Question 1: Michael Lovell estimated the following model of the gasoline mileage of various models of cars (standard errors in parentheses): i = 0.23 + 0.0030 x W, 1.16 x A 1.27 x D. + 0.812 x E; (0.0018) (0.05) (1.48) (0.065) where: Gi the miles per gallon of the ith model as reported by Consumers' Union based on actual road tests W; the gross weight (in pounds) of the ith model a dummy variable equal to 1 if the ith model has an automatic transmission and 0 otherwise Di = a dummy variable equal to 1 if the ith model has diesel engine and 0 otherwise E. the U.S. Environmental Protection Agency's estimate of the miles per gallon of the ith model a) To begin to understand this problem, think about the relationship between the variables Wi. A; and D; and the fuel consumption of a vehicle. What do you expect for the signs of the coefficients on these variables in the EPA's model i? Now suppose that the EPA had, in fact, produced the ideal model for the fuel consumption of a vehicle. That is, the EPA model perfectly captures the true relationship between the characteristics of a vehicle and its fuel consumption. This model completely captures the effects of weight, engine type and transmission type on the actual gas mileage of these cars. b) If the EPA had estimated this ideal true model, such that ; = Es, what would you expect for the coefficients on W;, A; and D;, when E, is included? To state this formally, consider the values of the coefficients Bo. Bw. BA. Bp and Bg that would satisfy the equation G; = Ej. c) Under the same ideal model, what should be the coefficients for the intercept and the slope coefficient on E? d) Carefully interpret the meanings of the estimated coefficients of A; and D; while Ez is in Michael Lovell's model above (not the EPA's model). e) Test for the statistical significance of each coefficient in the model. Which variables are statistically significant and which are not? f) How do your conclusions in part (e) reflect the quality of the EPA model? Is the EPA model the ideal model? Should the model be re-estimated? If so, what tells you the EPA model is right or wrong? Question 1: Michael Lovell estimated the following model of the gasoline mileage of various models of cars (standard errors in parentheses): i = 0.23 + 0.0030 x W, 1.16 x A 1.27 x D. + 0.812 x E; (0.0018) (0.05) (1.48) (0.065) where: Gi the miles per gallon of the ith model as reported by Consumers' Union based on actual road tests W; the gross weight (in pounds) of the ith model a dummy variable equal to 1 if the ith model has an automatic transmission and 0 otherwise Di = a dummy variable equal to 1 if the ith model has diesel engine and 0 otherwise E. the U.S. Environmental Protection Agency's estimate of the miles per gallon of the ith model a) To begin to understand this problem, think about the relationship between the variables Wi. A; and D; and the fuel consumption of a vehicle. What do you expect for the signs of the coefficients on these variables in the EPA's model i? Now suppose that the EPA had, in fact, produced the ideal model for the fuel consumption of a vehicle. That is, the EPA model perfectly captures the true relationship between the characteristics of a vehicle and its fuel consumption. This model completely captures the effects of weight, engine type and transmission type on the actual gas mileage of these cars. b) If the EPA had estimated this ideal true model, such that ; = Es, what would you expect for the coefficients on W;, A; and D;, when E, is included? To state this formally, consider the values of the coefficients Bo. Bw. BA. Bp and Bg that would satisfy the equation G; = Ej. c) Under the same ideal model, what should be the coefficients for the intercept and the slope coefficient on E? d) Carefully interpret the meanings of the estimated coefficients of A; and D; while Ez is in Michael Lovell's model above (not the EPA's model). e) Test for the statistical significance of each coefficient in the model. Which variables are statistically significant and which are not? f) How do your conclusions in part (e) reflect the quality of the EPA model? Is the EPA model the ideal model? Should the model be re-estimated? If so, what tells you the EPA model is right or wrong