Price and Weight of Bicycles Bicycling World, a magazine devoted to cycling, reviews hundreds of bicycles throughout the year Its Road Race category contains reviews of bicycles used by riders primarily interested in racing One of the most important factors in selecting a bicycle for racing is its weight The following data show the weight (pounds) and price ($) for 10 racing bicycles reviewed by the magazine a Develop a scatter chart with weight as the independent variable What does the scatter chart indicate about the relationship between the weight and price of these bicycles b Use the data to develop an estimated regression equation that could be used to estimate the price for a bicycle, given its weight What is the estimated regression model c Test whether each of the regression parameters0and1is equal to zero at a 0 05 level of significance What are the correct interpretations of the estimated regression parameters Are these interpretations reasonable d How much of the variation in the prices of the bicycles in the sample does the regression model you estimated inpart (b)explain e The manufacturers of the D'Onofrio Pro plan to introduce the 15 lb D'Onofrio Elite bicycle later this year Use the regression model you estimated inpart (a)to predict the price of the D'Ononfrio Elite f The owner of Michele's Bikes of Nesika Beach, Oregon is trying to decide in advance whether to make room for the D'Onofrio Elite bicycle in its inventory She is convinced that she will not be able to sell the D'Onofrio Elite for more than $7,000, and so she will not make room in her inventory for the bicycle unless its estimated price is less than $7,000 Under this condition and using the regression model you estimated inpart (a), what decision should the owner of Michele's Bikes make Machine Maintenance Jensen Tire Auto is deciding whether to purchase a maintenance contract for its new computer wheel alignment and balancing machine Managers feel that maintenance expense should be related to usage, and they collected the following information on weekly usage (hours) and annual maintenance expense (in hundreds of dollars) a Develop a scatter chart with weekly usage hours as the independent variable What does the scatter chart indicate about the relationship between weekly usage and annual maintenance expense b Use the data to develop an estimated regression equation that could be used to predict the annual maintenance expense for a given number of hours of weekly usage What is the estimated regression model c Test whether each of the regression parameters0and1is equal to zero at a 0 05 level of significance What are the correct interpretations of the estimated regression parameters Are these interpretations reasonable d How much of the variation in the sample values of annual maintenance expense does the model you estimated inpart (b)explain e If the maintenance contract costs $3,000 per year, would you recommend purchasing it Why or why not 3 Ratings of Beachfront Boutique Hotels Resorts Spas , a magazine devoted to upscale vacations and accommodations, published its Reader's Choice List of the top 20 independent beachfront boutique hotels in the world The data shown are the scores received by these hotels based on the results from Resorts Spas' annual Readers' Choice Survey Each score represents the percentage of respondents who rated a hotel as excellent or very good on one of three criteria (comfort, amenities, and in house dining) An overall score was also reported and used to rank the hotels The highest ranked hotel, the Muri Beach Odyssey, has an overall score of 94 3, the highest component of which is 97 7 for in house dining a Determine the estimated multiple linear regression equation that can be used to predict the overall score given the scores for comfort, amenities, and in house dining b Use the t test to determine the significance of each independent variable What is the conclusion for each test at the 0 01 level of significance c Remove all independent variables that are not significant at the 0 01 level of significance from the estimated regression equation What is your recommended estimated regression equation d Suppose Resorts Spas has decided to recommend each of the independent beachfront boutiques in its data that achieves an estimated overall score over 90 Use the regression equation developed in part (c) to determine which of the independent beachfront boutiques will receive a recommendation from Resorts Spas Model Fierro 7B HX 5000 Durbin Ultralight Schmidt WSilton Advanced bicyclette vlo Supremo Team XTC Racer D'Onofrio Pro Americana 6 Weight Price 17 9 2200 16 2 6350 15 0 8470 16 0 6300 17 3 4100 13 2 8700 16 3 6100 17 2 2680 17 7 3500 14 2 8100

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Price and Weight of Bicycles. Bicycling World, a magazine devoted to cycling, reviews hundreds of bicycles throughout the year. Its Road-Race category contains reviews of

Price and Weight of Bicycles. Bicycling World, a magazine devoted to cycling, reviews hundreds of bicycles throughout the year. Its Road-Race category contains reviews of bicycles used by riders primarily interested in racing. One of the most important factors in selecting a bicycle for racing is its weight. The following data show the weight (pounds) and price ($) for 10 racing bicycles reviewed by the magazine:

a. Develop a scatter chart with weight as the independent variable. What does the scatter chart indicate about the relationship between the weight and price of these bicycles?
b. Use the data to develop an estimated regression equation that could be used to estimate the price for a bicycle, given its weight. What is the estimated regression model?
c. Test whether each of the regression parameters β0 and β1 is equal to zero at a 0.05 level of significance. What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable?
d. How much of the variation in the prices of the bicycles in the sample does the regression model you estimated in part (b) explain?
e. The manufacturers of the D'Onofrio Pro plan to introduce the 15-lb D'Onofrio Elite bicycle later this year. Use the regression model you estimated in part (a) to predict the price of the D'Ononfrio Elite.
f. The owner of Michele's Bikes of Nesika Beach, Oregon is trying to decide in advance whether to make room for the D'Onofrio Elite bicycle in its inventory. She is convinced that she will not be able to sell the D'Onofrio Elite for more than $7,000, and so she will not make room in her inventory for the bicycle unless its estimated price is less than $7,000. Under this condition and using the regression model you estimated in part (a), what decision should the owner of Michele's Bikes make?
Machine Maintenance. Jensen Tire & Auto is deciding whether to purchase a maintenance contract for its new computer wheel alignment and balancing machine. Managers feel that maintenance expense should be related to usage, and they collected the following information on weekly usage (hours) and annual maintenance expense (in hundreds of dollars).
- a. Develop a scatter chart with weekly usage hours as the independent variable. What does the scatter chart indicate about the relationship between weekly usage and annual maintenance expense?
- b. Use the data to develop an estimated regression equation that could be used to predict the annual maintenance expense for a given number of hours of weekly usage. What is the estimated regression model?
- c. Test whether each of the regression parameters β0 and β1 is equal to zero at a 0.05 level of significance. What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable?
- d. How much of the variation in the sample values of annual maintenance expense does the model you estimated in part (b) explain?
- e. If the maintenance contract costs $3,000 per year, would you recommend purchasing it? Why or why not?
3.- Ratings of Beachfront Boutique Hotels. Resorts & Spas, a magazine devoted to upscale vacations and accommodations, published its Reader's Choice List of the top 20 independent beachfront boutique hotels in the world. The data shown are the scores received by these hotels based on the results from Resorts & Spas' annual Readers' Choice Survey. Each score represents the percentage of respondents who rated a hotel as excellent or very good on one of three criteria (comfort, amenities, and in-house dining). An overall score was also reported and used to rank the hotels. The highest ranked hotel, the Muri Beach Odyssey, has an overall score of 94.3, the highest component of which is 97.7 for in-house dining.

a. Determine the estimated multiple linear regression equation that can be used to predict the overall score given the scores for comfort, amenities, and in-house dining.
b. Use the t test to determine the significance of each independent variable. What is the conclusion for each test at the 0.01 level of significance?
c. Remove all independent variables that are not significant at the 0.01 level of significance from the estimated regression equation. What is your recommended estimated regression equation?
d. Suppose Resorts & Spas has decided to recommend each of the independent beachfront boutiques in its data that achieves an estimated overall score over 90. Use the regression equation developed in part (c) to determine which of the independent beachfront boutiques will receive a recommendation from Resorts & Spas.