A SAS analyst runs PROC PRINCOMP and requests the first 3 principal components. The cumulative variance explained is 45%, 62%, and 74%. Which statement about the 3rd principal component is correct?
Select an answer to reveal the explanation.
Short Explanation
Here's the deal — the 3rd component is orthogonal to the first two and adds 12% because 74% cumulative minus 62% cumulative equals 12%. You're measuring incremental variance, not total variance.
Full Explanation
Correct: the 3rd component is orthogonal to the first two and explains an additional 12% because cumulative variance rises from 62% with two components to 74% with three. The claim that it explains 74% on its own is wrong; 74% is cumulative, not individual. The claim that its eigenvalue exceeds the 2nd component's is wrong; components are ordered by decreasing variance, so the 3rd has a smaller eigenvalue. The claim that it corresponds to the largest singular value is wrong; the first component does.