Which of the following is true about the principal components explaining variance?

The statement that the first four principal components together explain 100% of the variance is grounded in the principles of principal component analysis (PCA). In PCA, components are derived from the original variables, and they are ordered by the amount of variance they capture from the dataset. The first component captures the largest portion of variance, followed by the second component, and so on.

In most cases, the sum of the variances explained by all principal components equates to the total variance present in the data. Therefore, it is possible that the first four components, particularly in datasets with distinct structures, encapsulate a substantial portion of the total variance, possibly leading to a situation where they explain 100% of the variance, especially if the data has been transformed or reduced fundamentally.

This makes the assertion that the first four principal components together account for all the variance a correct interpretation of PCA results if no information is lost during the computation or if the dataset was organized such that it allows this.

As a general context, each principal component is designed to capture a different orthogonal direction in the data, and collectively they can account for different proportions of the total variance, but it is not typically true that they all explain the same amount (as stated in the first