Consider the following statements:

• Principal Component Analysis (PCA) provide low-dimensional linear surfaces that are closest to the observations.
• The first principal component is the line in p-dimensional space that is closest to the observations.
• PCA finds a low dimension representation of a dataset that contains as much variation as possible.
• PCA serves as a tool for data visualization.

Determine which of the statements are correct.

• Statements I, II, and III only
  
• Statements I, II, and IV only
  
• Statements I, III, and IV only
  
• Statements II, III, and IV only
  
• Statements I, II, III, and IV are all correct

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Key: E

Statement I is correct – Principal components provide low-dimensional linear surfaces that are closest to the observations.

Statement II is correct – The first principal component is the line in p-dimensional space that is closest to the observations.

Statement III is correct – PCA finds a low dimension representation of a dataset that contains as much variation as possible.

Statement IV is correct – PCA serves as a tool for data visualization.

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.