Brand and ModelTypeWeightweight 2PriceKlein RÃªve vRoad204001800Giant OCR Composite 3Road224841800Giant OCR 1Road224841000Specialized RoubaixRoad214411300Trek Pilot 2.1Road214411320Cannondale Synapse 4Road214411050LeMond PopradRoad224841350Raleigh Cadent 1.0Road24576650Giant FCR3Fitness23529630Schwinn Super Sport GSFitness23529700Fuji Absolute 2.0Fitness24576700Jamis Coda CompFitness26676830Cannondale Road Warrior 400Fitness25625700Schwinn Sierra GSComfort31961340Mongoose Switchback SXComfort321024280Giant Sedona DXComfort321024360Jamis Explorer 4.0Comfort351225600Diamondback Wildwood DeluxeComfort341156350Specialized Crossroads SportComfort31961330PLEASE ROUND ALL ANSWERS TO 4 DECIMAL PLACES **Educational Resource: Analyzing Bike Price Prediction with Multiple Regression Models**1. **Scatter Diagram Assessment** - Selected diagram: 4 - Conclusion: A simple linear regression model does not appear to be appropriate.2. **Developing a Multiple Regression Equation** - Equation: \( \hat{y} = 11376 - 728 \times \text{Weight} + 12 \times \text{WeightSq} \) - Variables: - \( x \) = Weight - \( x^2 \) = WeightSq3. **Using Dummy Variables for Regression** - Equation: \( \hat{y} = 1284 + 572 \times \text{Type\_Fitness} - 907 \times \text{Type\_Comfort} \) - Dummy Variables: - \( \text{Type\_Fitness} = 1 \) if bike is a fitness bike, 0 otherwise. - \( \text{Type\_Comfort} = 1 \) if bike is a comfort bike, 0 otherwise. - Conclusion: Type of bike is a significant factor in predicting price. - Fit Comparison: Equation in part (b) provides a slightly better fit.4. **Accounting for Interaction in Regression** - Equation: \( \hat{y} = 5924 + 215 \times \text{Weight} - 6343 \times \text{Type\_Fitness} - 7232 \times \text{Type\_Comfort} + 261 \times \text{WxF} + 266 \times \text{WxC} \) - Interaction Terms: - WxF: Interaction between Weight and Type\_Fitness - WxC: Interaction between Weight and Type\_Comfort - Task: Determine the best predictor of price, rounded to four decimal places.**Feedback Section** - Status: Partially CorrectThis educational module guides the understanding of how different variables, including weight and type of bike, influence price prediction through regression analysis.

(b) The estimated multiple regression equation for x=weights and x2=weightSq is given below : Note : The WeightSq is a computed variable and will be regarded linear. That is, the equation can be written as : y=a+bx+cz,z=x2 The SPSS output is attached below The regression equation is : y^=11375.999-728.335 x +11.974 x2(c) Using the dummy variable, the data will be presented as : The output is : The regression equation using the dummy variable is : y^=1283.750-571.570 type_fitness - 907.083 type_comfort The difference between the results obtained from (b) and (c) is that in (b), we are testing the dependency of weight on price while in (c) we are checking the dependency type of bike on price. (d) The data for testing for the dependency of interaction between type of bike and weight of bike on price of bike is shown below : Running the regression, the following output were obtained : The regression equation is : y^=5923.544-214.557 weight -6343.250 type_fitness-7232.063 type_comfort +261.322 (WxF) + 266.409 (WxC)

Select the correct scatter diagram from the options above. 4 Does a simple linear regression model appear to be appropriate? A simple linear regression model does not appear to be appropriate. V Round your answers to four decimal places. b. Develop an estimated multiple regression equation with z = Weight and z? = WeightSq as the two independent variables. 11376 8 WeightSq 728 Weight + 12 c. 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; otherwise. Compare the results obtained to the results obtained in part (b). 1284 O 572 O Type_Fitness - 907 8 Type_Comfort Type of bike appears to be a(n) significant factor in predicting price. But, the estimated regression equation developed in part (b) appears to provide a slightly better fit. d. 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? Please round to four decimal places. 215 O Weight - Type_Fitness - Type_Comfort + & WxF + WxC 5924 6343 7232 261 266

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Klein RÃªve v	Road	20	400	1800
Giant OCR Composite 3	Road	22	484	1800
Giant OCR 1	Road	22	484	1000
Specialized Roubaix	Road	21	441	1300
Trek Pilot 2.1	Road	21	441	1320
Cannondale Synapse 4	Road	21	441	1050
LeMond Poprad	Road	22	484	1350
Raleigh Cadent 1.0	Road	24	576	650
Giant FCR3	Fitness	23	529	630
Schwinn Super Sport GS	Fitness	23	529	700
Fuji Absolute 2.0	Fitness	24	576	700
Jamis Coda Comp	Fitness	26	676	830
Cannondale Road Warrior 400	Fitness	25	625	700
Schwinn Sierra GS	Comfort	31	961	340
Mongoose Switchback SX	Comfort	32	1024	280
Giant Sedona DX	Comfort	32	1024	360
Jamis Explorer 4.0	Comfort	35	1225	600
Diamondback Wildwood Deluxe	Comfort	34	1156	350
Specialized Crossroads Sport	Comfort	31	961	330