Which statement about loadings in principal component analysis is true?

In principal component analysis (PCA), loadings represent the correlation coefficients between the original variables and the principal components. The statement that "the loadings are unique" is true because, given a specific dataset, the method of PCA generates a unique set of loadings for each principal component, as long as the dataset remains the same. This means that the relationships expressed in the loadings—how much each original variable contributes to each principal component—are determined directly by the underlying correlations among the variables in the data.

The other statements do not accurately reflect the properties of loadings. For instance, loadings do not inherently explain a fixed percentage of variance, such as 50%. Instead, the proportion of variance explained by each principal component is calculated from the eigenvalues derived during the PCA process, and these proportions can vary widely.

Furthermore, the sum of loadings does not equal the number of variables; loadings are not additive in this way. The sum of the squared loadings for each principal component can be understood in terms of variance explained, but they do not necessarily sum to the number of original variables.

Lastly, loadings can exhibit correlation, which indicates that they are not independent of one another. The relationships among variables influence the load