Question: The U.S. Department of Energy's Fuel Economy Guide provides fuel efficiency data for cars and trucks. A portion of the data for 311 compact, midsized, and large cars follows. The Class column identifies the size of the car; Compact, Midsize, or Large. The Displacement column shows the engine's displacement in liters. The Fuel Type column shows whether the car uses premium (P) or regular (R) fuel, and the Hwy MPG column shows the fuel efficiency rating for highway driving in terms of miles per gallon. The complete data set is contained in the file Fuel Data:
a. Develop an estimated regression equation that can be used to predict the fuel efficiency for highway driving given the engine's displacement. Test for significance using the 0.05 level of significance. How much of the variation in the sample values of Hwy MPG does this estimated regression equation explain?
b. Create a scatter chart with Hwy MPG on the y-axis and displacement on the x-axis for which the points representing compact, midsize, and large automobiles are shown in different shapes and/or colors. What does this chart suggest about the relationship between the class of automobile (compact, midsize, and large) and Hwy MPG?
c. Now consider the addition of the dummy variables Class Midsize and Class Large to the simple linear regression model in part a. The value of Class Midsize is 1 if the car is a midsize car and 0 otherwise; the value of Class Large is 1 if the car is a large car and 0 otherwise. Thus, for a compact car, the value of Class Midsize and the value of ClassLarge are both 0. Develop the estimated regression equation that can be used to predict the fuel efficiency for highway driving, given the engine's displacement and the dummy variables Class Midsize and Class Large. How much of the variation in the sample values of Hwy MPG does this estimated regression equation explain?
d. Use significance level of 0.05 to determine whether the dummy variables added to the model in part c are significant.
e. Consider the addition of the dummy variable Fuel Premium, where the value of Fuel Premium is 1 if the car uses premium fuel and 0 if the car uses regular fuel. Develop the estimated regression equation that can be used to predict the fuel efficiency for highway driving given the engine's displacement, the dummy variables Class Midsize and Class Large, and the dummy variable Fuel Premium. How much of the variation in the sample values of HwyMPG does this estimated regression equation explain?
f. For the estimated regression equation developed in part e, test for the significance of an overall regression relationship and relationships between each of the independent variables and the dependent variable using the 0.05 level of significance for each test.