Society of Actuaries (SOA) PA Practice Exam

What does PCA substitute in a predictive model in place of original variables?

1. Randomly generated features

2. Principal components

3. Weighted averages

4. Transformed outcome variables

The correct answer is: Principal components

The correct response is rooted in the understanding of Principal Component Analysis (PCA), which is a statistical technique used to reduce the dimensionality of a dataset while preserving as much variance as possible. In the context of a predictive model, PCA substitutes the original variables with principal components. Principal components are linear combinations of the original variables that capture the directions of the highest variance in the data. By using principal components, the resulting model is often more efficient and less prone to overfitting due to the reduction in the number of variables being considered. This transformation allows for a clearer interpretation and can often reveal underlying patterns that may not be immediately apparent when using the original variables. In contrast, randomly generated features, weighted averages, or transformed outcome variables do not align with the principles of PCA. Randomly generated features do not capture any systematic information from the data, weighted averages do not transform the dimensionality, and transformed outcome variables are separate from the predictor variables that PCA focuses on. Thus, using principal components is the definitive aspect of PCA in predictive modeling.