Question

Question #1

The sale of handguns is very popular in the Hill Country. A Criminal Justician researcher who has been investigating the prevalence of guns in the State came up with the following regression model to predict sales at one of the gun outlets.

where

X₁ = number of competitors who also sell guns within one mile
X₂ = population within 1 mile (1000s)

X₃= {=1 when purchase by drive-up window is allowed; =0 when purchase by drive-up window is not allowed}

y = sales ($ 1000s)

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

Y^ = 10.1 - 4.2x₁+ 6.8x₂+ 15.3x₃

1. What is the expected amount of sales attributable to the drive-up window?

2. Predict sales for a store with two competitors, a population of 8000 within 1 mile, and
   no drive-up window.
3. Predict sales for a store with one competitor, a population of 3000 within 1 mile, and
   a drive-up window
4. Interpret the coefficient for population within 1 mile
5. Interpret the coefficient for the number of competitors who sell guns within one mile

Answer 1

1. Predict sales for a store with two competitors, a population of 8000 within 1 mile, and
   no drive-up window.

Y = 10.1 - 4.2*2+ 6.8*8000+ 15.3*0

Y = 54401.7

1. Predict sales for a store with one competitor, a population of 3000 within 1 mile, and
   a drive-up window

Y = 10.1 - 4.2*1+ 6.8*3000+ 15.3*1

Y = 20421.2

1. Interpret the coefficient for population within 1 mile

For every additional population within 1 mile, sales will increase by 6.8.

1. Interpret the coefficient for the number of competitors who sell guns within one mile

For every additional competitor who sells guns within one mile, sales will decrease by 4.2.