Question

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.

Answer 1

Answer:

Check the explanation

Step-by-step explanation:

$S_{yy}=\sum y^{2}-\frac{\left (\sum y \right )^{2}}{n}=52120800$

$S_{xx}=\sum x^{2}-\frac{\left (\sum x \right )^{2}}{n}=21.74$

$S_{xy}=\sum xy-\frac{\left (\sum x \right )\left (\sum y \right )}{n}=-31284$

Slope of the regression equation is

$b_{1}=\frac{S_{xy}}{S_{xx}}=-1439.01$

and intercept of the equation will be

$b_{0}=\frac{1}{n}(\sum y - b_{1} \sum x)=28818.00$

So the regression equation will be

y'=28818.00-1439.01x

C.

the attached images below comprise of the output of the regression analysis generated by excel:

Intercept:

Hypotheses are:

$H_{0}:\beta_{0}=0,H_{a}:\beta_{0}\neq 0$

t-value of intercept is 8.820

P-value is 0.0000

Since p-value is less than 0.05 so intercept is significant to the model.

Slope:

Hypotheses are:

$H_{0}:\beta_{1}=0,H_{a}:\beta_{1}\neq 0$

t-value of intercept is -7.12

P-value is 0.0000

Since p-value is less than 0.05 so slope is significant to the model.

D.

Since from regression output R-square is 0.864 so 86.4% of the variation  in the prices of the bicycles is accounted for by the weight of bicycles.

E.

For X= 15 estimated y value is

y'=28818.00-1439.01*15 = 7232.85

hence, required predicted price is $7232.85.