The U. S. Department of Energy's Fuel Economy Guide provides fuel efficiency data for cars and trucks (U. S. Department of Energy website, February 22, 2008). A portion of the data for 311 compact, midsize, and large cars follows. The column labeled Class identifies the size of the car; Compact, Midsize, or Large. The column labeled Displacement shows the engine's displacement in liters. The column labeled Fuel Type shows whether the car uses premium (P) or regular (R) fuel, and the column labeled HwyMPG shows the fuel efficiency rating for highway driving in terms of miles per gallon. a) Develop an estimated regression equation that can be used to predict the fuel efficiency for highway driving, given the engine's displacement.
Let x represent the engine's displacement.
If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
Y = ___ + ___ x
b) How much of the variation in the sample values of HwyMPG does this estimated regression equation explain?: %
c) 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. Let x1 represent engine's displacement. Let x2 represent variable ClassMidsize. Let x3 represent variable ClassLarge. If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
Y = ___ + ___ x1 + ___ x2 + ___ x3
d) How much of the variation in the sample values of HwyMPG does this estimated regression equation explain? : ___ %
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 efficiency for highway driving, given the engine's displacement, the dummy variables ClassMidsize and ClassLarge, and the dummy variable FuelPremium. Let x1 represents engine's displacement. Let x2 represents variable ClassMidsize. Let x3 represents variable ClassLarge. Let x4 represents variable FuelPremium. If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
Y = ___ + ___ x1 + ___ x2 + ___ x3 + ___x4
f) How much of the variation in the sample values of HwyMPG does this estimated regression equation explain? : ___ %