This exercise considers the data described in the Section 13.2.2 ratemaking classification example using data in Table 13.3

Table 13.3 

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a. Fit a gamma regression model using a log-link function with claim counts as weights \(\left(w_{i}\right)\). Use the categorical explanatory variables age group and vehicle use to estimate expected average severity.

b. On the basis of your estimated parameters in part (a), verify the estimated expected severities in Table 13.4

 Table 13.4

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Age Vehicle Group Use Average Claim Severity Count Age Vehicle Group Use Average Claim Severity Count 17-20 Pleasure 250.48 21 35-39 Pleasure 153.62 151 17-20 DriveShort 274.78 40 35-39 DriveShort 201.67 479 17-20 DriveLong 244.52 23 35-39 DriveLong 238.21 381 17-20 Business 797.80 5 35-39 Business 256.21 166 21-24 Pleasure 213.71 63 21-24 DriveShort 298.60 21-24 DriveLong 298.13 92 21-24 Business 44 171 40-49 Pleasure 40-49 DriveShort 202.80 970 40-49 DriveLong 236.06 719 208.59 245 362.23 40-49 Business 352.49 304 25-29 Pleasure 250.57 140 50-59 Pleasure 207.57 266 25-29 DriveShort 248.56 25-29 DriveLong 297.90 318 343 50-59 DriveShort 202.67 859 50-59 DriveLong 253.63 504 25-29 Business 342.31 129 50-59 Business 340.56 162 30-34 Pleasure 229.09 123 60+ Pleasure 192.00 260 30-34 DriveShort 228.48 448 60+ DriveShort 196.33 578 30-34 DriveLong 293.87 361 60+ DriveLong 259.79 312 30-34 Business 367.46 169 60+ Business 342.58 96