1. What’s the estimated value from the ANOVA regression given by the slopes in Table 4 for the change in sales in the Midwest if ads feature the small labor partition? What’s the simple way to get this estimate?
2. The standard errors of the slopes of the dummy variables in Table 4 are all the same (80.57) and less than the common standard error of the interactions (113.94). Why is that?
3. What happens to the profile plot in Figure 1 if we reverse the rows and columns of the data? (Let Price Partition define the x-axis and connect points in the same region.) Sketch the new plot. Do you still see the presence of interaction?
4. We don’t actually need further calculations to compare the effects of the price partitions within regions; everything we need is in Table 1 and Table 2. Using those tables, identify a statistically significant difference among the means in the Northeast. Be sure to adjust for multiple comparisons (Chapter 26).
5. The analysis shown here uses a balanced experiment, with equal numbers of observations for each pairing of the factors. What happens to the estimates and their standard errors if that’s not the case? Does your software still work? Try it! Delete a few rows of the data and see what happens.
6. The structure of these data resembles the structure of the data in the pricing example, but there are differences.
(a) If we consider the satisfaction data as an experiment, with response Rating, are the data balanced?
(b) What are the implications for the later analysis of your answer to (a)?
7. (a) What do you learn from a one-way analysis of variance of Rating by Vehicle Category?
(b) What do you learn from a one-way analysis of variance of Rating by Manufacturer?
8. Perform a two-way analysis of variance of Rating by Vehicle Type and Manufacturer. Use economy cars from the United States as the baseline group.
(a) Summarize your model.
(b) Show a profile plot of the estimated model. Does the profile plot suggest the presence of an interaction?
(c) Are these data compatible with the assumptions of an ANOVA regression?
(d) If appropriate, which effects are statistically significant?
9. Show that the estimated rating from the model for premium cars from Asia matches the average rating of cars in this group.
10. Interpret the results of this model. How does the two-way analysis change your interpretation of the results found in Question 7?
A consumer products company surveys people who recently bought new cars. Each customer is asked to express satisfaction with the purchased car by stating the likelihood (from 0 to 10) of buying another of the same brand in the future. A rating of 0 means no chance of buying an-other, and 10 means the likelihood is almost certain. The data in this example give the ratings of 220 purchasers of economy, standard, and premium vehicles from Asian, European, and domestic manufacturers.