Manufacturer Engine Displacement (in liters) Grade of Gasoline Used (Regular or

Question

Manufacturer

Engine Displacement (in liters)

Grade of Gasoline Used (Regular or Premium)

Fuel Economy (Highway Miles per Gallon)

Build a regression model using displacement and fuel type to predict Highway MPG. Your model should have an R-Square equal to 0.684940889.

Manufacturer Hwy MPG Displacement Fuel Audi 30 2 Premium Audi 31 2 Premium Audi 31 2 Premium Audi 33 2 Premium Audi 29 2 Premium Audi 31 2 Premium Audi 27 2 Premium BMW 30 1.6 Premium BMW 35 1.6 Premium BMW 32 1.6 Premium BMW 32 1.6 Premium BMW 36 2 Premium BMW 34 2 Premium BMW 30 1.6 Premium BMW 31 1.6 Premium Chrysler Group LLC 29 2.4 Regular Ford Motor Company 38 2 Regular Ford Motor Company 37 2 Regular Ford Motor Company 36 2 Regular Ford Motor Company 38 2 Regular Ford Motor Company 36 2 Regular Ford Motor Company 40 2 Regular Ford Motor Company 40 2 Regular General Motors 32 2.4 Regular General Motors 37 1.4 Regular General Motors 40 1.4 Regular General Motors 35 1.8 Regular General Motors 35 1.8 Regular Honda 33 2.4 Regular Honda 32 2.4 Regular Honda 39 1.8 Regular Honda 36 1.8 Regular Honda 41 1.8 Regular Honda 44 1.5 Regular Honda 44 1.3 Regular Honda 44 1.3 Regular Honda 31 2.4 Premium Honda 29 2.4 Premium Honda 31 2.4 Premium Hyundai 40 1.6 Regular Hyundai 40 1.6 Regular Hyundai 38 1.6 Regular Hyundai 40 1.6 Regular Kia 34 2 Regular Kia 33 2 Regular Kia 31 2.4 Regular Kia 32 2.4 Regular Kia 40 1.6 Regular Kia 40 1.6 Regular MAZDA 34 1.5 Regular MAZDA 35 1.5 Regular MAZDA 33 2 Regular MAZDA 33 2 Regular MAZDA 29 2.5 Regular MAZDA 28 2.5 Regular MAZDA 40 2 Regular MAZDA 39 2 Regular Mercedes-Benz 31 1.8 Premium Mitsubishi Motors Co 34 2 Regular Mitsubishi Motors Co 34 2 Regular Mitsubishi Motors Co 30 2.4 Regular Mitsubishi Motors Co 31 2.4 Regular Mitsubishi Motors Co 29 2.4 Regular Mitsubishi Motors Co 25 2 Premium Mitsubishi Motors Co 22 2 Premium Mitsubishi Motors Co 23 2 Premium Nissan 38 1.6 Regular Nissan 36 1.6 Regular Nissan 32 1.8 Regular Nissan 34 1.8 Regular Nissan 31 1.8 Regular Subaru 36 2 Regular Subaru 34 2 Regular Subaru 25 2.5 Premium Subaru 23 2.5 Premium Suzuki 30 2.4 Regular Suzuki 29 2.4 Regular Suzuki 31 2.4 Regular Suzuki 31 2.4 Regular Suzuki 32 2 Regular Suzuki 33 2 Regular Suzuki 30 2 Regular Suzuki 32 2 Regular Suzuki 29 2.4 Regular Suzuki 30 2.4 Regular Toyota 40 1.8 Regular Toyota 34 2.4 Regular Toyota 31 2.5 Regular Toyota 31 2.5 Regular Toyota 34 1.8 Regular Toyota 34 1.8 Regular Toyota 46 1.5 Regular Toyota 35 1.5 Regular Toyota 38 1.5 Regular Volkswagen 29 2 Regular Volkswagen 34 2 Regular Volkswagen 31 2 Premium Volkswagen 32 2 Premium Volkswagen 33 2 Premium Audi 28 3 Premium Audi 27 3 Premium BMW 33 3 Premium BMW 30 3 Premium BMW 31 3 Premium BMW 33 3 Premium Chrysler Group LLC 29 3.6 Regular General Motors 30 3.6 Regular General Motors 29 3.6 Regular General Motors 28 3.6 Regular Honda 29 3.5 Regular Honda 26 3.5 Regular Honda 28 3.5 Premium Mercedes-Benz 29 3.5 Premium Mercedes-Benz 29 3.5 Premium Mercedes-Benz 29 3.5 Premium Volkswagen 25 3.6 Premium BMW 23 4.4 Premium BMW 22 4.4 Premium BMW 23 4.4 Premium BMW 22 4.4 Premium BMW 20 4.4 Premium General Motors 18 6.2 Regular General Motors 24 6.2 Regular General Motors 24 6.2 Regular General Motors 19 6.2 Premium Mercedes-Benz 19 6.2 Premium Mercedes-Benz 22 5.5 Premium Mercedes-Benz 25 4.7 Premium Mercedes-Benz 25 5.5 Premium Honda 34 2.4 Regular Honda 34 2.4 Regular Hyundai 34 2 Regular Hyundai 35 2.4 Regular Hyundai 35 2.4 Regular BMW 28 3 Premium BMW 25 3 Premium BMW 25 3 Premium BMW 27 3 Premium Chrysler Group LLC 27 3.6 Regular Chrysler Group LLC 31 3.6 Regular Chrysler Group LLC 27 3.6 Regular Chrysler Group LLC 31 3.6 Regular Chrysler Group LLC 27 3.6 Regular Chrysler Group LLC 27 3.6 Regular Ford Motor Company 28 3.5 Regular Ford Motor Company 27 3.5 Regular Ford Motor Company 25 3.5 Regular Ford Motor Company 26 3.5 Regular Ford Motor Company 25 3.5 Regular Ford Motor Company 25 3.5 Regular Ford Motor Company 23 3.7 Regular General Motors 30 3.6 Regular General Motors 30 3.6 Regular Honda 30 3.5 Regular Hyundai 29 3.3 Regular Hyundai 29 3.8 Regular Mercedes-Benz 25 3.5 Premium Porsche 27 3.6 Premium Porsche 30 3 Premium Toyota 28 3.5 Regular Audi 28 4.2 Premium BMW 22 4.4 Premium BMW 22 4.4 Premium BMW 22 4.4 Premium BMW 24 4.4 Premium BMW 22 4.4 Premium BMW 22 4.4 Premium BMW 19 4.4 Premium BMW 20 4.4 Premium BMW 20 4.4 Premium BMW 20 4.4 Premium BMW 20 4.4 Premium Chrysler Group LLC 23 6.4 Premium Chrysler Group LLC 23 6.4 Premium Hyundai 23 5 Premium Hyundai 26 4.6 Premium Hyundai 26 5 Premium Hyundai 25 5 Premium Jaguar Cars 23 5 Premium Jaguar Cars 21 5 Premium Jaguar Cars 21 5 Premium Jaguar Cars 22 5 Premium Mercedes-Benz 25 4.7 Premium Mercedes-Benz 23 5.5 Premium Porsche 24 4.8 Premium Porsche 24 4.8 Premium Porsche 23 4.8 Premium Porsche 23 4.8 Premium Audi 33 2 Premium BMW 34 2 Premium BMW 32 2 Premium Chrysler Group LLC 30 2.4 Regular Chrysler Group LLC 31 2.4 Regular Chrysler Group LLC 30 2.4 Regular Chrysler Group LLC 31 2.4 Regular Ford Motor Company 33 2.5 Regular Ford Motor Company 30 2.5 Regular Ford Motor Company 29 2.5 Regular Ford Motor Company 36 2.5 Regular Ford Motor Company 32 2.5 Regular Ford Motor Company 36 2.5 Regular General Motors 36 2.4 Regular General Motors 29 2 Regular General Motors 27 2 Regular General Motors 32 2 Regular General Motors 27 2 Regular General Motors 36 2.4 Regular General Motors 31 2.4 Regular General Motors 31 2.4 Regular General Motors 38 1.4 Regular General Motors 38 1.4 Regular General Motors 35 1.8 Regular General Motors 36 1.8 Regular General Motors 39 1.4 Regular General Motors 42 1.4 Regular General Motors 33 2.4 Regular General Motors 33 2.4 Regular General Motors 37 1.4 Regular Hyundai 40 1.8 Regular Hyundai 40 1.8 Regular Hyundai 40 2.4 Regular Kia 36 2 Regular Kia 34 2 Regular Kia 32 2.4 Regular Kia 32 2.4 Regular Kia 37 2 Regular Kia 34 2 Regular Kia 35 2.4 Regular Kia 35 2.4 Regular Kia 40 2.4 Regular MAZDA 39 2 Regular MAZDA 38 2 Regular MAZDA 31 2.5 Regular MAZDA 30 2.5 Regular MAZDA 25 2.3 Premium Nissan 32 2.5 Regular Nissan 34 2 Regular Nissan 31 2 Regular Nissan 30 2.5 Regular Nissan 28 2.5 Premium Subaru 31 2.5 Regular Subaru 27 2.5 Regular Subaru 25 2.5 Premium Toyota 35 2.5 Regular Toyota 39 2.5 Regular Toyota 38 2.5 Regular Toyota 48 1.8 Regular Audi 28 3 Premium Audi 28 3 Premium BMW 31 3 Premium BMW 30 3 Premium BMW 30 3 Premium Chrysler Group LLC 29 3.6 Regular Chrysler Group LLC 29 3.6 Regular Chrysler Group LLC 27 3.6 Regular Ford Motor Company 27 3.5 Regular Ford Motor Company 28 3 Regular Ford Motor Company 27 3.5 Regular Ford Motor Company 25 3.5 Regular Ford Motor Company 26 3 Regular Ford Motor Company 25 3.5 Regular General Motors 27 3.6 Regular General Motors 27 3.6 Regular General Motors 26 3.6 Regular General Motors 27 3.6 Regular General Motors 26 3.6 Regular General Motors 26 3.6 Regular General Motors 26 3 Regular General Motors 27 3.6 Regular Honda 29 3.5 Premium Honda 24 3.7 Premium Honda 26 3.7 Premium Honda 25 3.7 Premium MAZDA 27 3.7 Regular Mercedes-Benz 30 3.5 Premium Nissan 27 3.5 Regular Nissan 26 3.5 Premium Nissan 29 2.5 Premium Nissan 32 3.5 Premium Nissan 27 2.5 Premium Nissan 27 3.7 Premium Nissan 25 3.7 Premium Nissan 26 3.7 Premium Nissan 25 3.7 Premium Nissan 24 3.7 Premium Subaru 25 3.6 Regular Toyota 28 3.5 Regular Toyota 30 3.5 Regular Volkswagen 28 3.6 Premium Audi 28 4.2 Premium BMW 23 4.4 Premium BMW 22 4.4 Premium BMW 24 4.4 Premium BMW 20 4.4 Premium Chrysler Group LLC 23 6.4 Premium Chrysler Group LLC 23 5.7 Premium Chrysler Group LLC 23 6.4 Premium General Motors 18 6.2 Premium General Motors 19 6.2 Premium Jaguar Cars 21 5 Premium Jaguar Cars 23 5 Premium Mercedes-Benz 24 5.5 Premium Nissan 24 5.6 Premium Nissan 23 5.6 Premium Toyota 24 4.6 Premium Toyota 24 4.6 Premium Toyota 23 4.6 Premium Toyota 23 4.6 Premium Toyota 23 5 Premium

Explanation / Answer

Since fuel type is categorical varibale so we need to use dummy variable. let premimum =0 and regular =1

Following is the data set:

And folloiwng is the output of regression analysis:

So required model is

MPG' = 37.8716-3.1944 * Displacement + 2.7230* Fuel

Manufacturer Hwy MPG Displacement Fuel Audi 30 2 0 Audi 31 2 0 Audi 31 2 0 Audi 33 2 0 Audi 29 2 0 Audi 31 2 0 Audi 27 2 0 BMW 30 1.6 0 BMW 35 1.6 0 BMW 32 1.6 0 BMW 32 1.6 0 BMW 36 2 0 BMW 34 2 0 BMW 30 1.6 0 BMW 31 1.6 0 Honda 31 2.4 0 Honda 29 2.4 0 Honda 31 2.4 0 Mercedes-Benz 31 1.8 0 Mitsubishi Motors Co 25 2 0 Mitsubishi Motors Co 22 2 0 Mitsubishi Motors Co 23 2 0 Subaru 25 2.5 0 Subaru 23 2.5 0 Volkswagen 31 2 0 Volkswagen 32 2 0 Volkswagen 33 2 0 Audi 28 3 0 Audi 27 3 0 BMW 33 3 0 BMW 30 3 0 BMW 31 3 0 BMW 33 3 0 Honda 28 3.5 0 Mercedes-Benz 29 3.5 0 Mercedes-Benz 29 3.5 0 Mercedes-Benz 29 3.5 0 Volkswagen 25 3.6 0 BMW 23 4.4 0 BMW 22 4.4 0 BMW 23 4.4 0 BMW 22 4.4 0 BMW 20 4.4 0 General Motors 19 6.2 0 Mercedes-Benz 19 6.2 0 Mercedes-Benz 22 5.5 0 Mercedes-Benz 25 4.7 0 Mercedes-Benz 25 5.5 0 BMW 28 3 0 BMW 25 3 0 BMW 25 3 0 BMW 27 3 0 Mercedes-Benz 25 3.5 0 Porsche 27 3.6 0 Porsche 30 3 0 Audi 28 4.2 0 BMW 22 4.4 0 BMW 22 4.4 0 BMW 22 4.4 0 BMW 24 4.4 0 BMW 22 4.4 0 BMW 22 4.4 0 BMW 19 4.4 0 BMW 20 4.4 0 BMW 20 4.4 0 BMW 20 4.4 0 BMW 20 4.4 0 Chrysler Group LLC 23 6.4 0 Chrysler Group LLC 23 6.4 0 Hyundai 23 5 0 Hyundai 26 4.6 0 Hyundai 26 5 0 Hyundai 25 5 0 Jaguar Cars 23 5 0 Jaguar Cars 21 5 0 Jaguar Cars 21 5 0 Jaguar Cars 22 5 0 Mercedes-Benz 25 4.7 0 Mercedes-Benz 23 5.5 0 Porsche 24 4.8 0 Porsche 24 4.8 0 Porsche 23 4.8 0 Porsche 23 4.8 0 Audi 33 2 0 BMW 34 2 0 BMW 32 2 0 MAZDA 25 2.3 0 Nissan 28 2.5 0 Subaru 25 2.5 0 Audi 28 3 0 Audi 28 3 0 BMW 31 3 0 BMW 30 3 0 BMW 30 3 0 Honda 29 3.5 0 Honda 24 3.7 0 Honda 26 3.7 0 Honda 25 3.7 0 Mercedes-Benz 30 3.5 0 Nissan 26 3.5 0 Nissan 29 2.5 0 Nissan 32 3.5 0 Nissan 27 2.5 0 Nissan 27 3.7 0 Nissan 25 3.7 0 Nissan 26 3.7 0 Nissan 25 3.7 0 Nissan 24 3.7 0 Volkswagen 28 3.6 0 Audi 28 4.2 0 BMW 23 4.4 0 BMW 22 4.4 0 BMW 24 4.4 0 BMW 20 4.4 0 Chrysler Group LLC 23 6.4 0 Chrysler Group LLC 23 5.7 0 Chrysler Group LLC 23 6.4 0 General Motors 18 6.2 0 General Motors 19 6.2 0 Jaguar Cars 21 5 0 Jaguar Cars 23 5 0 Mercedes-Benz 24 5.5 0 Nissan 24 5.6 0 Nissan 23 5.6 0 Toyota 24 4.6 0 Toyota 24 4.6 0 Toyota 23 4.6 0 Toyota 23 4.6 0 Toyota 23 5 0 Chrysler Group LLC 29 2.4 1 Ford Motor Company 38 2 1 Ford Motor Company 37 2 1 Ford Motor Company 36 2 1 Ford Motor Company 38 2 1 Ford Motor Company 36 2 1 Ford Motor Company 40 2 1 Ford Motor Company 40 2 1 General Motors 32 2.4 1 General Motors 37 1.4 1 General Motors 40 1.4 1 General Motors 35 1.8 1 General Motors 35 1.8 1 Honda 33 2.4 1 Honda 32 2.4 1 Honda 39 1.8 1 Honda 36 1.8 1 Honda 41 1.8 1 Honda 44 1.5 1 Honda 44 1.3 1 Honda 44 1.3 1 Hyundai 40 1.6 1 Hyundai 40 1.6 1 Hyundai 38 1.6 1 Hyundai 40 1.6 1 Kia 34 2 1 Kia 33 2 1 Kia 31 2.4 1 Kia 32 2.4 1 Kia 40 1.6 1 Kia 40 1.6 1 MAZDA 34 1.5 1 MAZDA 35 1.5 1 MAZDA 33 2 1 MAZDA 33 2 1 MAZDA 29 2.5 1 MAZDA 28 2.5 1 MAZDA 40 2 1 MAZDA 39 2 1 Mitsubishi Motors Co 34 2 1 Mitsubishi Motors Co 34 2 1 Mitsubishi Motors Co 30 2.4 1 Mitsubishi Motors Co 31 2.4 1 Mitsubishi Motors Co 29 2.4 1 Nissan 38 1.6 1 Nissan 36 1.6 1 Nissan 32 1.8 1 Nissan 34 1.8 1 Nissan 31 1.8 1 Subaru 36 2 1 Subaru 34 2 1 Suzuki 30 2.4 1 Suzuki 29 2.4 1 Suzuki 31 2.4 1 Suzuki 31 2.4 1 Suzuki 32 2 1 Suzuki 33 2 1 Suzuki 30 2 1 Suzuki 32 2 1 Suzuki 29 2.4 1 Suzuki 30 2.4 1 Toyota 40 1.8 1 Toyota 34 2.4 1 Toyota 31 2.5 1 Toyota 31 2.5 1 Toyota 34 1.8 1 Toyota 34 1.8 1 Toyota 46 1.5 1 Toyota 35 1.5 1 Toyota 38 1.5 1 Volkswagen 29 2 1 Volkswagen 34 2 1 Chrysler Group LLC 29 3.6 1 General Motors 30 3.6 1 General Motors 29 3.6 1 General Motors 28 3.6 1 Honda 29 3.5 1 Honda 26 3.5 1 General Motors 18 6.2 1 General Motors 24 6.2 1 General Motors 24 6.2 1 Honda 34 2.4 1 Honda 34 2.4 1 Hyundai 34 2 1 Hyundai 35 2.4 1 Hyundai 35 2.4 1 Chrysler Group LLC 27 3.6 1 Chrysler Group LLC 31 3.6 1 Chrysler Group LLC 27 3.6 1 Chrysler Group LLC 31 3.6 1 Chrysler Group LLC 27 3.6 1 Chrysler Group LLC 27 3.6 1 Ford Motor Company 28 3.5 1 Ford Motor Company 27 3.5 1 Ford Motor Company 25 3.5 1 Ford Motor Company 26 3.5 1 Ford Motor Company 25 3.5 1 Ford Motor Company 25 3.5 1 Ford Motor Company 23 3.7 1 General Motors 30 3.6 1 General Motors 30 3.6 1 Honda 30 3.5 1 Hyundai 29 3.3 1 Hyundai 29 3.8 1 Toyota 28 3.5 1 Chrysler Group LLC 30 2.4 1 Chrysler Group LLC 31 2.4 1 Chrysler Group LLC 30 2.4 1 Chrysler Group LLC 31 2.4 1 Ford Motor Company 33 2.5 1 Ford Motor Company 30 2.5 1 Ford Motor Company 29 2.5 1 Ford Motor Company 36 2.5 1 Ford Motor Company 32 2.5 1 Ford Motor Company 36 2.5 1 General Motors 36 2.4 1 General Motors 29 2 1 General Motors 27 2 1 General Motors 32 2 1 General Motors 27 2 1 General Motors 36 2.4 1 General Motors 31 2.4 1 General Motors 31 2.4 1 General Motors 38 1.4 1 General Motors 38 1.4 1 General Motors 35 1.8 1 General Motors 36 1.8 1 General Motors 39 1.4 1 General Motors 42 1.4 1 General Motors 33 2.4 1 General Motors 33 2.4 1 General Motors 37 1.4 1 Hyundai 40 1.8 1 Hyundai 40 1.8 1 Hyundai 40 2.4 1 Kia 36 2 1 Kia 34 2 1 Kia 32 2.4 1 Kia 32 2.4 1 Kia 37 2 1 Kia 34 2 1 Kia 35 2.4 1 Kia 35 2.4 1 Kia 40 2.4 1 MAZDA 39 2 1 MAZDA 38 2 1 MAZDA 31 2.5 1 MAZDA 30 2.5 1 Nissan 32 2.5 1 Nissan 34 2 1 Nissan 31 2 1 Nissan 30 2.5 1 Subaru 31 2.5 1 Subaru 27 2.5 1 Toyota 35 2.5 1 Toyota 39 2.5 1 Toyota 38 2.5 1 Toyota 48 1.8 1 Chrysler Group LLC 29 3.6 1 Chrysler Group LLC 29 3.6 1 Chrysler Group LLC 27 3.6 1 Ford Motor Company 27 3.5 1 Ford Motor Company 28 3 1 Ford Motor Company 27 3.5 1 Ford Motor Company 25 3.5 1 Ford Motor Company 26 3 1 Ford Motor Company 25 3.5 1 General Motors 27 3.6 1 General Motors 27 3.6 1 General Motors 26 3.6 1 General Motors 27 3.6 1 General Motors 26 3.6 1 General Motors 26 3.6 1 General Motors 26 3 1 General Motors 27 3.6 1 MAZDA 27 3.7 1 Nissan 27 3.5 1 Subaru 25 3.6 1 Toyota 28 3.5 1 Toyota 30 3.5 1

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