Question

Bicycling World, a magazine devoted to cycling, reviews hundreds of bicycles throughout the year. It's 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 (Ib)	Price ($)
Fierro 7B	18	2,200
HX 5000	16	6,300
Durbin Ultralight	15	8,470
Schmidt	16	6,300
WSilton Advanced	17	4,100
Bicyclette velo	13	8,700
Supremo Team	16	6,100
XTC Racer	17	2,680
D’Onofrio Pro	18	3,500
Americana #6	14	8,100

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? Provide answer here.

b). Fit a regression line into the data. What is the estimated regression model represented by the regression line? Paste screenshot of scatter plot with fitted regression line and equation here.

c). Create a regression model output in Excel at 0.05 level of significance. Is there a significant relationship between Weight and Price for the bicycles? Explain answer here.

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 your answer here.

e). The manufacturers of the D’Onofrio Pro plan to introduce the 15.5 pounds D’Onofrio Elite bicycle later this year. Use the regression model you estimated to predict the price of the D’Onofrio Elite bicycle. Show your work here.

f). Create a scatter plot of residual versus x-variable. From this scatter plot, could the estimated regression model obtained from the bicycle sample data be used to make a statistical inference? Paste the screenshot of the residual plot here and explain how your plot of residual versus x-variable indicate whether or not the regression assumptions for statistical inference are met.

Answer 1

a)

The scatter plot indicates that there is a negative relationship between price and weight of a bicycle i.e as weight of the bicycle increases its price decreases.

The estimated regression model is: 27372-1357*X

c)

since p-value of X variable is .000147<.05

hence relationship between Weight and Price for the bicycles is statistically significant.

Here we see that R square is 0.85.

Hence 85% of the variation is explained by the linear model.

if the weight of D’Onofrio Elite bicycle is 15.5 pounds, then its price will be:

                                                      -1357*15.5+27372=6338.5

from the plot it is apparent that the points are randomly distributed.So the linear regression is appropriate for the data.