What is a true statement about principal components analysis (PCA)?

Principal components analysis (PCA) is a technique primarily used for reducing the dimensionality of a dataset while retaining as much variance as possible. This means that PCA aims to transform a large set of correlated variables into a smaller set of uncorrelated variables, known as principal components, that capture the most variability in the data. The focus on maximizing variance makes it a powerful tool for exploratory data analysis, feature reduction, and improving the interpretability of data.

By concentrating on the directions (principal components) that account for the most variability, PCA helps simplify datasets, making it easier to identify patterns, visualize data, and potentially improve the performance of other statistical modeling techniques. This property is fundamental to how PCA operates and underscores its utility in data analysis and dimension reduction tasks.

The other statements do not accurately reflect the characteristics or purposes of PCA. For instance, PCA is unsupervised rather than supervised, meaning it does not rely on labeled output data for its analysis. It also does not retain all original variables, as it selects a subset through the transformation to principal components. Furthermore, PCA does not produce regression coefficients; it focuses on variance and data structure rather than making predictions like regression analysis would.