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

Compared with a regression using all original predictors, a principal components regression (PCR) that uses the first few components has which main drawback?

The key drawback is that components are chosen by the variance they explain in the predictors, without regard to the target, so the retained components may not be the most predictive. Components are uncorrelated, not collinear, and PCR typically reduces variance.

  1. AThe leading components are chosen without reference to the target, so they may not be the most predictiveCorrect
  2. BThe components are perfectly collinear with each other
  3. CIt always has higher variance than the full regression
  4. DIt requires the number of components to exceed the number of variables

Explanation

PCA is unsupervised: components are ranked by variance explained in the predictors, not by relevance to the target. A low-variance component can still be highly predictive and be discarded. Components are orthogonal, not collinear, and the number of components cannot exceed the number of variables.

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