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. Click the icon to view the data table. @ 1007. .. Q DO Transfer Time (sec) File Size (MB) TTO File Size (MB) Transfer Time (sec) 20+441 °20 60 100 File Size (MB) Transfer Time (sec) Transfer Time (sec) File Size (MB) Does a line seem to you to be a good summary of the association between these variables? O A. No, because the scatterplot does not show any obvious pattern. CB Yes, because the scatterplot shows an approximate linear pattern. OC. Yes, because the scatterplot does not show any obvious pattern OD. 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.)

File_Size_(MB) Transfer_Time_(sec)

48 17.3

59 30.3

81 27.8

74 24.3

22 8.3

21 12.9

31 16.4

49 18.6

99 32.5

22 19.6

51 29.2

99 31.6

68 26.7

69 23.6

98 44.6

32 23.8

87 35.1

81 29.6

29 14.6

97 32.9

Answer 1

B. Yes, be calese fine con partan scaltexplot shows an approximate Estimated Transfer Time (sec) = 8.728 sec +0.267 sec pen MB. It is calculated in R using um function, • The slope of 0.267. seconds per megabyte. For every are megabyte increase, average transfer time increases by 0.267 seconds

1 2 3 se = 0.737 4.634 sec. ibes The value of a means that equation desce 73.7%. Of variation The value of se. means that standard deviation of reidual is & & 4.6 seconds. The The new new slope slope is 0.267 z = 0.000004357 GOXIoan misil kB The new intercept is 8-128 2 0.14 55 min f O B Do the regression in de verse and Che new fitted line. Estimated file size is 2-757 (10) = 27.57 MB

Size=c(48,59,81,74,22,21,31,49,99,22,51,99, 68,69,98,32,87,81,29,97) time=c(17.3,30.3,27.8,24.3,8.3,12.9,16.4,18 .6,32.5,19.6,29.2,31.6,26.7,23.6,44.6,23.8,35. 1,29.6,14.6,32.9) plot(time~Size) cor(Size,time) Reg=lm(time~Size) summary(Reg) Sizen=Size*1024 timen=time/60 Regn=lm(timen~Sizen) summary(Regn) Im(Size-time)

Call: lm( formula = time - Size) Residuals: Min 10 Median -6.306 -3.305 -1.591 3Q 3.595 Max 9.690 Coefficients Estimate Std. Error t value Pr(>|t|) (Intercept) 8.72828 2.51533 3.470 0.00273 ** Size 0.26716 0.03767 7.093 1.3e-06 *** Signif. codes: O '***' 0.001 '**' 0.01 "*' 0.05 '.' 0.1 ! ! 1 Residual standard error: 4.634 on 18 de grees of freedom Multiple R-squared: 0.7365, Adjuste d R-squared: 0.7218 F-statistic: 50.31 on 1 and 18 DF, P-V alue: 1.301e-06

Call: lm(formula = timen - Sizen) Residuals: Min 1Q Median 30 Max -0.10510 -0.05508 -0.02651 0.05992 0. 16150 Coefficients: Estimate Std. Error t valu e Pr(>1t|) (Intercept) 1.455e-01 4.192e-02 3.47 0 0.00273 ** Sizen 4.348e-06 6.1312-07 7.09 3 1.3e-06 *** Signif. codes: 0 '***' 0.001 '**' 0.01 **' 0.05 '.' 0.1 ''1 Residual standard error: 0.07723 on 18 degrees of freedom Multiple R-squared: 0.7365, Adjuste d R-squared: 0.7218 F-statistic: 50.31 on 1 and 18 DF, p-v alue: 1.301e-06

Call: Im( formula = Size - time) Coefficients: (Intercept) -8.027 time 2.757 40 30 0 time 0 20 20 OO - 10 60 80 100 Size