Society of Actuaries (SOA) PA Practice Exam

Which principal component is most important for explaining variation in data?

1. The last principal component

2. The first principal component

3. The average principal component

4. The median principal component

The correct answer is: The first principal component

The first principal component is the most important for explaining variation in data because it captures the highest variance available in the dataset. In principal component analysis (PCA), principal components are derived from the eigenvalues and eigenvectors of the covariance matrix of the data. The first principal component corresponds to the largest eigenvalue, meaning it accounts for the direction of maximum variance. This component is crucial because it provides the most significant information about the underlying structure in the data, allowing for effective dimensionality reduction and analysis. Subsequent principal components account for progressively smaller amounts of variance, which is why they are less significant in explaining the overall structure of the data. The average and median principal components are not standard terms used in PCA; thus, they do not have established meanings in this context. Their usage in this scenario may lead to confusion as they do not directly quantify the variance captured by the principal components.