as possible. To ins part (a) to explain as much of 15. Estimating Fuel Mileage by Car Size. The U.S. Department of Energy's Fuel Econ- omy Guide provides fuel efficiency data for cars and trucks. A portion of the data for bnom 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 FuelType column shows whether the car uses premium (P) or regular (R) fuel, and the HwyMPG column shows the fuel efficiency rating for high- into way driving in terms of miles per gallon. The complete data set is contained in the file 15 FuelData: 1 Car Class Displacement FuelType Hwy MPG wiod Compact ition 3.1 Side 2 Compact sri 1013 aimup Compact 3.1 3.0 P 25 P 25 loved P 25 IM Soi 161 on Midsize 2.4 R 30 162 Midsize 2.0 lobom: 32310 P 29 Large 3.0 R 25 a. Develop an estimated regression equation that can be used to predict the fuel effi- ups ciency 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 HwyMPG does this estimated regression equation explain? Inohe b. Create a scatter chart with HwyMPG 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 HwyMPG? c. Now consider the addition of the dummy variables ClassMidsize and ClassLarge to the simple linear regression model in part (a). The value of ClassMidsize is 1 if the car is a midsize car and 0 otherwise; the value of ClassLarge is 1 if the car is a large car and 0 otherwise. Thus, for a compact car, the value of ClassMidsize 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 ClassMidsize and ClassLarge. How much of the variation in the sample values of HwyMPG is explained by this estimated regression equation? d. Use significance level of 0.05 to determine whether the dummy variables added to the model in part (c) are significant. 16. Vehicle Speed and Traffic Flow. A highway department is studying the relationship between traffic flow and speed during rush hour on Highway 193. The data in the file Traffic Flow were collected on Highway 193 during 100 recent rush hours. a. Develop a scatter chart for these data. What does the scatter chart indicate about the relationship between vehicle speed and traffic flow? b. Develop an estimated simple linear regression equation for the data. How much variation in the sample values of traffic flow is explained by this regression model? Use a 0.05 level of significance to test the relationship between vehicle speed and traffic flow. What is the interpretation of this relationship? c. Develop an estimated quadratic regression equation for the data. How much vari- ation in the sample values of traffic flow is explained by this regression model? Test the relationship between each of the independent variables and the dependent variable at a 0.05 level of significance. How would you interpret this model? Is this model superior to the model you developed in part (b)? d. As an alternative to fitting a second-order model, fit a model using a piecewise linear regression with a single knot. What value of vehicle speed appears to be a good point for the placement of the knot? Does the estimated piecewise linear regression provide a better fit than the estimated quadratic regression developed in part (c)? Explain. e. Separate the data into two sets such that one data set contains the observations of vehicle speed less than the value of the knot from part (d) and the other data set con- tains the observations of vehicle speed greater than or equal to the value of the knot from part (d). Then fit a simple linear regression equation to each data set. How does this pair of regression equations compare to the single piecewise linear regres- sion with the single knot from part (d)? In particular, compare predicted values of traffic flow for values of the speed slightly above and slightly below the knot value from part (d). f. What other independent variables could you include in your regression model to explain more variation in traffic flow? 1 nef