Consider the following statements:

• The proportion of variance explained by an additional principal component never decreases as more principal components are added.
• The cumulative proportion of variance explained never decreases as more principal components are added.
• Using all possible principal components provides the best understanding of the data
• A scree plot provides a method for determining the number of principal components to use.

Determine which of the statements are correct.

• Statements I and II only
• Statements I and III only
• Statements I and IV only
• Statements II and III only
• Statements II and IV only

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

Key: E

Statement I is incorrect – The proportion of variance explained by an additional principal component decreases or stays the same as more principal components are added.

Statement II is correct – The cumulative proportion of variance explained increases or stays the same as more principal components are added.

Statement III is incorrect – We want to use the least number of principal components required to get the best understanding of the data.

Statement IV is correct – Typically, the number of principal components is chosen based on a scree plot.

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