Question 750484: A manufacturer of exercise bicycles is studying the relationship between the number of months an exercise bicycle has been owned and the length of time it was used last week. Data for a random sample of 7 owners are provided in the table below.
month owned (x)---------- 14,8,5,3,10,4,12
Hours used last week (y)- 6, 8,7,9,6, 8, 7
a) Construct a scatter diagram for these data with "month owned" on the horizontal (x) axis, and "Hours used last week" on the vertical (y) axis.
b)Describe the general pattern of the relationship between the two variables.
c)Calculate the least squares regression line with hours used as the dependent variables and months owned as the independent variables.
d)Plot the regression line on the scatter diagram you constructed in part(a). Note: show your calculations for x=4 and x=12.
e)Cab it be concluded that the slope of regression line is negative? Formulate and test the appropriate hypotheses at the 5% significance level. Use the critical value approach.
f)construct a 95% confidence interval for B.
g) interpret the numerical value of b in the sample regression line. What does it mean in the context of this question?
h) Use the equation of the regression line to predict hours used last week if an exercise bicycle has been owned for 11 months.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A manufacturer of exercise bicycles is studying the relationship between the number of months an exercise bicycle has been owned and the length of time it was used last week. Data for a random sample of 7 owners are provided in the table below.
month owned (x)---------- 14,8,5,3,10,4,12
Hours used last week (y)- 6, 8,7,9,6, 8, 7
a) Construct a scatter diagram for these data with "month owned" on the horizontal (x) axis, and "Hours used last week" on the vertical (y) axis.
Comment: A scatter cannot be shown on this site.
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b)Describe the general pattern of the relationship between the two variables.
As x increases, y decreases/
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c)Calculate the least squares regression line with hours used as the dependent variables and months owned as the independent variables.
y = -0.208x+8.95
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d)Plot the regression line on the scatter diagram you constructed in part(a). Note: show your calculations for x=4 and x=12.
f(4) = 8.116
f(12) = 6.456
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e)Can it be concluded that the slope of regression line is negative?
Yes, it is -0.208
Formulate and test the appropriate hypotheses at the 5% significance level. Use the critical value approach.
I'll leave that to you.
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f)construct a 95% confidence interval for B.
For you to do
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g) interpret the numerical value of b in the sample regression line. What does it mean in the context of this question?
When 1st purchased the hours used was 8.95 hours
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h) Use the equation of the regression line to predict hours used last week if an exercise bicycle has been owned for 11 months.
f(11) = 6.663
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Cheers,
Stan H.
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