Before taking the plunge into videoconferencing, 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. Twenty 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. Complete parts a through f below.
File Size (MB) Transfer Time (sec)
77 25.8
57 26.7
24 17.5
77 34.8
22 9.5
22 8.7
35 14.6
47 21.5
97 36.3
22 20.5
54 27.9
99 34.3
78 29.8
68 30.3
97 41.4
31 14.9
85 39.5
35 17.2
22 14.4
97 30.7
(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?
Does a line seem to you to be a good summary of the association between these variables?
A. Yes, because the scatterplot shows an approximate linear pattern.
B. No, because the scatterplot shows an obvious curved line.
C. Yes, because the scatterplot does not show any obvious pattern.
D. No, because the scatterplot does not show any obvious pattern
(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.
Complete the equation for the fitted line below.
Estimated Transfer Time (sec) = 7.109 + 0.309 File Size (MB)
(Round to three decimal places as needed.)
What is the correct interpretation of the intercept? Select the correct choice below and fill in the answer box(es) to complete your choice.
(Round to three decimal places as needed.)
A. The intercept is 7.109 seconds per megabyte. For every one megabyte increase, average transfer times increase by 7.109 seconds.
B. The intercept is 7.109 megabytes per second. For every one second increase, average file sizes increase by 7.109 megabytes.
C. The intercept of 7.109 seconds is a large extrapolation and not directly interpretable.
D. The intercept of 7.109 seconds estimates "latency" in the network that delays the initial transfer of data.
What is the correct interpretation of the slope? Select the correct choice below and fill in the answer box(es) to complete your choice.
(Round to three decimal places as needed.)
A. The slope of 0.309 seconds is the transfer time for a file of size 0 MB.
B. The slope of 0.309 seconds per megabyte is a large extrapolation and not directly interpretable.
C. The slope is 0.309 megabytes per second. For every one second increase, average file sizes increase by 0.309 megabytes.
D. The slope is 0.309 seconds per megabyte. For every one megabyte increase, average transfer times increase by 0.309 seconds.
What is the correct interpretation of the summary values r squared (r^2) and s Subscript e (s_e)?
Select the correct choice below and fill in the answer boxes to complete your choice.
(Round to one decimal place as needed.)
A. The value of r squared (r^2) means that the average residual is ____ megabytes. The value of s Subscript e (s_e) means that the equation does not describe about __% of the variation.
B. The value of r squared (r^2) means that the equation describes about _% of the variation. The value of s Subscript e (s_e) means that the standard deviation of the residuals is __ seconds.
C. The value of r squared (r^2) means that the equation describes about __% of the variation. The value of s Subscript e (s_e) means that the average residual is __ seconds.
(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 fit the data any better than the equation obtained in part b?
The new slope is __ minutes per kilobyte.
(Round to eight decimal places as needed.)
The new intercept is __ minutes.
(Round to four decimal places as needed.)
Does the new equation fit the data any better than the equation obtained in part b? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. No; it does not fit as well because the new value of r squared (r^2) is __.
(Round to one decimal place as needed.)
B. Yes, because the new value of s Subscript e (s_e) is __ seconds.
(Round to one decimal place as needed.)
C. No; it fits equally well because the value of r squared (r^2) is the same.
D. No; it fits equally well because the value of s Subscript e (s_e) is the same.
E. Yes, because the new value of r squared (r^2) is __.
(Round to one decimal place as needed.)
(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?
Does the plot suggest that the residuals reveal patterns in the residual variation?
A. Yes, because the plot shows an obvious bend.
B. No, because the plot shows consistent vertical scatter with no obvious pattern.
C. Yes, because the plot shows decreasing variation.
D. Yes, because the plot shows increasing variation.
E. Yes, because the plot shows a linear pattern.
(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? Select the correct choice below and fill in the answer box to complete your choice.
(Round to two decimal places as needed.)
A. Do the regression in reverse and use the new fitted line. The estimated file size is __ MB.
B. Use the equation from part b. The estimated file size is __ MB.