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clairee002
05.05.2020 •
Mathematics
The time it takes to transmit a file always depends on the file size. Suppose you transmitted 30 files, with the average size of 126 Kbytes and the standard deviation of 35 Kbytes. The average transmittance time was 0.04 seconds with the standard deviation of 0.01 seconds. The correlation coefficient between the time and the size was 0.86.
Based on this data, fit a linear regression model and predict the time it will take to transmit a 400 Kbyte file.
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Ответ:
Y = 0.009042 + 0.0002457X
Y = 0.1073 seconds
Step-by-step explanation:
In the given problem we have two variables: the transmission time and average size of file.
Y = transmission time
X = average file size
The linear regression model is given by
Y = a + bX
The slope b is given by
b = correlation coefficient*(SDy/SDx)
Where SDy is the standard deviation of average transmittance time and SDx is the standard deviation of average file size.
b = 0.86(0.01/35)
b = 0.0002457
The y-intercept a is given by
a = y - bx
a = 0.04 - (0.0002457)126
a = 0.04 - 0.030958
a = 0.009042
Therefore, the linear regression model is
Y = 0.009042 + 0.0002457X
Predict the time it will take to transmit a 400 Kbyte file.
Substitute X = 400 in the regression model
Y = 0.009042 + 0.0002457(400)
Y = 0.009042 + 0.09828
Y = 0.1073 seconds
Therefore, the predicted time to transmit a 400 Kbyte file is 0.1073 seconds.
Ответ:
Step-by-step explanation:
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