5.57

CO C OTITOUTTOI TOTHOM ! P9 COITOTUOT ' b. Could a cubic model be fit to the data? Explain. c. Suppose the research and development department develops three new types of paint to be tested. Thus, 90 cars are to be tested30 for each type of paint. Write the complete second-order model for E(y) as a function of the type of paint and bake time. 5.57. Modeling product sales. A company wants to model the total weekly sales, y, of its product as a function of the variables packaging and location. Two types of packaging, p1 and P2, are used in each of four locations, L1,L2,L3, and L4. a. Write a main effects model to relate E(y) to packaging and location. What implicit assumption are we making about the interrelationships between sales, packaging, and location when we use this model? b. Now write a model for E(y) that includes interaction between packaging and location. How many parameters are in this model (remember to include Bo)? Compare this number to the number of packaging-location combinations being modeled. c. Suppose the main effects and interaction models are fit for 40 observations on weekly sales. The values of SSE are SSE for main effects model = 422.36 SSE for interaction model = 346.65 Determine whether the data indicate that the interaction between location and packaging is important in estimating mean weekly sales. Use a =.05. What implications does your conclusion have for the company's marketing strategy? 5.58. Earnings of Mexican street vendors. Refer to the World Development (February 1998) study of street vendors in the city of Puebla, Mexico, Exercise 4.94 (p. 253). Recall that the vendors' mean annual earnings, E(y), was modeled as a first-order function of age (X1) and hours worked (x2). The data for the study are reproduced in the table. & STREETVEN VENDOR NUMBER ANNUAL EARNINGS, Y AGE, 31 HOURS WORKED PER DAY, 29