The cases that make up this dataset are types of cars. The data include the engine size or displacement (in liters) and horsepower (HP) of 318 vehicles sold in the United States in 2011. Use the SRM of the horsepower on the engine displacement to answer these questions.
(a) A manufacturer offers 3 and 3.5 liter engines in a particular model car. Based on these data, how much more horsepower should one expect the larger engine to produce? Give your answer as a 95% confidence interval.
(b) Do you have any qualms about presenting this interval as an appropriate 95% range?
(c) Based on the ft of this regression model, what is the expected horsepower of a car with a 3.5 liter engine? Give your answer as a 95% prediction interval. Do you think that standard prediction interval is reasonable? Explain.