Question

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

                           Y=60-2X1+30X2+10X3

                           Where

                           X1= competitor’s previous day’s sales (in $1,000s)

                           X2=population within 1 mile (in 1,000s)

                           X3= 1 if radio advertising was used; 0 if otherwise

1. What is the estimated regression equation if no radio advertising was used?

2. What is the estimated regression equation if radio advertising was used?

3. What is the expected amount of sales attributable to radio advertising?

                           Y= Sales (in $1,000s)

Answer 1

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

                           Y=60-2X1+30X2+10X3

                           Where

                           X1= competitor’s previous day’s sales (in $1,000s)

                           X2=population within 1 mile (in 1,000s)

                           X3= 1 if radio advertising was used; 0 if otherwise

a)What is the estimated regression equation if no radio advertising was used?

X3= 1 if radio advertising was used; 0 if otherwise

Here it is absent, so x3 = 0

Y=60-2X1+30X2+10X3

Y=60-2X1+30X2+10*0

Y=60-2X1+30X2

The estimated regression equation if no radio advertising was used:-  Y=60-2X1+30X2

b)  

What is the estimated regression equation if radio advertising was used?

Here it is present , so x3 = 1

Y=60-2X1+30X2+10X3

Y=60-2X1+30X2+10*1

Y=60-2X1+30X2+10

Y=70-2X1+30X2

The estimated regression equation if radio advertising was used:- Y=70-2X1+30X2

c) What is the expected amount of sales attributable to radio advertising?

The coefficient of radio advertising is 10

So we may conclude that the expected amount of sales attributed to radio advertising is 10.

But Y= Sales (in $1,000s)

So $ 1,000 * 10 = $10000

Answer:-The expected amount of sales attributable to radio advertising $ 10,000.