The marketing manager of a large supermarket chain faced the business problem of determining the effect on the sales of pet food of shelf space and whether the product was placed at the front (=1) or back (=0) of the aisle. Data are collected from a random sample of equal-sized stores. The results are shown in the following table (and organized and stored in Petfood):
|
Store
|
Shelf Space (Feet)
|
Location
|
Weekly Sales (Dolllars)
|
|
1
|
5
|
0
|
160
|
|
2
|
5
|
0
|
220
|
|
3
|
5
|
0
|
140
|
|
4
|
10
|
0
|
190
|
|
5
|
10
|
0
|
240
|
|
6
|
10
|
1
|
260
|
|
7
|
15
|
0
|
230
|
|
8
|
15
|
0
|
270
|
|
9
|
15
|
1
|
280
|
|
10
|
20
|
0
|
260
|
|
11
|
20
|
0
|
290
|
|
12
|
20
|
1
|
310
|
Store Shelf Space (Feet) Location Weekly Sales (Dolllars) 1 5 0 160 2 5 0 220 3 5 0 140 4 10 0 190 5 10 0 240 6 10 1 260 7 15 0 230 8 15 0 270 9 15 1 280 10 20 0 260 11 20 0 290 12 20 1 310 For (a) through (m), do not include an interaction term.
A. State the multiple regression equation that predicts sales based on shelf space and location. a. Y=a + b1X1 + b2X2 + b3X3
B. Interpret the regression coefficients in (a).
C. Predict the weekly sales of pet food for a store with 8 feet of shelf space situated at the back of the aisle. Construct a 95% confidence interval estimate and a 95% prediction interval.
D. Perform a residual analysis on the results and determine whether the regression assumptions are valid.