A medium-sized automobile insurance company is interested in developing a regression model to help predict the monthly collision claims of its policyholders. A company analyst
A medium-sized automobile insurance company is interested in developing a regression model to help predict the monthly collision claims of its policyholders. A company analyst has proposed modeling monthly collision claims (y) in the Middle Atlantic states as a function of the percentage of claims by drivers under age 30 (x1) and the average daily temperature during the month (x2). She believes that as the percentage of claims by drivers under age 30 increases, claims will rise because younger drivers are usually involved in more serious accidents than older drivers. She also believes that claims will rise as the average daily temperature decreases because lower temperatures are associated with icy, hazardous driving conditions. In order to develop a preliminary model, data were collected for the state of New Jersey over a 3 year period. The data are in the attached file.
- Use a software package to fit the complete second order modelE(y) = 0+1x1+2x2+ 3x1x2+4x12+ 5x22
- Test the hypothesis H0: 4=5=0 using alpha = 0.05. Interpret the results in practical terms.
- Do the results support the analysts' beliefs? Explain.
Data:
Month:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
Collition:
116250
217180
43436
159265
130308
72393
174740
101351
144787
28957
173744
86872
108420
203288
40658
149078
121973
67763
163130
94858
135525
27105
162631
81315
114890
217726
43084
157973
129910
71808
172005
103166
143612
28722
175335
87157
154886
290411
58082
212966
174247
96804
230329
136528
193608
38722
212309
118796
PctUnder30:
50
60.8
45.1
56.4
53.3
46.9
57.8
50.6
55
35.8
57.9
49.9
51
62.9
45.1
55.2
53.7
47.2
56.1
48.3
54.7
45.4
56.5
47.7
51.3
61.6
45.9
55.2
53.6
46.9
58.2
51.1
55.4
28.2
57.5
48.2
56.9
66.5
45.9
61.4
57.7
48.9
64.3
53.1
59.8
45.6
63.9
52.3
Temperature:
31.5
33
45
53.9
63.9
74.5
79.4
75.3
68.7
53.7
47.6
38.4
28.7
34.4
43.9
51.1
63.4
73
80.5
79.8
68
52.6
48.9
35.5
37
34.2
42.4
52.5
63.2
74.3
77.2
76.3
69.9
59.1
45
25.6
40.4
39.8
44.9
53.3
61.1
73.4
77.8
76.6
68.6
62.4
50
42.3
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Authors: Stephen Lynch
2nd Edition
3319068202, 9783319068206
