Type Weight Price Klein Reve V Road 20 1800 Giant OCR Composite 3 Road 22 1800 Giant OCR 1 Road
Consumer Reports tested 19 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 (lbs.), and price ($) for the 19 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 |
a. Develop an estimated multiple regression equation with x=Weight and x^2=Weight Sq. as the two independent variables.
y-hat = _____ - _____weight + _____weight sq.
b. 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 = 1 if the bike is a comfort bike; 0 otherwise.
y-hat = _____ - _____Type_Fitness - _____Type_Comfort
c. 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 (b). What estimated regression equation appears to be the best predictor of price? Please round to four decimal places.
y-hat = _____ - _____Weight - _____Type_Fitness - _____Type_Comfort +_____WxF + _____WxC
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