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FRM Part I · FRM Exam Part I · Machine Learning and Prediction

An analyst applies principal components analysis (PCA) to a set of highly correlated predictors before fitting a prediction model. Which statement best describes the first principal component?

The first principal component is the linear combination of the original variables, with unit-length weights, that has the largest possible variance. PCA is unsupervised and ignores the target, so it does not select an original variable or target-related combination.

  1. AIt is the linear combination of the original variables, with unit-length weights, that has the largest varianceCorrect
  2. BIt is the original variable that has the highest correlation with the target
  3. CIt is the linear combination of the variables that is uncorrelated with the target
  4. DIt is the variable with the smallest variance after standardization

Explanation

PCA finds weights (a unit-length vector) that maximize the variance of the resulting linear combination; this is the first component. It does not use the target, so options about correlation with the target are wrong. Component selection is based on variance explained, not on picking one original variable.

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