A study was done to assess the cost effectiveness of driving a four door sedan instead of a van or an SUV (sports utility vehicle). The continuous variables are odometer reading and octane of the gasoline used, the response variable is miles per gallon. The data are presented here.(a) Fit a linear regression model including two indicator variables. Use 0, 0 to denote the four-door sedan(b) Which type of vehicle appears to get the best gas mileage?(c) Discuss the difference in a van and an SUV in terms of gas mileageperformance.

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Car Type odometer sedan MPG 3 1.5 Octane 75000 87.5 33.3 87.5 sedan 00000 sedan 30.4 88000 78.0 sedan 15000 25000 78.0 32.8 90.0 35.0 sedan 29.0 sedan 35000 78.0 sedan sedan 102000 90.0 32.5 87.5 29.6 98000 56000 87.5 16.8 van 72000 90.0 19.2 van 14500 22.6 87.5 90.0 van 24.4 22000 van 78.0 20.7 66500 van 90.0 25.1 3.5000 van 87.5 18.8 97500 van 15.8 65500 78.0 van 78.0 17.4 42000 van SUV SUV SUV SUV SUV SUV SUV SUV 78.0 15.6 65000 87.5 17.3 55500 26500 87.5 20.8 90.0 22.2 11500 16.5 38000 78.0 77500 90.0 21.3 19500 78.0 20.7 24.1 87000 90.0