You may need to use the appropriate technology to answer this question. An investors association's on-line discount broker survey polls members on their experiences with electronic trades handled by discount brokers. As part of the survey, members were asked to rate their satisfaction with t trade price and the speed of execution, as well as provide an overall satisfaction rating. Possible responses (scores) were no opinion (O), unsatisfied (1), somewhat satisfied (2), satisfied (3), and very satisfied (4). For ea broker, summary scores were computed by computing a weighted average of the scores provided by each respondent. A portion of the survey results follow. (Let x, represent satisfaction with trade price, x, represent satisfaction with speed of execution, and y represent overall satisfaction with electronic trades.) Brokerage Satisfaction with Trade Price Satisfaction with Speed of Execution Overall Satisfaction with Electronic Trades Brokerage 1 3.3 3.5 3.4 Brokerage 2 3.1 3.2 3.5 Brokerage 3 3.2 3.3 3.9 Brokerage 4 3.0 3.5 3.6 Brokerage 5 3.0 3.1 2.8 Brokerage 6 2.6 3.3 2.8 Brokerage 7 2.5 3.9 2.7 Brokerage 8 2.5 3.9 3.5 Brokerage 9 2.7 2.7 2.5 Brokerage 10 2.4 2.8 2.2 Brokerage 11 3.8 4.0 4.0 Brokerage 12 2.4 2.4 2.6 Brokerage 13 3.1 3.1 4.0 Brokerage 14 4.0 1.1 2.1 (a) Develop an estimated regression equation using trade price and speed of execution to predict the overall satisfaction with the broker. (Round your numerical values to four decimal places.) = Interpret the coefficient of determination. (Round your answer to two decimal places.) This regression model explains approximately % of the variation in the values of overall satisfaction in the sample. . (b) Use the t test to determine the significance of each independent variable. Test whether the regression parameter, is equal to zero. Find the p-value. (Round your answer to four decimal places.) p-value- What is the conclusion for the test at the 0.05 level of significance? O we fail to reject H . We can conclude that there is a relationship between satisfaction with trade price and overall satisfaction with the electronic trade. We reject H. We can conclude that there is a relationship between satisfaction with trade price and overall satisfaction with the electronic trade. O We reject H . We cannot conclude that there is a relationship between satisfaction with trade price and overall satisfaction with the electronic trade. O we fail to reject H. We cannot conclude that there is a relationship between satisfaction with trade price and overall satisfaction with the electronic trade. Test whether the regression parameter, is equal to zero. Test whether the regression parameter 8, is equal to zero. Find the p-value. (Round your answer to four decimal places.) p-value What is the conclusion for the test at the 0.05 level of significance? o We fail to reject Ho. We cannot conclude that there is a relationship between satisfaction with speed of execution and overall satisfaction with the electronic trade. O We reject H. We can conclude that there is a relationship between satisfaction with speed of execution and overall satisfaction with the electronic trade. Owe reject H. We cannot condude that there is a relationship between satisfaction with speed of execution and overall satisfaction with the electronic trade. O we fail to reject H. We can condude that there is a relationship between satisfaction with speed execution and overall satisfaction with the electronic trade. (c) Interpret the estimated regression parameters. is our estimate of the overall satisfaction with the electronic trade when satisfaction with trade price and satisfaction with speed of execution are both --Select-- . . is our estimate of change in overall satisfaction with the electronic trade if we hold satisfaction with ...Select- constant and have a 1 point increase in satisfaction with ---Select- V., is our estimate of change in overall satisfaction with the electronic trade if we hold satisfaction with ---Select--- constant and have a 1 point increase in satisfaction with --Select-- Are the relationships indicated by these estimates what you would expect? Yes O No (d) An investment company has developed a new electronic trading system and would like to predict overall customer satisfaction assuming they can provide satisfactory service levels (3) for both trade price and speed of execution. Use the estimated regression equation developed in part (a) to predict the overall satisfaction level for the investment company if they can achieve these performance levels. (Round your answer to one decimal place.) (e) What concerns (if any) do you have with regard to the possible responses the respondents could select on the survey? This answer has not been graded yet. DATA File: FuelDate You may need to use the appropriate technology to answer this question. The U.S. Department of Energy's Fuel Ecoromy 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 galon. The complete data set is contained in the file Fuldata. (Let x, represent the engine's displacement, x, represent Class Midsize, a represent ClassLarge, a represent FuelPremium, and y represent HwMPG.) (a) Develog un es.imated regression equation that can be used to predict the fuel efficiency for highway ciriving given the engine's displacernent. (Round your numerical values to four decimal plece.) Test significance using the 0.05 level of significance. (Use the test.) Find the p-value. (Round your answer to four decimal places.) p-value State your conclusion Owe reject He. We cannot conclude that there is a relationship between HwyMPG and displacement. w O we tall to reject it. We cannot conclude that there is a relationship between HWYMPG and displacement. O we reject. We can conclude that there is a relationship between HwyMPG and displacement. O We fail to reject I,. Ve can 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.) (6) Create a scatter chart with HWYMPG on the y-axis and displacement on the x-axis for which the points maresenting 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 automobila (compact, midsze, and large) and HwyMPG? This chart suggests that for each class of automobile compact. midsize, and large) HWPG --Select-- V as disolacement increases. The chart also suggests that --Select--- v automobiles generally have the highest Hwy MPG while --Select-- v automobiles generally have the lowest HWYMPG. (c) Now consider the addition of the dummy variables Class Midsize and ClassLarge to the simple linear regression model in part (a). The value of ClassMidsize is 1 if the car is a mids ze car and otherwise; the value of ClassLarge is 1 if the car is a large car and o otherwise. Thus, for a compact car, the value of Class Midsize and the value of Class Large are both D. 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 ClassLarge. (Round your numerical values to four decimal places.) 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.) 44 (a} Use significance level of 0.05 to determine whether the dummy variables added to the model in part (c) are significant Test whether the regression parameters, is equal to zero. Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion Owe fail to reject H. We cannot conclude that there is a difference in HwMPG between minsized automobiles and compact automobiles. We reject Rg. We cannot conclude that there is a difference in HWYMPG between midsized automobiles and compact automobiles O We reject y. We can conclude that there is a difference in HwyMPG between midsized automobiles and compact automobiles. Owe fail to reject H. We can conclude that there is a difference in HWYMPG hetween midsized automobiles and compact automobiles. Test whether the regression parameters is equal to zero. Find the p-value. (Round your answer to four decimal places.) p-value State your conclusion O We reject Hy. We cannot conclude that there is a difference in HwyMPG between large automobiles and compact automobiles. Owe fail to reject Hg. We cannot conclude that there is a difference in HwyMFG between lange automobiles and compact automobiles O we fail to reject H. We can conclude that there is a difference in HWYMPG between large automobiles and compact automobiles. We reject Hy. We can conclude that there is a difference in HwyMPG between large automobiles and compact automobiles. (e) Consider the addition of the dummy variable Fuel Premium, where the value of FuelPremium is 1 if the car uses premium fuel and Dit 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 ClassLarge, and the dummy variable FuelPremium. (Round your numerical values to four decimal places.) 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.) (a} Use significance level of 0.05 to determine whether the dummy variables added to the model in part (c) are significant Test whether the regression parameters, is equal to zero. Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion Owe fail to reject H. We cannot conclude that there is a difference in HwMPG between minsized automobiles and compact automobiles. We reject Rg. We cannot conclude that there is a difference in HWYMPG between midsized automobiles and compact automobiles O We reject y. We can conclude that there is a difference in HwyMPG between midsized automobiles and compact automobiles. Owe fail to reject H. We can conclude that there is a difference in HWYMPG hetween midsized automobiles and compact automobiles. Test whether the regression parameters is equal to zero. Find the p-value. (Round your answer to four decimal places.) p-value State your conclusion O We reject Hy. We cannot conclude that there is a difference in HwyMPG between large automobiles and compact automobiles. Owe fail to reject Hg. We cannot conclude that there is a difference in HwyMFG between lange automobiles and compact automobiles O we fail to reject H. We can conclude that there is a difference in HWYMPG between large automobiles and compact automobiles. We reject Hy. We can conclude that there is a difference in HwyMPG between large automobiles and compact automobiles. (e) Consider the addition of the dummy variable Fuel Premium, where the value of FuelPremium is 1 if the car uses premium fuel and Dit 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 ClassLarge, and the dummy variable FuelPremium. (Round your numerical values to four decimal places.) 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.) (n) For the estimated regression equation developed in part (c), test for the significance of the relationship between each of the independent variables and the dependent variable using the O.Os level of significance for each test. Test whether the regression parameter 1, is equal to zero. Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion, O we reject Hy, we cannot condude that there is a relationship between HWYMPG and displacement. O we fail to reject H. We can conclude that there is a relationship between HWYMPG and displacement. O we fail to reject H. We cannot conclude that there is a relationship between HwyMPG and displacement. o We reject H. We can conclude that there is a relationship between Hwy MPG and displacement. Test whether the regression paramete, is equal to zero. Find the p-value. (Round your answer to four decimal places.) P-value = 1 State your conclusion O We reject Hg. We cannot condude that there is a difference in HWYMPG between midsized automobiles and compact automobiles, O we fail to reject H. We cannot conclude that there is a difference in HwyMPG between midsized automobiles and compact automobiles. O We reject. We can conclude that there is a difference in Hwy MPG between midsized automobiles and compact automobiles. O we fail to reject H. We can condude that there is a difference in HWYMPG between midsized automobiles and compact automobiles. Test whether the regression parameter, is equal to zero. Find the p-value. (Round your answer to four decimal places.) p-value - 18347x State your conclusion, We fail to reject H. We carinet conclude that there is a difference in HwyMPG between large automobiles and compact autarabiles. O we fail to reject ,. We can conclude that there is a difference in Hwy MPC between large automobiles and compact automobiles. We reject H. Vie can conclude that there is a difference in HWYMPG between large automobiles and compact automobiles. We reject M. Vic cannot conclude that there is a difference in Hwy MPG between large automobiles and compact automobiles (9) An automobile manufacturer is designing a new compact model with a displacement of 3.1 liters with the objective of creating a model that will achieve at least 24 estimated highway MPG. The manufacturer must now decide if the car can be designed to use premium fuel and still achieve the objective of 24 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 24.9 X MPG on the highway and a new model that is designed to use premium fuel would have 23.7 X MPG on the highway. Therefore, the new model should be designed to use regular fuel. You may need to use the appropriate technology to answer this question. An investors association's on-line discount broker survey polls members on their experiences with electronic trades handled by discount brokers. As part of the survey, members were asked to rate their satisfaction with t trade price and the speed of execution, as well as provide an overall satisfaction rating. Possible responses (scores) were no opinion (O), unsatisfied (1), somewhat satisfied (2), satisfied (3), and very satisfied (4). For ea broker, summary scores were computed by computing a weighted average of the scores provided by each respondent. A portion of the survey results follow. (Let x, represent satisfaction with trade price, x, represent satisfaction with speed of execution, and y represent overall satisfaction with electronic trades.) Brokerage Satisfaction with Trade Price Satisfaction with Speed of Execution Overall Satisfaction with Electronic Trades Brokerage 1 3.3 3.5 3.4 Brokerage 2 3.1 3.2 3.5 Brokerage 3 3.2 3.3 3.9 Brokerage 4 3.0 3.5 3.6 Brokerage 5 3.0 3.1 2.8 Brokerage 6 2.6 3.3 2.8 Brokerage 7 2.5 3.9 2.7 Brokerage 8 2.5 3.9 3.5 Brokerage 9 2.7 2.7 2.5 Brokerage 10 2.4 2.8 2.2 Brokerage 11 3.8 4.0 4.0 Brokerage 12 2.4 2.4 2.6 Brokerage 13 3.1 3.1 4.0 Brokerage 14 4.0 1.1 2.1 (a) Develop an estimated regression equation using trade price and speed of execution to predict the overall satisfaction with the broker. (Round your numerical values to four decimal places.) = Interpret the coefficient of determination. (Round your answer to two decimal places.) This regression model explains approximately % of the variation in the values of overall satisfaction in the sample. . (b) Use the t test to determine the significance of each independent variable. Test whether the regression parameter, is equal to zero. Find the p-value. (Round your answer to four decimal places.) p-value- What is the conclusion for the test at the 0.05 level of significance? O we fail to reject H . We can conclude that there is a relationship between satisfaction with trade price and overall satisfaction with the electronic trade. We reject H. We can conclude that there is a relationship between satisfaction with trade price and overall satisfaction with the electronic trade. O We reject H . We cannot conclude that there is a relationship between satisfaction with trade price and overall satisfaction with the electronic trade. O we fail to reject H. We cannot conclude that there is a relationship between satisfaction with trade price and overall satisfaction with the electronic trade. Test whether the regression parameter, is equal to zero. Test whether the regression parameter 8, is equal to zero. Find the p-value. (Round your answer to four decimal places.) p-value What is the conclusion for the test at the 0.05 level of significance? o We fail to reject Ho. We cannot conclude that there is a relationship between satisfaction with speed of execution and overall satisfaction with the electronic trade. O We reject H. We can conclude that there is a relationship between satisfaction with speed of execution and overall satisfaction with the electronic trade. Owe reject H. We cannot condude that there is a relationship between satisfaction with speed of execution and overall satisfaction with the electronic trade. O we fail to reject H. We can condude that there is a relationship between satisfaction with speed execution and overall satisfaction with the electronic trade. (c) Interpret the estimated regression parameters. is our estimate of the overall satisfaction with the electronic trade when satisfaction with trade price and satisfaction with speed of execution are both --Select-- . . is our estimate of change in overall satisfaction with the electronic trade if we hold satisfaction with ...Select- constant and have a 1 point increase in satisfaction with ---Select- V., is our estimate of change in overall satisfaction with the electronic trade if we hold satisfaction with ---Select--- constant and have a 1 point increase in satisfaction with --Select-- Are the relationships indicated by these estimates what you would expect? Yes O No (d) An investment company has developed a new electronic trading system and would like to predict overall customer satisfaction assuming they can provide satisfactory service levels (3) for both trade price and speed of execution. Use the estimated regression equation developed in part (a) to predict the overall satisfaction level for the investment company if they can achieve these performance levels. (Round your answer to one decimal place.) (e) What concerns (if any) do you have with regard to the possible responses the respondents could select on the survey? This answer has not been graded yet. DATA File: FuelDate You may need to use the appropriate technology to answer this question. The U.S. Department of Energy's Fuel Ecoromy 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 galon. The complete data set is contained in the file Fuldata. (Let x, represent the engine's displacement, x, represent Class Midsize, a represent ClassLarge, a represent FuelPremium, and y represent HwMPG.) (a) Develog un es.imated regression equation that can be used to predict the fuel efficiency for highway ciriving given the engine's displacernent. (Round your numerical values to four decimal plece.) Test significance using the 0.05 level of significance. (Use the test.) Find the p-value. (Round your answer to four decimal places.) p-value State your conclusion Owe reject He. We cannot conclude that there is a relationship between HwyMPG and displacement. w O we tall to reject it. We cannot conclude that there is a relationship between HWYMPG and displacement. O we reject. We can conclude that there is a relationship between HwyMPG and displacement. O We fail to reject I,. Ve can 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.) (6) Create a scatter chart with HWYMPG on the y-axis and displacement on the x-axis for which the points maresenting 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 automobila (compact, midsze, and large) and HwyMPG? This chart suggests that for each class of automobile compact. midsize, and large) HWPG --Select-- V as disolacement increases. The chart also suggests that --Select--- v automobiles generally have the highest Hwy MPG while --Select-- v automobiles generally have the lowest HWYMPG. (c) Now consider the addition of the dummy variables Class Midsize and ClassLarge to the simple linear regression model in part (a). The value of ClassMidsize is 1 if the car is a mids ze car and otherwise; the value of ClassLarge is 1 if the car is a large car and o otherwise. Thus, for a compact car, the value of Class Midsize and the value of Class Large are both D. 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 ClassLarge. (Round your numerical values to four decimal places.) 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.) 44 (a} Use significance level of 0.05 to determine whether the dummy variables added to the model in part (c) are significant Test whether the regression parameters, is equal to zero. Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion Owe fail to reject H. We cannot conclude that there is a difference in HwMPG between minsized automobiles and compact automobiles. We reject Rg. We cannot conclude that there is a difference in HWYMPG between midsized automobiles and compact automobiles O We reject y. We can conclude that there is a difference in HwyMPG between midsized automobiles and compact automobiles. Owe fail to reject H. We can conclude that there is a difference in HWYMPG hetween midsized automobiles and compact automobiles. Test whether the regression parameters is equal to zero. Find the p-value. (Round your answer to four decimal places.) p-value State your conclusion O We reject Hy. We cannot conclude that there is a difference in HwyMPG between large automobiles and compact automobiles. Owe fail to reject Hg. We cannot conclude that there is a difference in HwyMFG between lange automobiles and compact automobiles O we fail to reject H. We can conclude that there is a difference in HWYMPG between large automobiles and compact automobiles. We reject Hy. We can conclude that there is a difference in HwyMPG between large automobiles and compact automobiles. (e) Consider the addition of the dummy variable Fuel Premium, where the value of FuelPremium is 1 if the car uses premium fuel and Dit 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 ClassLarge, and the dummy variable FuelPremium. (Round your numerical values to four decimal places.) 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.) (a} Use significance level of 0.05 to determine whether the dummy variables added to the model in part (c) are significant Test whether the regression parameters, is equal to zero. Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion Owe fail to reject H. We cannot conclude that there is a difference in HwMPG between minsized automobiles and compact automobiles. We reject Rg. We cannot conclude that there is a difference in HWYMPG between midsized automobiles and compact automobiles O We reject y. We can conclude that there is a difference in HwyMPG between midsized automobiles and compact automobiles. Owe fail to reject H. We can conclude that there is a difference in HWYMPG hetween midsized automobiles and compact automobiles. Test whether the regression parameters is equal to zero. Find the p-value. (Round your answer to four decimal places.) p-value State your conclusion O We reject Hy. We cannot conclude that there is a difference in HwyMPG between large automobiles and compact automobiles. Owe fail to reject Hg. We cannot conclude that there is a difference in HwyMFG between lange automobiles and compact automobiles O we fail to reject H. We can conclude that there is a difference in HWYMPG between large automobiles and compact automobiles. We reject Hy. We can conclude that there is a difference in HwyMPG between large automobiles and compact automobiles. (e) Consider the addition of the dummy variable Fuel Premium, where the value of FuelPremium is 1 if the car uses premium fuel and Dit 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 ClassLarge, and the dummy variable FuelPremium. (Round your numerical values to four decimal places.) 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.) (n) For the estimated regression equation developed in part (c), test for the significance of the relationship between each of the independent variables and the dependent variable using the O.Os level of significance for each test. Test whether the regression parameter 1, is equal to zero. Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion, O we reject Hy, we cannot condude that there is a relationship between HWYMPG and displacement. O we fail to reject H. We can conclude that there is a relationship between HWYMPG and displacement. O we fail to reject H. We cannot conclude that there is a relationship between HwyMPG and displacement. o We reject H. We can conclude that there is a relationship between Hwy MPG and displacement. Test whether the regression paramete, is equal to zero. Find the p-value. (Round your answer to four decimal places.) P-value = 1 State your conclusion O We reject Hg. We cannot condude that there is a difference in HWYMPG between midsized automobiles and compact automobiles, O we fail to reject H. We cannot conclude that there is a difference in HwyMPG between midsized automobiles and compact automobiles. O We reject. We can conclude that there is a difference in Hwy MPG between midsized automobiles and compact automobiles. O we fail to reject H. We can condude that there is a difference in HWYMPG between midsized automobiles and compact automobiles. Test whether the regression parameter, is equal to zero. Find the p-value. (Round your answer to four decimal places.) p-value - 18347x State your conclusion, We fail to reject H. We carinet conclude that there is a difference in HwyMPG between large automobiles and compact autarabiles. O we fail to reject ,. We can conclude that there is a difference in Hwy MPC between large automobiles and compact automobiles. We reject H. Vie can conclude that there is a difference in HWYMPG between large automobiles and compact automobiles. We reject M. Vic cannot conclude that there is a difference in Hwy MPG between large automobiles and compact automobiles (9) An automobile manufacturer is designing a new compact model with a displacement of 3.1 liters with the objective of creating a model that will achieve at least 24 estimated highway MPG. The manufacturer must now decide if the car can be designed to use premium fuel and still achieve the objective of 24 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 24.9 X MPG on the highway and a new model that is designed to use premium fuel would have 23.7 X MPG on the highway. Therefore, the new model should be designed to use regular fuel