H13-311_V3.5 · Question #146
Principal Component Analysis (PCA) is a statistical method. A set of variables that may be related to each other is transformed into a set of linearly related variables by orthogonal transformation…
The correct answer is B. False. Option B (False) is correct because the definition contains a critical error: PCA transforms a set of possibly correlated variables into a set of uncorrelated (linearly independent) variables - not "linearly related" ones. The whole point of PCA is to remove linear…
Question
Principal Component Analysis (PCA) is a statistical method. A set of variables that may be related to each other is transformed into a set of linearly related variables by orthogonal transformation The converted set of variables is called the principal component
Options
- ATrue
- BFalse
How the community answered
(27 responses)- A22% (6)
- B78% (21)
Explanation
Option B (False) is correct because the definition contains a critical error: PCA transforms a set of possibly correlated variables into a set of uncorrelated (linearly independent) variables - not "linearly related" ones. The whole point of PCA is to remove linear relationships between variables, not create or preserve them.
Option A is wrong because accepting the statement as true would mean endorsing an inverted definition that contradicts PCA's fundamental purpose.
The orthogonal transformation mentioned in the question is real - PCA does use orthogonal transformations - but that fact doesn't save the definition, since the output (principal components) must be orthogonal to each other, meaning they are uncorrelated.
Memory tip: Think of PCA as a "detangler" - it takes variables that are tangled together (correlated) and straightens them out into independent, uncorrelated components. If the output were still "linearly related," nothing would have been untangled.
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