Question

Management proposed the following regression model to predict sales at fast food outlet. ? = ?0 + ?1?1 + ?2?2 + ?3?3 + ? where ?1 = ?????? ?? ??????????? ???ℎ??? ??? ???? ?2 = ?????????? ???ℎ?? ??? ????(1000?) ?3 = { 1 ?? ???? − ?? ?????? ??????? 0 ??ℎ?? ???? ? = ????? ($1000?) The following estimated regression equation was developed after 20 outlets were surveyed. ?̂ = 20.2 + 3.2?1 + 5.8?2 + 25.7?3 a. What is the expected amount of sales attributable to the drive-up window? b. Predict sales for a store with two competitors, a population of 2000 within one mole, and no dive-up window. c. Predict sales for a store with two competitors, a population of 2000 within one mole, and a dive-up window.

Answer 1

Given eqn:

?̂ = 20.2 + 3.2?1 + 5.8?2 + 25.7?3

a.)

Expected value of sales when drive up window is present

E(y) = 20.2 + 25.7 * 1 = 45.9

When window is not present

E(y) = 20.2 + 25.7 * 0 = 20.2

This means if drive window is present Sales increases by 25.7 units

b.)

Here, x1 = 2, x2 = 2000, x3 = 0 ( no window)

Hence, y = 20.2 + 3.2 * 2 + 5.8 * 2000 + 0

y = 11626.6$

c.)

In this case x3 = 1

Hence, y = 20.2 + 3.2 * 2 + 5.8 * 2000 + 25.7

y = 11652.3$