The marketing manager of a supermarket wants to determine the effect of shelf space (in square feet) and shelf location (front, middle, or back of the aisle) on sales of a product. Data are collected from a random sample of 16 equal-sized stores, and the results are summarized in the table below. In store #1, the product was put on 20 square feet of shelf space, and the shelf was located at the back of the aisle. The weekly sales of the product were $294. Similarly, in store #2, the product was put on 15 square feet of space, but the shelf was located in the middle of the aisle. The weekly sales were $321.
The manager wants to use a multiple regression analysis that predicts weekly sales based on shelf space and location, but she is not sure how to include the location variable into the model. She asks for your help to solve the problem.
[a] How can she include location as an independent variable?
[b] Run the regression analysis using SALES as the dependent variable and SPACE, FRONT, and BACK as the independent variables.
[c] State clearly the estimated regression equation in [b].
[d] Interpret the regression slopes in the above equation.
[e] Is there a significant relationship between SALES and the three independent variables at the 0.05 level of significance?
[f] At the 0.05 level of significance, determine whether each independent variable makes a strong contribution to the regression model.
[g] Predict the weekly sales of the product for a store with 16 square feet of space situated at the back of the aisle.
[h] Predict the weekly sales of the product for a store with 16 square feet of space situated in the middle of the aisle.
Store Sales Shelf Space Aisle Location
1 294 20 back
2 321 15 middle
3 190 10 back
4 231 5 middle
5 267 15 back
6 348 20 middle
7 166 5 back
8 288 20 middle
9 396 20 front
10 266 10 middle
11 347 15 front
12 140 5 back
13 246 15 middle
14 278 5 front
15 334 10 front
16 238 10 back