Exam MAS-I Practice Question 128
Study guide: Exam MAS-I
Two severity GLMs were fitted to the same training data and are compared on a holdout sample. For each model separately, the holdout claims are sorted by that model's predicted severity and split into five groups of equal claim count. Average predicted and actual severity (in thousands) are:
| Quintile | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Model 1 predicted | 4.0 | 5.0 | 6.0 | 7.0 | 8.0 |
| Model 1 actual | 5.2 | 5.4 | 6.0 | 6.6 | 6.8 |
| Model 2 predicted | 3.6 | 4.8 | 6.0 | 7.4 | 9.0 |
| Model 2 actual | 3.8 | 4.7 | 6.1 | 7.3 | 9.2 |
The pricing team will prefer the model whose actual-to-predicted ratios are closest to 1 across the quintiles and whose actual results separate the low-severity groups from the high-severity groups more. For Model 1, the ratio of actual severity in quintile 5 to that in quintile 1 is 6.8 / 5.2 = 1.31.
Part a (1 point)
Calculate the same ratio for Model 2: actual severity in quintile 5 divided by actual severity in quintile 1. Give your answer to two decimal places.
Part b (1 point)
Using the team's two criteria, which model should be preferred?
- A) Model 1, since its overall actual-to-predicted ratio is exactly 1
- B) Model 2, since its ratios stay near 1 and its actual spread is wider
- C) Model 1, since its narrower predicted range makes overfitting less likely
- D) Model 2, since a wider predicted range by itself shows a better fit
- E) Neither, since both overall ratios are near 1, so the two fit equally well
Part c (1 point)
Explain what Model 1's pattern of actual-to-predicted ratios says about its relativities, and what the pricing team would charge if it adopted Model 1.
Answer this question and see the worked solution