Consumer Reports tested different brands and models of road, fitness, and comfort bikes. Road bikes are designed for long road trips; fitness bikes are designed for regular workouts or daily commutes; and comfort bikes are designed for leisure rides on typically flat roads. The following data show the type, weight (), and price () for the bicycles tested. Brand and Model Type Weight Price
Klein Reve V Road 20 1800
Giant OCR Composite 3 Road 22 1800
Giant OCR 1 Road 22 1000
Specialized Roubaix Road 21 1300
Trek Pilot 2.1 Road 21 1320
Cannondale Synapse 4 Road 21 1050
LeMond Poprad Road 22 1350
Raleigh Cadent 1.0 Road 24 650
Giant FCR3 Fitness 23 630
Schwinn Super Sport GS Fitness 23 700
Fuji Absolute 2.0 Fitness 24 700
Jamis Coda Comp Fitness 26 830
Cannondale Road
Warrior 400 Fitness 25 700
Schwinn Sierra GS Comfort 31 340
Mongoose Switchback SX Comfort 32 280
Giant Sedona DX Comfort 32 360
Jamis Explorer 4.0 Comfort 35 600
Diamondback Wildwood
Deluxe Comfort 34 350
Specialized Crossroads
Sport Comfort 31 330
1. Develop a scatter diagram with weight as the independent variable and price as the dependent variable. Does a simple linear regression model appear to be appropriate?
2. Develop an estimated multiple regression equation with x weight and x2 as the two independent variables.
3. Use the following dummy variables to develop an estimated regression equation that can be used to predict the price given the type of bike: Type Fitness 1 if the bike is a fitness bike, 0 otherwise; and Type-Comfort m 1 if the bike is a comfort bike; 0 otherwise. Compare the results obtained to the results obtained in part (b).
4. To account for possible interaction between the type of bike and the weight of the bike, develop a new estimated regression equation that can be used to predict the price of the bike given the type, the weight of the bike, and any interaction between weight and each of the dummy variables defined in part (c). What estimated regression equation appears to be the best predictor of price? Explain.