Question

In: Statistics and Probability

Administrators of a computer system are gathering data to try to explain the number of interruptions...

Administrators of a computer system are gathering data to try to explain the number of interruptions in their network. For a sample of 22 days, they measured the number of interruptions per day and the daily usage (measured by the average number of users of the system per hour of that day). Fit an appropriate regression model to predict the number of interruptions based on the usage. Assess the fit of the model. Formally assess whether usage is a significant predictor of mean interruptions, providing numerical justification (test statistic and P-value) for your conclusion. Carefully interpret what the estimated model tells you about how the expected number of interruptions changes as the daily usage changes. Predict the

expected number of interruptions for a day that has 150 users per hour on average, using a point estimate and a 95% interval.

SAS code:

DATA four;
INPUT interruptions usage;
cards;
0 104.2
2 124.6
5 176.3
6 169.3
1 104.6
2 115.8
3 127.8
6 179.4
8 210.5
4 126.7
0 100.5
1 119.5
1 123.8
0 106.4
4 156.7
3 148.2
5 156.2
6 167.3
8 198.2
2 124.6
3 145.9
4 156.2
;
run;

Solutions

Expert Solution

ANSWER::

using excel>addin>phstat>Regression

we have

Regression Analysis
Regression Statistics
Multiple R 0.957817698
R Square 0.917414742
Adjusted R Square 0.913285479
Standard Error 9.278932038
Observations 22
ANOVA
df SS MS F Significance F
Regression 1 19128.8634 19128.8634 222.1739715 2.70383E-12
Residual 20 1721.971595 86.09857976
Total 21 20850.835
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 101.5836195 3.402697427 29.85385026 4.61625E-18 94.485717 108.6815219
usage 12.2683834 0.82307754 14.90550138 2.70383E-12 10.55147374 13.98529307
Confidence Interval Estimate
Data
X Value 150
Confidence Level 95%
Intermediate Calculations
Sample Size 22
Degrees of Freedom 20
t Value 2.085963
XBar, Sample Mean of X 3.363636
Sum of Squared Differences from XBar 127.0909
Standard Error of the Estimate 9.278932
h Statistic 169.2332
Predicted Y (YHat) 1941.841
For Average Y
Interval Half Width 251.7952
Confidence Interval Lower Limit 1690.046
Confidence Interval Upper Limit 2193.636
For Individual Response Y
Interval Half Width 252.538
Prediction Interval Lower Limit 1689.303
Prediction Interval Upper Limit 2194.379

let y = interruptions

x= usage

the regression model is y = 101.5836 +12.2684 x

For the predictor usage, the value of test stat t= 14.9055

p-value is 0.0000

since p-value is less than 0.05 so we can say that usage is a significant predictor of mean interruptions.

the estimated model tells us that for everyone number increase in usage there is a corresponding 12.2684 unit increase in interruptions.

the expected number of interruptions for a day that has 150 users per hour on average lies in between (1690.046 , 2193.636)

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