Before taking the plunge into video-conferencing, a company ran tests of its current internal computer network. The goal of the tests was to measure how rapidly data moved through the 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.
(a) Create a scatterplot of Transfer Time on File Size. Does a line seem to you to be a good summary of the association between these variables?
(b) Estimate the least squares linear equation for Transfer Time on File Size. Interpret the fitted intercept and slope. Be sure to include their units. Note if either estimate represents a large extrapolation and is consequently not reliable.
(c) Interpret the summary values r2 and se associated with the fitted equation. Attach units to these summary statistics as appropriate.
(d) To make the system look more impressive (i.e., have smaller slope and intercept), a colleague changed the units of Y to minutes and the units of X to kilobytes (1 MB = 1,024 kilobytes). What does the new equation look like? Does it ft the data any better than the equation obtained in part (b)?
(e) Plot the residuals from the regression fit in part (b) on the sizes of the files. Does this plot suggest that the residuals reveal patterns in the residual variation?
(f) Given a goal of getting data transferred in no more than 15 seconds, how much data do you think can typically be transmitted in this length of time? Would the equation provided in part (b) be useful, or can you offer a better approach?