Mathematics · Principal Component Analysis
Let a 3-dimensional random vector have a positive definite dispersion matrix given by all diagonal entries equal to 1 and all off-diagonal entries equal to ρ. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1ρ may be equal to 0.47.✓
- 2The first principal component can explain at most 32% of the total variation for some valid ρ.
- 3The second principal component can explain more than 50% of the total variation for any valid ρ.
- 4The variance of the first principal component is 1 + ρ for any valid ρ.
Correct answer
ρ may be equal to 0.47.
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