Discussion
What is the percentage of variance first unrotated PCA shall explain ?
Answer: D
The first unrotated component explains 40% of the variance.
In PCA of a correlation matrix each standardized variable contributes a variance of 1, so the total variance equals the number of variables, 8, which is also the sum of all the eigenvalues. A component's share is its eigenvalue divided by that total:
\[ \begin{aligned} \text{total} &= 3.2 + 2.4 + 0.54 + 0.42 \\ &\quad + 0.41 + 0.39 + 0.37 + 0.27 = 8 \\ \text{share} &= \frac{3.2}{8} = 0.40 = 40\% \end{aligned} \]
12.5% is one variable's share, 1/8, and 32% comes from treating the eigenvalue 3.2 as a share of 10 instead of 8. 10% has no basis in these figures.
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