CAS Exam 5 Fall 2019, Question 10
Study guide: Exam 5
The following graph shows pure premium relativities produced by a generalized linear model (GLM). The variable indicates whether the risk has had a claim in the most recent prior year or not.
Prior Claim History — a combination chart with two vertical axes. The horizontal axis is "Claim in the Prior Year" with two levels, No and Yes. The left axis is "Number of Policies" (0 to 140,000) and is read by the grey bars; the right axis is "Factor" (0.9 to 1.5) and is read by seven plotted series, one for each model year 2012 through 2018.
Exposure volume behind each level (grey bars, read off the left axis):
| Claim in the Prior Year | Number of Policies (approximate) |
|---|---|
| No | ~120,000 |
| Yes | ~45,000 |
Fitted relativities (seven series, read off the right axis):
| Series | Factor at "No" | Factor at "Yes" |
|---|---|---|
| Year (2012), (2013), (2014), (2015), (2016), (2017), (2018) | all seven series sit on top of one another at approximately 1.00 | a tight band spread over roughly 1.28 to 1.38 |
Every one of the seven year-lines slopes upward from "No" to "Yes", and the seven lines are nearly parallel — the individual year values at "Yes" cannot be read off the graph more finely than the band above.
Part a (0.5 points)
Describe the type of test for which the above graph is used.
Part b (0.25 points)
Briefly state the conclusion that can be drawn from the above graph, using the test described in part a.
Part c (1 point)
Describe two other tests to consider when evaluating the inclusion of this variable in the model.
Answer this question and see the worked solution