, X3= 0

Y=10.1 -4.2(2)+ 6.8(8000) + 15.3(0) =54401.7