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

Interpret the coefficient on X3: If all other variables (X2, and X3) remain constant and if drive up window present then there is an increase in sales by $15.3 (in thousand).

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Here we have X1=2, X2= 8 and X3 =0 so Predict sales is

Y=10.1 -4.2X1 + 6.8X2 + 15.3X3=10.1-4.2*2+6.8*8+15.3*0=56.1

hence, predicted sale is $56,100.