Which of the following statements about principal components is true?

The statement about principal components that is true is that the cumulative proportion of variance explained never decreases. This is fundamental to the concept of principal component analysis (PCA).

In PCA, each principal component captures a portion of the total variance in the dataset, and as more components are added, the total explained variance accumulates. The first principal component explains the most variance, the second the second most, and so forth. As you include additional components, they can only add to or maintain the total explained variance, never subtract from it. Thus, it makes intuitive sense that the cumulative proportion of variance explained would be non-decreasing throughout this process.

Conversely, the other choices present ideas inconsistent with the principles of PCA. Some principal components may not contribute significantly to the understanding of data, and while scree plots can aid in visualizing the explained variance, they do not strictly define a threshold for variance explanation. Overall, the nature of PCA guarantees that as we include more components, the total variance accounted for can only stay the same or increase, solidifying the correctness of the cumulative variance explained statement.