5. A large Toyota car dealership offers purchasers of new Toyota cars the option to buy their used car as part of a trade-in.  In particular, a new promotion promises to pay high prices for used Toyota Corolla cars for purchasers of a new car.  The dealer then sells the used cars for a small profit.  To ensure a reasonable profit, the dealer needs to be able to predict the price that the dealership will get for the used cars.  For that reason, data were collected on all previous sales of used Toyota Corollas at the dealership.  The data include the sales price and other information on the car, such as its age, mileage, fuel type, engine size, etc.  A portion of the data set is shown below. 

For this problem, let’s consider building a Two-Way ANOVA model to predict the price of the used car based on the Age of the car (less than 2 years old vs. more than 2 years old) and the Horsepower (90 vs 110 vs 192).   Ignore the rest of the data, for the purpose of this problem.  Output from JMP is found below. 

a. This is a replicated Two-way ANOVA problem.  Are you able to estimate the interaction of the two Factors?

b. List the two Factors (A and B) and the number of levels of each

c. Using the JMP output, what can we conclude about the main effect of Age, main effect of Horsepower, and interaction of Age*Horsepower? If applicable, write each of these conclusions in a sentence and report the corresponding p-value.

d. In a sentence or two, interpret the interaction plot.  (i.e. What insight do you gain from this plot?)

e. If you were employed at this dealership, what would be your recommendation for the combination of Age and Horsepower levels that will sell at the highest average price of used Toyota Corollas? (could be more than 1 correct answer)

f. If you were employed at this dealership, what would be your recommendation for the combination of Age and Horsepower levels that will sell at the lowest average price of used Toyota Corollas? (could be more than 1 correct answer)

g. Interpret the 95% confidence interval for the difference in used Corolla price for cars with 90 Horsepower that are less than 2 years old compared to cars with 192 Horsepower that are more than 2 years old.

h. If the next customer wants to trade-in their used Toyota Corolla that is 4 years old with 192 Horsepower, predict the car’s price that the dealership should be able to sell this car.