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IAI Actuarial Core Principles · Actuarial Statistics · Exploratory data analysis

Three variables are standardised before PCA, so PCA is applied to their correlation matrix. The first two eigenvalues are 1.8 and 0.9. Which statement is correct?

The third eigenvalue is 0.3 and the first component explains 60%. Eigenvalues of a 3x3 correlation matrix sum to 3, so 3-1.8-0.9=0.3, and 1.8/3=0.6.

  1. AThe third eigenvalue is 0.3 and the first component explains 50% of variance
  2. BThe third eigenvalue is 0.3 and the first component explains 60% of varianceCorrect
  3. CThe third eigenvalue is 0.9 and the first component explains 60% of variance
  4. DThe third eigenvalue is 0.3 and the first two components explain 60% of variance
  5. The third eigenvalue cannot be determined

Explanation

For a correlation matrix of 3 variables the eigenvalues sum to 3. So the third is 3-1.8-0.9=0.3. The first explains 1.8/3=60%. The first two explain 90%, not 60%.

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