1. A supermarket chain is interested in exploring the relationship between the s

Question

1. A supermarket chain is interested in exploring the relationship between the sales of its store-band canned vegetables (y), the amount spent on promotion of the vegetables in local newspapers (x1), and the amount of shelf space allocated to the brand (x2). One of the chain’s supermarkets was randomly selected, and over a 20-week period, x1 and x2 were varied, as reported in the data below

Minitab Data

a. Test for the presence of an interaction between advertising expenditures and shelf space. Use = 0.05.

b. What is the expected change in mean sales for a 1 sq. ft. increase in shelf space when advertising expenditures is $500?

Explanation / Answer

a. I have done this presence test in Excel. Where i have tested interaction between advertising expenditures and shelf space. Alpha = 0.05

Here we can see the Interaction level X1X2

The t - stat = 7.59

P- value = 1.13 x 10-6 which is under significane level alpha 0.05 so it can be said that interaction level between advertising expenditures and shelf space is stastically significant.

b. The linear regression equation is when there is interaction of advertising expenditure and shelf space taken .

y = 1333.178 -0.15122 x1 -2.62532 x2 + 0.051954 (x1x2)

so at x1 = 500 for change in 1 sq. ft. in x2

lets say for x2 = x

yx = 1333.178 -0.15122 * 500 -2.62532 x + 0.051954 (500x)

yx+1 = 1333.178 -0.15122 * 500 -2.62532 (x+1) + 0.051954 [500(x+1)]

yx+1 - yx = -2.62532 + 0.051954 * 500 = 23.35

so there is $23.35 change in mean sales for a 1 sq. ft. increase in shelf space when advertising expenditure is $ 500.

Week AdExp(X1) Shelf Spc(x2) X1X2 Sales 1 201 75 15075 2010 2 205 50 10250 1850 3 355 75 26625 2400 4 208 30 6240 1575 5 590 75 44250 3550 6 397 50 19850 2015 7 820 75 61500 3908 8 400 30 12000 1870 9 997 75 74775 4877 10 515 30 15450 2190 11 996 75 74700 5005 12 625 50 31250 2500 13 860 50 43000 3005 14 1012 50 50600 3480 15 1135 75 85125 5500 16 635 30 19050 1995 17 837 30 25110 2390 18 1200 50 60000 4390 19 990 30 29700 2785 20 1205 30 36150 2989

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