A consumer products company relies on direct mail marketing pieces as a major component of its advertising campaigns. The company has three different designs for a new brochure and wants to evaluate their effectiveness, as there are substantial differences in costs between the three designs.
The company decides to test the three designs by mailing 5000 samples of each to potential customers in four different regions of the country. Since there are known regional differences in the customer base, regions are considered as blocks. The number of responses to each mailing is given below.
(a) Write the appropriate terms in this model.
(b) Analyze the data from this experiment.
(c) Use the Fisher LSD method to make comparisons among the three designs to determine specifically which designs differ in the mean response rate.
(d) Analyze the residuals from this experiment.

Design Region Number of Responses
1 NE 250
1 NW 350
1 SE 219
1 SW 375
2 NE 400
2 NW 525
2 SE 390
2 SW 580
3 NE 275
3 NW 340
3 SE 200
3 SW 310