FRM Part I · FRM Exam Part I · Machine Learning and Prediction
A PCA on six standardized predictors yields eigenvalues of 3.0, 1.5, 0.6, 0.45, 0.3 and 0.15. What is the smallest number of components needed to explain at least 85% of total variance?
Three components are needed. Total variance is 6.0, and the cumulative eigenvalues are 3.0, 4.5 and 5.1, giving 50%, 75% and 85% of variance. Two components explain only 75%, so the threshold of at least 85% is first met with three.
- A2
- B3
- C4Correct
- D5
Explanation
The eigenvalues sum to 6.0, equal to the number of standardized variables. Cumulative shares: 3.0/6 = 50%; 4.5/6 = 75%; 5.1/6 = 85%; so three components reach exactly 85%. Two components give only 75%, which is insufficient.
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