Refer to the Market share data set in Appendix C3 and Project 19.55. Use price (variable 3) as a concomitant variable.
a. Obtain the residuals for covariance model (22.26).
b. For each treatment, plot the residuals against the fitted values. Also prepare a normal probability plot of the residuals and calculate the coefficient of correlation between the ordered residuals and their expected values under normality. What do you conclude from your analysis?
c. State the generalized regression model to be employed for testing whether or not the treatment regression lines have the same slope. Conduct this test using α = .05. State the alternatives, decision rule, and conclusion. What is the P-value of the test?
Project 19.55
Refer to the Market share data set in Appendix C.3. A balanced ANOYA study of the effect of discount price (factor A:variable 5) and package promotion (factor B: variable 6) on: average monthly market share (variable 2) is to be conducted. Order the observations in the four factor-level combination cells from smallest to largest observation number and retain first 7 observations in each cell for a total of 28 observations. (This process omits cases with identification numbers (variable I) equal to 24, 25, 27.28,30,33,34, and 36.)
a. Assemble the required data and obtain the fitted values for ANOYA model (19.23).
b. Obtain the residuals.
c. Plot the residuals against the fitted values. What departures from ANOYA model (19.23) can be studied from this plot? What are your findings?
d. Prepare a normal probability plot of the residuals. Also obtain the coefficient of correlation between the ordered residuals and their expected values under normality. Does the normality assumption appear to be reasonable here?
Appendix C.3
Company executives from a large packaged foods manufacturer wished to determine which factors influence the market share of one of its products. Data were collected from a national database (Nielsen) for 36 consecutive months. Each line of the data set has an identification number and provides information on 6 other variables for each month. The data presented here are for September, 1999, through August, 2002. The variables are:
