FRM Part I · FRM Exam Part I · Machine Learning and Prediction
A PCA on six standardized variables yields eigenvalues of 3.0, 1.5, 0.6, 0.45, 0.30 and 0.15. What is the minimum number of components needed to explain at least 85% of total variance?
Three components are needed. Total variance is 6.0, the sum of the eigenvalues. The first two components explain 4.5/6 = 75%, while adding the third gives 5.1/6 = 85%, which meets the threshold exactly.
- A2
- B3
- C4Correct
- D5
Explanation
For standardized variables, total variance equals the sum of eigenvalues, 6.0. Cumulative shares are: 3.0/6 = 50%, 4.5/6 = 75%, 5.1/6 = 85%. Three components reach exactly 85%, so the answer is 3. Choosing 2 reaches only 75%.
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