U.S. and foreign used cars Refer to the used car data file from Exercise 13.11. The prediction equation relating y = selling price of used car (in $) as a function of ₁ = age of car and ₂ = type of car 11 = US, 0 = Foreign2 is  = 20,493 – 1,185₁  2,379₂.

a. Using this equation, find the prediction equation relating selling price and age, separately for U.S. and foreign cars.

b. Predict by how much the price changes for a one year increase in the age of the car. Does this apply for both types of cars? Explain.

c. Find the predicted price of a (i) U.S. and (ii) foreign car that is eight years old. Show how the difference between them relates to a parameter estimate for the model.

Exercise 13.11

Used cars The following data (also available from the book’s website) is from a random sample of campus newspaper ads on used cars for sale. Consider the age and horsepower (HP) of a car to predict its selling price. (The variable Type stands for whether the car is from the United States, coded as 1, or a foreign car, coded as 0. This variable will be considered in Exercise 13.48.)

a. Construct a scatterplot matrix (or separate scatterplots) to investigate the relationship among price, age, and horsepower and interpret.

b. Find the multiple regression prediction equation for the selling price in terms of age and horsepower of a car. What is the predicted price for a car that has a horsepower of 80 and (i) is 8 years old, (ii) 10 years old, rounded to the nearest hundred?

c. Based on this multiple regression, can you predict the price difference between a car with 60 HP and a car with 80 HP without knowing the ages of the two cars? Explain.

Exercise 13.48

Equal slopes for car prices? Refer to Exercise 13.41, with  = predicted selling price of used car and ₁ = age of car. When equations are fitted separately for U.S. and foreign cars, we get  = 23,417 – 1,715₁ for U.S. cars and  = 15,536 – 557₁ for foreign cars.

a. In allowing the lines to have different slopes, we allow for an ____________ between age and type of car in their effects on the price. (Fill in the correct word.)

b. Predict by how much the price changes for a one-year increase in the age of the car. Do you need to do this separately for each type of car? Explain.

c. Based on the separate prediction equations, find the predicted price of a (i) U.S. and (ii) foreign car that is eight years old.