A computer repair service is examining the time taken on service calls to repair computers. Data were obtained for 30 service calls. The data are available in the worksheet entitled "COMPREP5". Information obtained includes:
x1 = number of machines to be repaired (NUMBER)
x2 = years of experience of service person (EXPER)
y = time taken (in minutes) to provide service (TIME)
Develop a polynomial regression model to predict average time on the service calls using EXPER and NUMBER as explanatory variables by fitting ALL the models below (Let NUMBERSQR and EXPERSQR represent squared variables.) Hint: Yes, this means that you have to fit ALL six of the models listed below separately.
Create a table in EXCEL that organizes the standard error of the regression (se) and R2adj for each model to easily compare models based on these two indicators of model fit.
(a) Choose the best fitting model.
TIME = 289 + 33 NUMBER − 92 EXPER + 5.488 EXPERSQRTIME = 69 + 3.865 NUMBER + 0.944 NUMBERSQR TIME = −84 + 33 NUMBERTIME = 66 + 3.887 NUMBER + 0.943 NUMBERSQR + 0.371 EXPERTIME = −179 + 33 NUMBER + 10.189 EXPERTIME = 286 + 16 EXPER
(b) Justify your model choice. (Use a 5% significance level.)
This model has significant p values for each coefficient, with a large standard error of the regression and a low R2adj.This model has the largest standard error of the regression and the lowest R2adj of all the models. This model has the largest standard error of the regression and the highest R2adj of all the models.This model has the smallest standard error of the regression and the smallest R2adj of all the models.This model has significant p values for each coefficient, with a small standard error of the regression and a high R2adj.
(c) What is the standard error of the regression for the best fitting model that you evaluated above? (Enter your answer to two decimal places.)
se =
(d) What is R2adj for the best fitting model that you evaluated above? (Enter your answer as a proportion and round to four decimal places.)
R2adj =
(e) What is the standard error of the regression for the worst fitting model that you evaluated? (Enter your answer to two decimal places.)
se =
(f) What is R2adj for the worst fitting model that you evaluated above? (Enter your answer as a proportion and round to four decimal places.)
NUMBER EXPER TIME
1 9 66
1 11 74
3 11 88
4 8 99
6 9 134
6 9 120
7 10 178
8 9 139
9 8 187
11 10 227
11 10 225
12 7 270
13 9 265
14 9 301
15 10 343
16 11 383
17 10 383
20 9 515
19 9 474
20 9 495
22 9 628
22 9 636
23 10 660
24 10 731
25 11 752
26 8 800
27 10 863
28 9 918
29 9 976
30 10 1027
