Question

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)
92	31.9
56	18.4
28	21.2
78	27.7
22	7.9
21	14.8
36	13.5
43	16.1
49	25.7
24	19.2
33	15.4
99	31.8
72	34.4
66	27.8
98	43.8
54	25.8
82	32.8
89	40.6
48	21.2
98	32.7

​(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?

Construct the scatterplot. Choose the correct graph below.

Does a line seem to you to be a good summary of the association between these​ variables?

A. Yes, because the scatterplot does not show any obvious pattern.

B. ​No, because the scatterplot does not show any obvious pattern.

C. ​Yes, because the scatterplot shows an approximate linear pattern.

D. No, because the scatterplot shows an obvious curved line.

______________________________________________________________________________________________________________________________________

(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) =  _____ + _____ 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 ___ megabytes per second. For every one second​ increase, average file sizes increase by ___

megabytes.

B.The intercept of ___ seconds is a large extrapolation and not directly interpretable.

C.The intercept is ___ seconds per megabyte. For every one megabyte​ increase, average transfer times increase by ___ seconds.

D.The intercept of ____ 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 is ___ seconds per megabyte. For every one megabyte​ increase, average transfer times increase by

___ seconds.

B.The slope of ____ seconds per megabyte is a large extrapolation and not directly interpretable.

C.The slope is ____ megabytes per second. For every one second​ increase, average file sizes increase by

___ megabytes.

D.The slope of ___ seconds is the transfer time for a file of size 0 MB.

______________________________________________________________________________________________________________________________________

​(c) Interpret the summary values R squared and Se associated with the fitted equation. Attach units to these summary statistics as appropriate.

R Squared = _____ with ___ (units, units of seconds per megabyte, units of megabytes per second, units of seconds, units of megabytes)

Se = ____ with____ (units of seconds, no units. units of seconds, units of megabytes, units of seconds per megabyte, units of megabytes per second)

​(Round to three decimal places as​ needed.)

What is the correct interpretation of the summary values R squared and Se​?

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 means that the average residual is ____ megabytes. The value of Se means that the equation does not describe about _____​%

of the variation.

B.The value of R2 means that the equation describes about ____​% of the variation. The value of Se means that the standard deviation of the residuals is

____ seconds.

C.The value of R2 means that the equation describes about ______​% of the variation. The value of Se 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

MBequals=​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 R2 is _____ . ​(Round to one decimal place as​ needed.)

B.​Yes, because the new value of R2 is _____ . ​(Round to one decimal place as​ needed.)

C.​No; it fits equally well because the value of Se is the same.

D.​Yes, because the new value of Se is _____ seconds. ​(Round to one decimal place as​ needed.)

E.​No; it fits equally well because the value of R2 is the same.

______________________________________________________________________________________________________________________________________

​(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?

Plot the residuals on the sizes of the files. Choose the correct graph below.

Does the plot suggest that the residuals reveal patterns in the residual​ variation?

A. ​No, because the plot shows consistent vertical scatter with no obvious pattern.

B. ​Yes, because the plot shows a linear pattern.

C. ​Yes, because the plot shows an obvious bend.

D. ​Yes, because the plot shows decreasing variation.

E. ​Yes, because the plot shows increasing variation.

(f) Given a goal of getting data transferred in no more than 20 ​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.

Answer 1

​(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?

Construct the scatterplot. Choose the correct graph below.

Does a line seem to you to be a good summary of the association between these​ variables?

Ans: C. ​Yes, because the scatterplot shows an approximate linear 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) = 6.963 + 0.306 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.)

Ans: D.The intercept of 6.963 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.)

Ans: A.The slope is 0.306 seconds per megabyte. For every one megabyte​ increase, average transfer times increase by

0.306 seconds.

​(c) Interpret the summary values R squared and Se associated with the fitted equation. Attach units to these summary statistics as appropriate.

R Squared = 0.7858 with no unit.

Se = 4.526 with units of seconds.

What is the correct interpretation of the summary values R squared and Se​?

Select the correct choice below and fill in the answer boxes to complete your choice. (Round to one decimal place as​ needed.)

Ans:

B. The value of R2 means that the equation describes about 78.58​% of the variation. The value of Se means that the standard deviation of the residuals is 4.526 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

MBequals=​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 0.00000498 minutes per kilobyte. ​(Round to eight decimal places as​ needed.)

The new intercept is 0.116 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.

Ans:E.​No; it fits equally well because the value of R2 is the same.

______________________________________________________________________________________________________________________________________

​(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?

Plot the residuals on the sizes of the files. Choose the correct graph below.

Does the plot suggest that the residuals reveal patterns in the residual​ variation?

A. ​No, because the plot shows consistent vertical scatter with no obvious pattern.

(f) Given a goal of getting data transferred in no more than 20 ​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.)

B.Use the equation from part b. The estimated file size is 6.963+0.306*20=13.083 MB.