You can read about the copiers dataset here, and download it from here: https://dcgerard.github.io/stat_415_615/data/copiers.csv
Obtain the estimated regression function of a regression of minutes on number of copiers.
Plot the estimated regression function and the data. How well does the estimated regression function fit the data?
Interpret \(\hat{\beta}_0\) in your estimated regression function. Does \(\hat{\beta}_0\) provide any relevant information here?
Obtain a point estimate of the mean service time when \(X=5\) copiers are serviced.
Estimate the difference in the mean service time when servicing one more copier. Use a 90% confidence interval. Interpret your confidence interval.
Adjust your confidence interval from part 5 to estimate the difference in mean service time when servicing two more copiers.
Test whether or not there is a linear association between the number of copiers and the time of service. State your conclusion.
Are your results in parts (6) and (7) consistent? Explain.
The manufacturer has suggested that the mean required time should not be more than 14 additional minutes for each additional copier that is serviced on a service call. Conduct a test to decide whether this standard is being satisfied by the company. State your conclusions.
Obtain a 90% confidence interval for the mean service time on calls in which six copiers are serviced. Interpret your confidence interval.
Obtain a 90% prediction interval for the service time on the next call in which six copiers are serviced. Is your prediction interval wider than the corresponding confidence interval in part (10)? Should it be?
Management wished to estimate the expected service time per copier on calls in which six copiers are serviced. Obtain an appropriate 90% confidence interval by converting the interval obtained in part (10). Interpret the converted confidence interval.
Use augment() from the {broom} package
to obtain the residuals of the regression of service time on copier
number.
Calculate the SSTO, SSE, and SSR by hand. Use these to write out an ANOVA table.
Use the sums of squares from part 13 to conduct an F-test to determine whether or not there is a linear association between time spent and the number of copiers serviced. State your conclusions.
Verify parts (13) and (14) using the Anova()
function from the {car} package.