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

A risk analyst applies principal components analysis (PCA) to a set of 10 highly correlated yield-curve variables. Which statement best describes the first principal component?

The first principal component is the unit-length linear combination of the original variables that captures the largest possible share of total variance. It is found without reference to any target variable, and every later component is uncorrelated with it.

  1. AIt is the linear combination of the original variables, with unit-length weights, that explains the largest share of total varianceCorrect
  2. BIt is the original variable that has the highest correlation with the target variable being predicted
  3. CIt is the linear combination of the variables that is correlated with all the other principal components
  4. DIt is the combination of variables that minimizes the in-sample prediction error for a chosen response

Explanation

PCA finds the unit-length weight vector that maximizes the variance of the resulting linear combination; this is the first component. Later components are uncorrelated with earlier ones, so the third option is wrong. PCA is unsupervised and does not use a target variable, so the options on prediction error and target correlation are wrong.

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