CAS Data Analysis and Interpretation 2

Question 1

When fitting a generalized linear model (GLM) to insurance loss data, which link function is most commonly used for modeling claim frequency?

Accepted Answer

Log link

Answer

The log link is standard for Poisson-distributed claim frequency models because it ensures predicted frequencies remain positive.

Question 2

A claims analyst observes that residuals from a regression model exhibit a funnel shape when plotted against fitted values. This pattern most likely indicates:

Accepted Answer

Heteroscedasticity in the error terms

Answer

A funnel-shaped residual plot is the classic diagnostic for heteroscedasticity, where error variance is not constant across fitted values.

Question 3

In credibility theory, the Bühlmann credibility factor Z is defined as n/(n+k). As the number of observations n increases toward infinity, Z approaches:

Accepted Answer

1

Answer

As n → ∞, the credibility factor Z = n/(n+k) approaches 1, meaning full weight is given to observed experience.

Question 4

Which of the following best describes the use of a Q-Q plot in actuarial data analysis?

Accepted Answer

Assessing whether data follow a specified theoretical distribution

Answer

A Q-Q plot compares empirical quantiles of data against theoretical quantiles of a reference distribution to assess distributional fit.

Question 5

An insurer uses principal component analysis (PCA) on 20 rating variables. The first three principal components explain 85% of total variance. The primary benefit of using these three components instead of all 20 is:

Accepted Answer

Reducing dimensionality while retaining most variance

Answer

PCA's main benefit is dimensionality reduction — capturing most variance with far fewer uncorrelated components, which simplifies modeling.

(CAS) Casualty Actuarial Society Practice Test

(CAS) Casualty Actuarial Society Practice Test

CAS Data Analysis and Interpretation 2