The US Department of Energy’s Fuel Economy Guide provides fuel efficiency data for cars and trucks.   A portion of the data for 35 standard pickup trucks produced by Chevrolet and General Motors is listed below (scroll down).  The column labeled Drive identifies whether the vehicle has two-wheel drive (2WD) or four-wheel drive (4WD).  The column labeled Displacement shows the engine’s displacement in liters indicating its size and power, the column labeled Cylinders specifies the number of cylinders the engine has, and the column labeled Transmission shows whether the truck has automatic transmission or a manual transmission.  The column labeled City mpg shows the fuel efficiency rating for the truck for city driving in terms of miles per gallon (mpg).  

Part a)Develop an estimated regression equation that can be used to predict the fuel efficiency given the engine’s displacement and whether the truck is 2WD or 4WD.  Clearly define your variables. 

Part b) Comment on the significance of the model and the variables, for the model developed in part (a).  

Part c)Provide an interpretation for the coefficient of each independent variable in the model developed in part (a).

Part d)Predict the fuel efficiency for a 4WD truck with an engine displacement of 5.1 liters. 

Part e)Starting with the variables Drives, Displacement, Cylinders and Transmission, write down the estimated regression equation for the best model that you could build using the Backward Elimination algorithm. Comment on how good you think this model is.