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 ten racing bicycles reviewed by the magazine:

model

weight (lbs)

price ($)

fierro 7b

17.9

2200

hx 5000

16.2

6350

durbin ultralight

15.0

8470

schmidt

16.0

6300

wsilton advanced

17.3

4100

bicyclette vélo

13.2

8700

supremo team

16.3

6100

xtc racer

17.2

2680

d’onofrio pro

17.7

3500

americana #6

14.2

8100

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 and 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-pound 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.