Before purchasing videoconferencing equipment, a company tested its current internal computer network. The tests measured how rapidly data moved through its network given the current demand on the network. Eighty files ranging in size from 20 to 100 megabytes (MB) were transmitted over the network at various times of day, and the time to send the files (in seconds) recorded. The time is given as the number of hours past 8 A.M. on the day of the test. Use the transfer time as the response, with the file size and time of day as explanatory variables.
(a) Examine scatterplots of the response versus the two explanatory variables as well as the scatterplot between the explanatory variables. Do you notice any unusual features in the data? Do the relevant plots appear straight enough for multiple regression?
(b) Do you think, before fitting the multiple regression, that the partial slope for the file size will be the same as its marginal slope? Explain.
(c) Fit the multiple regression of the transfer time on the file size and the time of day. Summarize the estimates obtained for the fitted model.
(d) Does the fit of this model meet the conditions of the MRM?
(e) Compare the sizes of the t-statistics of the fitted model to the overall F-statistic. Do these tests agree with each other?
(f) Compare the confidence interval for the marginal slope for file size to the confidence interval for the partial slope for file size. How are these different?
(g) Does the path diagram for the multiple regression offer a suggestion for the differences noticed in the previous questions?