Question

The following regression model has been proposed to predict sales at a computer store:

y_hat = 50 – 3x₁ + 20x₂ + 10x₃

where

x₁ = competitor's previous day's sales (in $1000s)

x₂ = population within 1 mile (in 1000s)

x₃ =  ​1 if any radio advertising was used and 0 otherwise.

y_hat= sales (in $1000s)

Predict the change in sales (in dollars) when radio advertising was used, all else constant.

The first problem was Predict sales (in dollars) for a store with the competitor's previous day's sale of $5000, a population of 20,000 within 1 mile, and nine radio advertisements.

y_hat= 525k

Predicting change in sales when radio advertising was used and all else is constant is my question.

Answer 1

y_hat = 50 – 3x1 + 20x2 + 10x3

First calculate y_hat for x1=5000

x2=20000

x3=0

y_hat = 50 – 3*5 + 20*20 + 10*0

=50-15+40

=75

Now y_hat for

x1=5000

x2=20000

x3=1

y_hat = 50 – 3*5 + 20*20 + 10*1

=85

Hence sale will increase by 10 K if radio advertising was used