Free SOA Exam SRM (Statistics for Risk Modeling) Linear Models Practice Questions
Linear models are the largest topic on SOA Exam SRM (SOA). Questions cover simple and multiple regression, generalized linear models (GLMs), regularization methods (ridge, LASSO, elastic net), and model diagnostics.
Sample Questions
Question 1
Easy
In a GLM, Pearson residuals are defined as:
Solution
D is correct.
The Pearson residual for observation in a GLM is defined as:
where is the variance function of the assumed distribution evaluated at the fitted mean. This standardizes the raw residual by the expected standard deviation under the model.
The Pearson residual for observation in a GLM is defined as:
where is the variance function of the assumed distribution evaluated at the fitted mean. This standardizes the raw residual by the expected standard deviation under the model.
Question 2
Medium
Which of the following statements about lasso regression is FALSE?
Solution
B is correct.
Lasso does not always select the correct set of important variables. Its variable selection performance depends on conditions such as the irrepresentable condition, signal strength, and correlation among predictors. With highly correlated predictors, lasso may arbitrarily select one from a group of correlated variables.
Lasso does not always select the correct set of important variables. Its variable selection performance depends on conditions such as the irrepresentable condition, signal strength, and correlation among predictors. With highly correlated predictors, lasso may arbitrarily select one from a group of correlated variables.
Question 3
Hard
Gamma GLM: fitted mu=8500, SE(eta)=0.15, shape alpha=5. 95% CI for mean and 95% PI for single claim.
Solution
C is correct.
Ln(8500) +/- 1.96*0.15 => exp => (6370, 11340). PI: Gamma(5,1700) quantiles => (3200, 22560).
Ln(8500) +/- 1.96*0.15 => exp => (6370, 11340). PI: Gamma(5,1700) quantiles => (3200, 22560).