Which statements regarding principal components are correct?

The cumulative proportion of variance explained always increases because principal component analysis (PCA) is designed to account for as much variance as possible with the components derived from the data. When the first principal component is added, it captures the maximum variance available in the data, and each subsequent component captures the maximum variance remaining orthogonal to the previous components. As a result, adding more components can only maintain or increase the cumulative proportion of variance explained. Thus, the cumulative sum of the explained variance from all components will naturally reflect an increasing trend as each component is added.

This understanding is fundamental in PCA, where the goal is to find the directions (or "principal components") that maximize the variance in the data. As you progress in this analysis by including additional components, the total explained variance continues to grow, reinforcing the validity of the cumulative proportion of variance being non-decreasing.