Question

Management of a fast-food chain proposed the following regression model to predict sales at outlets: y = β0 + β1x1 + β2x2 + β3x3 + ε, where y = sales ($1000s) x1 = number of competitors within one mile x2 = population (in 1000s) within one mile x3 is 1 if a drive-up window is present, 0 otherwise The following estimated regression equation was developed after 20 outlets were surveyed: begin mathsize 14px style y with hat on top end style = 14.8 − 3.5x1 + 3.2x2 + 15.8x3 Use this equation to predict sales for a store with 3 competitors, a population of 5100 within one mile, and no drive-up window. Note: omit the $ symbol in your answer

Answer 1

y [ Expected Sales ] = 20.62 thousands

Explanation:

Regression line : y = 14.8 − 3.5x1 + 3.2x2 + 15.8x3 ; where

y = sales (in 1000s), x1 = number of competitors within one mile, x2 = population (in 1000s) within one mile, x3 = 1 (if a drive-up window is present) or x3 = 0 (if a drive-up window is not present)

x1 (competitors) = 3 , x2 (population) = 5100 = 5.1 thousands , x3 (no drive up window) = 0

y = 14.8 − 3.5 (3) + 3.2 (5.1) + 15.8 (0)

y = 14.8 - 10.5 + 16.32

y [ Expected Sales ] = 20.62 thousands