Society of Actuaries (SOA) PA Practice Exam

Why is scaling the variance to 1 important in PCA?

1. It ensures that all variables have equal influence

2. It prevents smaller variance variables from dominating associations

3. It allows for better visualization of PCA results

4. It simplifies the computation of correlations

The correct answer is: It prevents smaller variance variables from dominating associations

Scaling the variance to 1 in Principal Component Analysis (PCA) is crucial because it ensures that each variable contributes equally to the analysis. When the variables are on different scales, those with larger variances can disproportionately influence the results, leading to a distorted understanding of the underlying data structure. By standardizing the data—transforming each variable to have a mean of 0 and a variance of 1—PCA can then treat all variables uniformly, allowing for more balanced contributions. While preventing smaller variance variables from dominating associations is a key consideration, it’s also essential to recognize that scaling allows PCA to capture the true relationships within the data without being swayed by the scale of the variables. Other options may touch on related benefits of PCA, such as better visualization or computational convenience, but the principal importance of scaling revolves around ensuring that all variables have equal influence, preventing any one variable from overshadowing the others based on its variance.