Question

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

Months 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 “Months Owned” on the horizontal axis, and “Hours Used Last Week” on the vertical axis.

B)Then, calculate the least squares regression line with hours used as the dependent variable and months owned as the independent variable.
Note: Express a and b to 4 decimal places of accuracy.

C) Plot the regression line on the scatter diagram you constructed.
Note: Show your calculations for x=4 and x=12 to four decimal places.

D) Can it be concluded that the slope of the regression line is negative? Formulate and test the appropriate hypotheses at the 5% significance level. Use the critical value approach.

E) Construct a 95% confidence interval for B.