Classified ads in the Australian offered several used Toyota Corollas for sale

Subject:MathPrice:4.87 Bought7

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Classified ads in the Australian offered several used Toyota Corollas for sale. Listed below are the ages of the cars and the advertised prices.

Age (yr)

Prices Advertised ($)

1 12995, 10950

2 10495

3 10995, 10995

4 6995, 7990

5 8700, 6995

6 5990, 4995

9 3200, 2250, 3995

11 2900, 2995

13 1750

a) Make a scatterplot for these data.

b) Describe the association between age and price of a used Corolla. Do you think a linear model is appropriate?

c) Computer software says that r 2 = 0.894. What is the correlation between age and price? Explain the meaning of r 2 in this context.

d) Why doesn't this model explain 100% of the variability in the price of a used Corolla?

e) Given the estimated linear model for the relationship between a car's age and its price is: P = 12319.6 - 924A, where P is predicted price and A is age of car. Answer the following questions:

1. If you want to sell a 7-year-old Corolla, what price seems appropriate?

2. You have a chance to buy one of two cars. They are about the same age and appear to be in equally good condition. Would you rather buy the one with a positive residual or a negative residual? Explain.

3. You see a "For Sale" sign on a 10-year-old stating the asking price as $1500. What is the residual?

4. Would this regression model be useful in establishing a fair price for a 20-year-old car? Explain