Society of Actuaries (SOA) PA Practice Exam

What are Principal Components?

1. Random samples from the original dataset

2. New variables that are linear combinations of initial variables

3. Statistical measures of central tendency

4. Unrelated variables that distort analysis

The correct answer is: New variables that are linear combinations of initial variables

Principal Components are defined as new variables that are linear combinations of the initial variables in a dataset. This concept arises from Principal Component Analysis (PCA), which is a statistical technique used to reduce the dimensionality of data while preserving as much variance as possible. The principal components are created by transforming the original variables into a new set of variables that are orthogonal (uncorrelated) to each other. The first principal component captures the largest possible variance in the data, and each subsequent component captures the remaining variance under the constraint of being orthogonal to the preceding components. This transformation helps to simplify the data structure, making it easier to analyze while retaining the essential information. Understanding that principal components are linear combinations highlights the method's powerful application in various fields such as data compression, noise reduction, and exploratory data analysis. By transforming the data into a set of principal components, analysts can identify patterns and relationships that may not be apparent in the original variables, facilitating enhanced insights. The other choices do not align with the definition of Principal Components. Random samples from the original dataset refer to statistical sampling methods rather than variable transformations. Statistical measures of central tendency focus on mean, median, and mode, which do not reflect the multi-dimensional nature of PCA. Finally, unrelated