Question

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.

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;

Answer 1

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)