The regression tree shown below was produced from a dataset of auto claim payments. Age Category (agecat: 1, 2, 3, 4, 5, 6) and Vehicle Age (veh_age: 1, 2,3,4) are both predictor variables, and log of claim amount (LCA) is the dependent variable.

Consider three autos I, II, III:

• An Auto in Age Category 1 and Vehicle Age 4
• An Auto in Age Category 5 and Vehicle Age 5
• An Auto in Age Category 5 and Vehicle Age 3

Rank the estimated LCA of Autos I, II, and

• LCA(I) < LCA(II) < LCA(III)
• LCA(I) < LCA(III) < LCA(II)
• LCA(II) < LCA(I) < LCA(III)
• LCA(II) < LCA(III) < LCA(I)
• LCA(III) < LCA(II) < LCA(I)

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Key: E

LCA(I) = 8.146

LCA(II) = 8.028

LCA(III) = 7.771

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.