Question

3. The same marketing manager from problem #1 wants to consider another variable in determining product location for paper products. In addition to shelf space, the manager wants to consider whether placing the product at the front (= 1) or back (= 0) of the aisle influences weekly sales. Use the data file PaperProducts(2).

a. Run a multiple regression using shelf space (X₁) and location (X₂) to predict sales (Y). Report your regression equation.

b. Is the regression model you ran statistically significant? How can you tell?

c. Using the regression equation you generated in (a), predict the amount of sales if 8 square feet of shelving is used for paper products at the front of the isle and compare it to the sales if 8 square feet of shelving is used for paper products at the back of the isle. Discuss your results.

d. What is the relationship (correlation) between the predictors in the model and sales?

e. How much variance in sales is explained by the predictors?

f. Which of your predictors explain a unique amount of variance in sales?

Shelf Space	Aisle Location	Sales
5	0	160
5	1	220
5	0	140
10	0	190
10	0	240
10	1	260
15	0	230
15	0	270
15	1	280
20	0	260
20	0	290
20	1	310

Answer 1

a. Run a multiple regression using shelf space (X₁) and location (X₂) to predict sales (Y). Report your regression equation.

Y = 130 + 7.4*X1 + 45*X2

b. Is the regression model you ran statistically significant? How can you tell?

The hypothesis being tested is:

H₀: β₁ = β₂ = 0

H₁: At least one β_i ≠ 0

The p-value is 0.0001.

Since the p-value (0.0001) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the model is significant.

c. Using the regression equation you generated in (a), predict the amount of sales if 8 square feet of shelving is used for paper products at the front of the isle and compare it to the sales if 8 square feet of shelving is used for paper products at the back of the isle. Discuss your results.

Y = 130 + 7.4*8 + 45*1 = 234.2

Y = 130 + 7.4*8 + 45*0 = 189.2

The results are different.

d. What is the relationship (correlation) between the predictors in the model and sales?

r = 0.834

e. How much variance in sales is explained by the predictors?

R² = 0.864

f. Which of your predictors explain a unique amount of variance in sales?

Both X1 and X2