Question

A company ran tests of its current internal computer network. Thirty 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​ recorded, as shown in the accompanying data table. Formulate the simple linear regression with Y given by Transfer Time and X given by File Size. Complete parts​ (a) through​ (f) below.

Data table of file sizes and transfer times

File size (MB)   Time (sec)
70   25.8
73   28.4
44   19.8
23   10.5
76   28.3
93   33.1
34   15.8
88   32.1
64   25.3
55   21.4
41   20.1
85   30.6
80   31.7
64   22.3
72   24.8
43   18.4
100   33.4
58   21.2
71   27.9
76   29.5
57   19.7
69   26.5
25   11.5
50   21.8
70   23.2
84   32.6
76   29.7
96   36.2
84   31.7
67   24.5

(A). Use Excel to conduct a simple linear regression analysis and answer the following questions.

Find the value of the test statistic t associated with β1.

t= ? (round to two decimal points as needed)

(B). Find the p-value for this test

p-value= ? (round to four decimal places as needed)

(C). Estimate the average​ "setup" time to start the file transfer. This time is used to synchronize the computers making the transfer and is unrelated to file size. Use a confidence level of​ 95%.

The average setup time is ? to ? seconds. ​(Round to one decimal place as​ needed.)

(D). Estimate the average change in transfer time when the size of a file is reduced by​ 1-MB. Use a confidence level of​ 95%.

The average transfer time is decreased by ? to ? seconds. (round to three decimal places as needed. Use ascedning order)

(E). To speed​ transfers, the company introduced compression software that halves the size of a file when sent over the network. On​ average, what is the improvement in time when sending a 50​-MB file​ (note that the file starts at​ 50-MB)? Use a confidence level of​ 95% to state your answer as a range.

On​ average, the improvement in time is ? to ? seconds. (Round to one decimal place as needed. Use ascending order.​)

Answer 1

The regression output is:

	r²	0.942
	r	0.970
	Std. Error	1.589
	n	30
	k	1
	Dep. Var.	Time (sec)
ANOVA table
Source	SS	df	MS	F	p-value
Regression	1,142.6647	1	1,142.6647	452.49	8.00E-19
Residual	70.7073	28	2.5253
Total	1,213.3720	29
Regression output					confidence interval
variables	coefficients	std. error	t (df=28)	p-value	95% lower	95% upper
Intercept	4.5028
File size (MB)	0.3132	0.0147	21.27	8.00E-19	0.2831	0.3434

(a) 21.27

(b) 0.0000

(c) 2.4, 6.6

(d) 2.075, 6.304

(e) 19.4, 20.9