IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Elementary principles of machine learning
In principal components analysis (PCA) of a standardised data set with 5 variables, the eigenvalues of the correlation matrix are 2.5, 1.3, 0.7, 0.3 and 0.2. What proportion of total variance is explained by the first two principal components?
The first two components explain 76% of the variance. The eigenvalues total 5, the number of standardised variables, and the first two sum to 3.8, so the proportion is 3.8 divided by 5, which equals 0.76.
- A38%
- B50%
- C62%
- D76%Correct
- 84%
Explanation
The eigenvalues sum to 5, equal to the number of standardised variables. The first two give 2.5+1.3 = 3.8. The proportion is 3.8/5 = 0.76, or 76%. Choosing 2.5/5 = 50% counts only the first component.
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