1.
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.
a.
Is this a single replicate or
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.
Write out the model the dealership
is interested in investigating as well as the three sets of hypotheses to be
tested
d.
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.
e.
In a sentence or two, show and
interpret the interaction plot. (i.e.
What insight do you gain from this plot?)
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 highest average price of used Toyota
Corollas? (could be more than 1 correct answer)
g. 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)
h. 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.
i.
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.
Note* If you scroll down, you will find all
the screenshots for question # 2. You don’t have to run the data, just use the
screen shots to answer the questions.
