CAS Exam MAS-I Spring 2019, Question 39
Study guide: Exam MAS-I
Three actuaries were given a dataset and asked to build a model to predict claim frequency using any of 5 independent predictors \{1, 2, 3, 4, 5\} as well as an intercept \{I\}.
- Actuary A chooses the model using Best Subset Selection
- Actuary B chooses the model using Forward Stepwise Regression
- Actuary C chooses the model using Backwards Stepwise Regression
- When evaluating the models they all used R-squared to compare models with the same number of parameters, and AIC to compare models with different numbers of parameters.
Below are the results for all possible models:
| Model | # of Non Intercept Parameters | Parameters | R^2 |
AIC |
|---|---|---|---|---|
| 1 | 0 | I | 0 | 1.9 |
| 2 | 1 | I, 1 | 0.56 | 1.4 |
| 3 | 1 | I, 2 | 0.57 | 1.2 |
| 4 | 1 | I, 3 | 0.55 | 1.6 |
| 5 | 1 | I, 4 | 0.52 | 1.7 |
| 6 | 1 | I, 5 | 0.51 | 1.8 |
| 7 | 2 | I, 1, 2 | 0.61 | 1.0 |
| 8 | 2 | I, 1, 3 | 0.64 | 0.5 |
| 9 | 2 | I, 1, 4 | 0.63 | 0.8 |
| 10 | 2 | I, 1, 5 | 0.69 | 0.0 |
| 11 | 2 | I, 2, 3 | 0.61 | 1.0 |
| 12 | 2 | I, 2, 4 | 0.62 | 0.9 |
| 13 | 2 | I, 2, 5 | 0.68 | 0.2 |
| 14 | 2 | I, 3, 4 | 0.66 | 0.4 |
| 15 | 2 | I, 3, 5 | 0.64 | 0.5 |
| 16 | 2 | I, 4, 5 | 0.60 | 1.1 |
| 17 | 3 | I, 1, 2, 3 | 0.73 | 1.3 |
| 18 | 3 | I, 1, 2, 4 | 0.71 | 1.5 |
| 19 | 3 | I, 1, 2, 5 | 0.72 | 1.4 |
| 20 | 3 | I, 1, 3, 4 | 0.75 | 1.0 |
| 21 | 3 | I, 1, 3, 5 | 0.76 | 0.8 |
| 22 | 3 | I, 1, 4, 5 | 0.79 | 0.2 |
| 23 | 3 | I, 2, 3, 4 | 0.78 | 0.6 |
| 24 | 3 | I, 2, 3, 5 | 0.74 | 1.2 |
| 25 | 3 | I, 2, 4, 5 | 0.75 | 1.1 |
| 26 | 3 | I, 3, 4, 5 | 0.73 | 1.3 |
| 27 | 4 | I, 1, 2, 3, 4 | 0.88 | 1.6 |
| 28 | 4 | I, 1, 2, 3, 5 | 0.80 | 2.1 |
| 29 | 4 | I, 1, 2, 4, 5 | 0.87 | 1.8 |
| 30 | 4 | I, 1, 3, 4, 5 | 0.83 | 2.0 |
| 31 | 4 | I, 2, 3, 4, 5 | 0.85 | 1.9 |
| 32 | 5 | I, 1, 2, 3, 4, 5 | 0.90 | 3.5 |
\text{AIC}_jis the AIC of the model chosen by Actuaryj
Determine the correct ordering of the AIC values of the three selected models.
- A)
\text{AIC}_A < \text{AIC}_B < \text{AIC}_C - B)
\text{AIC}_A = \text{AIC}_B < \text{AIC}_C - C)
\text{AIC}_A < \text{AIC}_C < \text{AIC}_B - D)
\text{AIC}_A = \text{AIC}_C < \text{AIC}_B - E) The answer is not given by (A), (B), (C) or (D)
Answer this question and see the worked solution