The Tastee Bakery Company supplies a bakery product to many supermarkets in a metropolitan area. The company
Question:
y = βB + BMDM + BTDT + ε
Here DM equals 1 if a middle display height is used and 0 otherwise: DT equals 1 if a top display height is used and 0 otherwise. Figure 14.20 on the next page presents the MINITAB output of a regression analysis of the bakery sales study data using this model.1
FIGURE 14.20
MINITAB Output of a Dummy Variable Regression Analysis of the Bakery Sales Data in Table 14.11
a. By using the definitions of the dummy variables, show that
µB - βB µm = βB + βM µT = βB + βT
b. Use the overall P statistic to test H0: βM = βT = 0, or, equivalently, H0: µB = µM = µT. Interpret the practical meaning of the result of this test.
c. Show that your results in part a. imply that
µM - µB - βM µT - µB = βT µM - µT = βM - βT
Then use the least squares point estimates of the model parameters to find a point estimate of each of the three differences in means. Also, find a 95 percent confidence interval for and test the significance of each of the first two differences in means. Interpret your results.
d. Find a point estimate of mean sales when using a middle display height, a 95 percent confidence interval for mean sales when using a middle display height, and a 95 percent prediction interval for sales at an individual supermarket that employs a middle display height (see the bottom of the MINITAB output in Figure 14.20).
e. Consider the following alternative model
y = βT + βBDB + βMDM + ε
Here Dβ equals 1 if a bottom display height is used and 0 otherwise. The MINITAB output of the least squares point estimates of the parameters of this model is as follows:
Since βM expresses the effect of the middle display height with respect to the effect of the top display height, βM equals µM - µT. Use the MINITAB output to calculate a 95 percent confidence interval for and test the significance of µM - µT Interpret your results.
Step by Step Answer:
Business Statistics In Practice
ISBN: 9780073401836
6th Edition
Authors: Bruce Bowerman, Richard O'Connell