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.

458 Questions
129 Easy
255 Medium
74 Hard
2026 Syllabus

Sample Questions

Question 1 Easy
In a GLM, Pearson residuals are defined as:
Solution
D is correct.

The Pearson residual for observation ii in a GLM is defined as:
rP,i=yi−μ^iV(μ^i)r_{P,i} = \frac{y_i - \hat{\mu}_i}{\sqrt{V(\hat{\mu}_i)}}
where V(μ^i)V(\hat{\mu}_i) 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
In a GLM, the systematic component specifies:
Solution
C is correct.

The systematic component of a GLM specifies the linear predictor, which is a linear combination of the predictors: η=β0+β1x1+⋯+βpxp\eta = \beta_0 + \beta_1 x_1 + \cdots + \beta_p x_p. This determines how the covariates enter the model.
Question 3 Hard
In OLS regression, which of the following conditions ensures that the coefficient estimates are unbiased?
Solution
E is correct.

For OLS estimates to be unbiased, two conditions are essential: (1) the model must be correctly specified (the true relationship is linear in the parameters included), and (2) the errors have zero conditional mean, E(ε∣X)=0E(\varepsilon|X) = 0. This ensures E(β^)=βE(\hat{\beta}) = \beta. Unbiasedness does not require normality, homoscedasticity, or uncorrelated predictors.
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Guides & Articles

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