Free SOA Exam PA (Predictive Analytics) Data Transformations and Unsupervised Learning Techniques Practice Questions
Data transformations and unsupervised learning on SOA Exam PA cover feature engineering (log transforms, binning, factor handling), principal component analysis, and k-means and hierarchical clustering, with emphasis on interpreting R output and justifying each transformation in writing.
75 questions20 easy47 medium8 hard2026 syllabus
Sample Questions
Question 1
Easy
Which statement about principal components analysis is CORRECT?
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Correct Answer: B
Solution
B is correct. PCA is an unsupervised technique: it constructs orthogonal (uncorrelated) linear combinations of the predictors ordered so that PC1 has the greatest variance, PC2 the next greatest, and so on. It does not use a response variable, keeping all components achieves no reduction, loadings can be negative, and predictive improvement is not guaranteed.
Question 2
Medium
Which statement about the standard K-means algorithm is correct?
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Correct Answer: B
Solution
B is correct. K-means requires K to be specified up front and its iterative assignment/update steps can converge to different local optima depending on the starting centroids, which is why running multiple initializations (e.g., nstart in R) is recommended. It does not build a hierarchy, is not seed-independent, does not standardize automatically, and produces hard assignments.
Question 3
Hard
A data scientist notices that K-means struggles to recover two clearly separated but long, thin, crescent-shaped groups in a scatterplot, splitting each crescent instead. What is the best explanation?
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Correct Answer: A
Solution
A is correct. Because K-means assigns points to the nearest centroid and minimizes within-cluster squared distance, its implied cluster boundaries are convex and it tends to carve out compact, spherical, comparably sized groups. Elongated, non-convex crescents cross those boundaries, so K-means splits them. Standardization, an even-K rule, and a global-optimum guarantee are not the issue, and K-means runs fine in two dimensions.
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