Question

(Data source: Applied Linear Statistical Models, 5th Ed., by Kutner, Nachtsheim, Neter, and Li, McGraw-Hill, 2005)

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.

(1) The first service call scheduled for tomorrow involves servicing 5 copiers. Predict, with a .95 level of confidence, the time that will be required for this service call. Note that you need to use a PI, not a point predictor. Please explain the thought process behind your work.

(2) Repeat (a) but now assume that the call involves servicing 13 copiers rather than 5 copiers. Please explain the thought process behind your work.

(3) What key assumption is made when doing the prediction requested in (2) that is not necessary for the prediction requested in (1)? Please explain the thought process behind this. Why is solving for 5 copiers different than solving for 13 copiers?

Date below

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

Answer 1

Answer:

() The R command to find the prediction interval is: newdata<-data. frame (Serviced-5) > predict (Model, newdata, interval="predict", conf.level-o.95) fit lwr upr 1 74.59608 s6.42133 92.77084 Therefore, the 95% prediction interval for the time spent on service calls for calls that involve 5 copiers is (56.42133, 92.77084) (i) The R command to find the confidence interval is: newdatac-data.frame (Serviced-13 ) > predict (Model, newdata, interval="confidence ", conf.level-o.95) fit 1wr upr 1 194.8781 18e6.7387 203.0175 Therefore, the 95% confidence interval for the mean time spent on service calls for calls that involve 13 copiers is (186.7387, 203.0175) (iii) There are two key assumptions in making the prediction interval that are: 1. The value for which the prediction needs to be made is in the scope of the model. 2. The prediction interval strongly require that the error terms are normally distributed.