4. [-/1 Points] DETAILS CAMMBA4 7.E.015. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER DATAFile: FuelData You may need to use the appropriate technology to answer this 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 FuelData. (Let x, represent the engine's displacement, X2 represent ClassMidsize, X3 represent ClassLarge, X represent FuelPremium, and y represent HwyMPG.) (a) Develop an estimated regression equation that can be used to predict the fuel efficiency for highway driving given the engine's displacement. (Round your numerical values to four decimal places.) y : Test for significance using the 0.05 level of significance. (Use the t test.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. O We reject Ho. We can conclude that there is a relationship between HwyMPG and displacement. O We fail to reject Ho. We cannot conclude that there is a relationship between HwyMPG and displacement. O We fail to reject Ho. We can conclude that there is a relationship between HwyMPG and displacement. O We reject Ho. We cannot conclude that there is a relationship between HwyMPG and displacement. How much of the variation in the sample values of HwyMPG (in %) does this estimated regression equation explain? (Round your answers to two decimal places.) (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? This chart suggests that for each class of automobile.(compact, midsize, and large) HwyMPG |---Select--- | as displacement increases. The chart also suggests that ---Select--- |automobiles generally have the highest HwyMPG while ---Select--- |automobiles generally have the lowest 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 othenNise. 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 efciency for highway driving, given the engine's displacement and the dummy variables ClassMidsize and ClassLarge. (Round your numerical values to four decimal places.) y: How much of the variation in the sample values of HwyMPG (in %) is explained by this estimated regression equation? (Round your answer to two decimal places.) 81.82 % (d) Use signicance level of 0.05 to determine whether the dummy variables added to the model in part (c) are signicant. Test whether the regression parameter #2 is equal to zero. Find the p-value. (Round your answer to four decimal places.) p-value = 0.0000 State your conclusion. 0 We reject H0. We cannot conclude that there is a difference in HwyMPG between midsized automobiles and compact automobiles. C We fail to reject H0. We can conclude that there is a difference in HwyMPG between midsized automobiles and compact automobiles. O We fail to reject \"0' We cannot conclude that there is a difference in HwyMPG between midsized automobiles and compact automobiles. Q We reject H0. We can conclude that there is a difference in HwyMPG between midsized automobiles and compact automobiles. I Test whether the regression parameter [i3 is equal to zero. Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. (9 We fail to reject H0. We can conclude that there is a difference in HwyMPG between large automobiles and compact automobiles. Q We reject \"0' We can conclude that there is a difference in HwyMPG between large automobiles and compact automobiles. Q We fail to reject Ho. We cannot conclude that there is a difference in HwyMPG between large automobiles and compact automobiles. 0 We reject \"0' We cannot conclude that there is a difference in HwyMPG between large automobiles and compact automobiles. (e) Consider the addition of the dummy variable FuelPremium, where the value of FuelPremium 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 efciency for highway driving given the engine's displacement, the dummy variables ClassMidsize and ClassLarge, and the dummy variable FuelPremium. (Round your numerical values to four decimal places.) y: How much of the variation in the sample values of HwyMPG (in %) does this estimated regression equation explain? (Round your answer to two decimal places.) 0/0 (f) For the estimated regression equation developed in part (e), test for the signicance of the relationship between each of the independent variables and the dependent variable using the 0.05 level of signicance for each test. Test whether the regression parameter [71 is equal to zero. Find the p-value. (Round your answer to four decimal places.) State your conclusion. 0 We reject Ho. We can conclude that there is a relationship between HwyMPG and displacement. O We fail to reject H0. We cannot conclude that there is a relationship between HwyMPG and displacement. 0 We reject H0. We cannot conclude that there is a relationship between HwyMPG and displacement. Q We fail to reject \"0' We can conclude that there is a relationship between HwyMPG and displacement. Test whether the regression parameter [12 is equal to zero. Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. 0 We fail to reject H0. We can conclude that there is a difference in HwyMPG between midsized automobiles and compact automobiles. Q We fail to reject Ho. We cannot conclude that there is a difference in HwyMPG between midsized automobiles and compact automobiles. 0 We reject HO' We cannot conclude that there is a difference in HwyMPG between midsized automobiles and compact automobiles. 0 We reject H0. We can conclude that there is a difference in HwyMPG between midsized automobiles and compact automobiles. Test whether the regression parameter '93 is equal to zero. Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Q We reject HO' We can conclude that there is a difference in HwyMPG between large automobiles and compact automobiles. 0 We reject Ho' We cannot conclude that there is a difference in HwyMPG between large automobiles and compact automobiles. 0 We fail to reject \"0' We can conclude that there is a difference in HwyMPG between large automobiles and compact automobiles. Q We fail to reject \"0' We cannot conclude that there is a difference in HwyMPG between large automobiles and compact automobiles. (9) Test whether the regression parameter [)4 is equal to zero. Find the p-value. (Round your answer to four decimal places.) p-value = 0.0000 State your conclusion. Q We fail to reject \"0' We cannot conclude that there is a difference in HwyMPG between premium fuel and regular fuel. 0 We fail to reject H0. We can conclude that there is a difference in HwyMPG between premium fuel and regular fuel. 0 We reject HO' We cannot conclude that there is a difference in HwyMPG between premium fuel and regular fuel. We reject H0. We can conclude that there is a difference in HwyMPG between premium fuel and regular fuel. An automobile manufacturer is designing a new compact model with a displacement of 2.8 liters with the objective of creating a model that will achieve at least 25 estimated highway MPG. The manufacturer must now decide if the car can be designed to use premium fuel and still achieve the objective of 25 MPG on the highway. Use the model developed in part (e) to recommend a decision to this manufacturer. (Round your answers to one decimal place.) Using the estimated multiple linear regression equation developed in part (e), a new model that is designed to use regular fuel would have 23.7 that is designed to use premium fuel would have 24.9 MPG on the highway. Therefore, the new model should be designed to use MPG on the highway and a new model reg ular v fuel