Refer to Product display Problem 22.13. Assume that covariance model (22.3) is applicable.
a. Prepare a symbolic scatter plot of the data. Does it appear that there are display effects on mean sales? Discuss.
b. State the regression model equivalent to covariance model (22.3) for this case; use 1, -1,0 indicator variables. Also state the reduced regression model for testing for treatments effects.
c. Fit the full and reduced regression models and test for treatment effects: use a = .05. State the alternatives, decision rule, and conclusion. What is the P-value of the test?
d. Is MSE( F) for the covariance model substantially smaller than the mean square error if analysis of variance model (16.2) had been employed?
e. Estimate the mean sales with display treatment 2 for stores whose sales in the preceding three-week period were $75: use a 95 percent confidence interval.
f. Make all pairwise comparisons between the treatment effects: use either the Bonferroni or the Scheffe procedure with a 90 percent family confidence coefficient. whichever is more efficient. State your findings.
Problem 22.13
Product display. A manufacturer of felt-tip markers investigated by an experiment whether a proposed new display, featuring a picture of a physician, is more effective in drugstores than the present counter display, featuring a picture of an athlete and designed to b I in the stationery area. Fifteen drugstores of similar characteristics were chosen for study. They were assigned at random in equal numbers 10 one of the following three tree study.
( I ) present counter display in stationery area,(2) new display in stationery area,(3) new display in check out area. Sales with the present display (Xij) were recorded in all 15 stores for a three in week period. Then the new display was set up in the 10 stores receiving it, and sales for the next three - week period (Yij) were recorded in all 15 stores. The data on sales (in dollars) follow.
The analyst wishes to analyze the effects of the three different display treatments by means of covariance analysis.
a. Obtain the residuals for covariance model (22.3).
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 a = .05. State the alternatives, decision rule, and conclusion. What is the P-value of the test?
d. Could you conduct a formal test here as to whether the regression functions are linear? Explain.