Society of Actuaries (SOA) PA Practice Exam

What is the primary purpose of conducting a PCA on certain variables?

1. To find significant predictors in a model

2. To reduce dimensionality and combine information

3. To analyze the distribution of each variable

4. To enhance model interpretability through complexity

The correct answer is: To reduce dimensionality and combine information

The primary purpose of conducting a Principal Component Analysis (PCA) is to reduce dimensionality and combine information. PCA transforms a large set of correlated variables into a smaller set of uncorrelated variables known as principal components. This is achieved by identifying directions (principal components) in the data that account for the most variance. By doing so, PCA simplifies the dataset while preserving as much variability as possible, making it easier to visualize and analyze. In practice, this reduction in dimensionality helps to alleviate issues such as multicollinearity and can improve the performance of subsequent analyses or modeling. By focusing on a fewer number of components, analysts can streamline their work and optimize the data processing steps necessary for further investigations. Additionally, this combined information may also lead to insights that would be obscured in the original higher-dimensional space. While the other options refer to aspects related to data analysis, they do not capture the essence of PCA as effectively. For instance, finding significant predictors in a model typically involves techniques like regression analysis rather than PCA, which focuses on the variance rather than direct relationships that predict outcomes. Analyzing the distribution of each variable is more aligned with descriptive statistics rather than the dimensionality reduction approach of PCA. Enhancing model interpretability can occur