Question

The following is the regression output for fitting the regression model that predicts the monthly sales of the power bars from the price of the power bar and the monthly budget for the in-store promotional expenditures. Constant Price Promotion Coefficient 6310.55 -50.855 3.5554 95% CI 95% CI Lower Limit Upper Limit 4052.83138 8568.26862 -79.76212 -21.94788 1.72715 5.38365 TP-value 5.89715 2e-05 -3.7117 0.00173 4.10297 0.00074 Use the regresion output above to answer the following questions. Part A What is the predicted sales of the power bars for a store spending 500 dollars on promotional expenditures in a month and (Round the answers to 5 decimal places if possible) (1) charging 50 cents on the power bar? (2) charging 60 cents on the power bar? (3) charging 70 cents on the power bar? (4) charging 80 cents on the power bar? (5) charging 90 cents on the power bar? Part B What is the predicted sales of the power bars for a store charging 70 cents on the power bar and spending (Round the answers to 5 decimal places if possible) (1) 200 dollars on the promotional expenditures in a month? (2) 400 dollars on the promotional expenditures in a month? (3) 600 dollars on the promotional expenditures in a month? (4) 800 dollars on the promotional expenditures in a month? (5) 1,000 dollars on the promotional expenditures in a month?

Answer 1

Part A:

(1)

The Regression Equation is:

$\hat{y}$ = 6310.55 - 50.855 x1 + 3.5554 x2

For x1= 0.50 and x2 =500, we get:

$\hat{y}$ = 6310.55 - (50.855 X 0.50) + (3.5554 X 500)

= 6310.55 - 25.4275 + 1777.7

= 8062.82250

So,

Answer is:

8062.82250

(2)

The Regression Equation is:

$\hat{y}$ = 6310.55 - 50.855 x1 + 3.5554 x2

For x1= 0.60 and x2 =500, we get:

$\hat{y}$ = 6310.55 - (50.855 X 0.60) + (3.5554 X 500)

= 6310.55 - 30.513 + 1777.7

= 8057.73700

So,

Answer is:

8057.73700

(3)

The Regression Equation is:

$\hat{y}$ = 6310.55 - 50.855 x1 + 3.5554 x2

For x1= 0.70 and x2 =500, we get:

$\hat{y}$ = 6310.55 - (50.855 X 0.70) + (3.5554 X 500)

= 6310.55 - 35.5985 + 1777.7

= 8052.6515

So,

Answer is:

8052.65150

(4)

The Regression Equation is:

$\hat{y}$ = 6310.55 - 50.855 x1 + 3.5554 x2

For x1= 0.80 and x2 =500, we get:

$\hat{y}$ = 6310.55 - (50.855 X 0.80) + (3.5554 X 500)

= 6310.55 - 40.684 + 1777.7

= 8047.56600

So,

Answer is:

8047.56600

(5)

The Regression Equation is:

$\hat{y}$ = 6310.55 - 50.855 x1 + 3.5554 x2

For x1= 0.90 and x2 =500, we get:

$\hat{y}$ = 6310.55 - (50.855 X 0.90) + (3.5554 X 500)

= 6310.55 - 45.7695 + 1777.7

= 8042.48050

So,

Answer is:

8042.48050

Part B:

(1)

The Regression Equation is:

$\hat{y}$ = 6310.55 - 50.855 x1 + 3.5554 x2

For x1= 0.70 and x2 =200, we get:

$\hat{y}$ = 6310.55 - (50.855 X 0.70) + (3.5554 X 200)

= 6310.55 - 35.5985 + 711.08

= 6986.03150

So,

Answer is:

6986.03150

(2)

The Regression Equation is:

$\hat{y}$ = 6310.55 - 50.855 x1 + 3.5554 x2

For x1= 0.70 and x2 =400, we get:

$\hat{y}$ = 6310.55 - (50.855 X 0.70) + (3.5554 X 400)

= 6310.55 - 35.5985 + 1422.16

= 7697.11150

So,

Answer is:

7697.11150

(3)

The Regression Equation is:

$\hat{y}$ = 6310.55 - 50.855 x1 + 3.5554 x2

For x1= 0.70 and x2 =600, we get:

$\hat{y}$ = 6310.55 - (50.855 X 0.70) + (3.5554 X 600)

= 6310.55 - 35.5985 + 2133.24

= 8408.19150

So,

Answer is:

8408.19150

(4)

The Regression Equation is:

$\hat{y}$ = 6310.55 - 50.855 x1 + 3.5554 x2

For x1= 0.70 and x2 =800, we get:

$\hat{y}$ = 6310.55 - (50.855 X 0.70) + (3.5554 X 800)

= 6310.55 - 35.5985 + 2844.32

= 9119.2715

So,

Answer is:

9119.27150

(5)

The Regression Equation is:

$\hat{y}$ = 6310.55 - 50.855 x1 + 3.5554 x2

For x1= 0.70 and x2 =1000, we get:

$\hat{y}$ = 6310.55 - (50.855 X 0.70) + (3.5554 X 1000)

= 6310.55 - 35.5985 + 3555.4

= 9830.3515

So,

Answer is:

9830.35150