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 data in Table 15 provides the type, weight (lb.), and price ($) for the 19 bicycles tested.

Use the sample data provided in the Table 15 to answer the following questions:

1. Provide descriptive statistics of the data divided according to the divisions in the variable type and develop a scatter diagram with weight as the independent variable and price as the dependent variable, and comment on appropriateness of a simple linear regression model on dependence of price on the weight.
2. Develop a multiple regression equation with x = weight and x² as the two independent variables, then add a dummy variable to incorporate the effect of the type.
3. Compare the results obtained in these two regressions.
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 d, describe if adding interaction improves predicting the price.
5. For a choice of combination of weight and type not given above, use the best model to predict the price.

In the regression models stated above, include the hypotheses on the coefficients, justify formulation of these hypotheses, and interpret the results. Use = .05 in all regressions. Include all phases of assessment of the model.

Table 15

Data on Type, Weight, and Price for each 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 G	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