Question

An office equipment corporation performs preventive maintenance and repair on the line of copiers that it sells. For 45 recent service calls data has been collected on the number of copiers serviced during the call and the number of minutes spent on the call by the service person. The company would like to develop a regression model that can be used to predict the amount of time (in minutes) that a call will require based on the number of copiers that need to be serviced.

Minutes	Serviced
20	2
60	4
46	3
41	2
12	1
137	10
68	5
89	5
4	1
32	2
144	9
156	10
93	6
36	3
72	4
100	8
105	7
131	8
127	10
57	4
66	5
101	7
109	7
74	5
134	9
112	7
18	2
73	5
111	7
96	6
123	8
90	5
20	2
28	2
3	1
57	4
86	5
132	9
112	7
27	1
131	9
34	2
27	2
61	4
77	5

(c)        Interpret the value of the sample slope in the context of this problem.

(d)          Find a 95% confidence interval for the population slope.

(e)          Report and interpret the value of the coefficient of determination R². Also calculate the value of the correlation coefficient r.

Answer 1

Below is the excel output of the regression:

	SUMMARY OUTPUT
	Regression Statistics
	Multiple R	0.978517
	R Square	0.957495
	Adjusted R Square	0.956507
	Standard Error	8.913508
	Observations	45
	ANOVA
		df	SS	MS	F	Significance F
	Regression	1	76960.42	76960.42	968.6572	4.01E-31
	Residual	43	3416.377	79.45063
	Total	44	80376.8
		Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
	Intercept	-0.5802	2.8039	-0.2069	0.8371	-6.2348	5.0745	-6.2348	5.0745
	Serviced	15.0352	0.4831	31.1233	0.0000	14.0610	16.0095	14.0610	16.0095

(c). If the number of copier to be serviced is increased by one then the amount of time of a call increases by 15.0352 minutes on average.

(d). 95% confidence interval for the population slope is

Lower 95%

Upper 95%

14.0610

16.0095

(e).

Correlation	0.978517
R Square	0.957495

R square is almost 95.75% and this means that the variation in number of copier to be serviced explains around 95.75% of variation in call time.