CAS Exam 8 Fall 2017, Question 6
Study guide: Exam 8
A logistic model was built to predict the probability of a claim being fraudulent. Consider the predicted probabilities for the 10 claims below to be a representative sample of the total model.
| Claim Number | Actual Fraud Indicator | Predicted Probability of Fraud |
|---|---|---|
| 1 | Y | 11% |
| 2 | N | 23% |
| 3 | N | 15% |
| 4 | N | 70% |
| 5 | Y | 91% |
| 6 | Y | 30% |
| 7 | N | 11% |
| 8 | Y | 75% |
| 9 | N | 58% |
| 10 | N | 27% |
Part a (1 point)
Construct confusion matrices for discrimination thresholds of 0.50 and 0.25.
Part b (1.5 points)
Plot the Receiver Operating Characteristic (ROC) curve with the discrimination thresholds of 0.50 and 0.25. Label each axis and the coordinates and discrimination threshold of each point on the curve.
Part c (0.5 points)
Describe an advantage and a disadvantage of selecting a discrimination threshold of 0.25 instead of 0.50.
Part d (0.5 points)
Describe whether a discrimination threshold of 0.25 or 0.50 is more appropriate for a line of business with low frequency and high severity.
Answer this question and see the worked solution