What is the primary purpose of Principal Component Analysis (PCA)?

• A. A statistical method to test hypothesis
• B. A linear method that identifies orthogonal factors from a dataset
• C. A technique monitoring stock prices
• D. A method for calculating average returns

Answer: (B)

The primary purpose of Principal Component Analysis (PCA) is to reduce the dimensionality of a dataset while preserving as much variance as possible. This is achieved by identifying orthogonal factors, known as principal components, that capture the underlying structure of the data.

Option B correctly highlights this fundamental aspect of PCA. By converting correlated variables into a set of values of uncorrelated variables (the principal components), PCA helps to simplify complex datasets. It reduces redundancy by allowing analysts to focus on the most significant variance-driving factors within the data without losing vital information. This orthogonality ensures that the components are independent of one another, making analysis more efficient and interpretable.

In contrast, the other choices do not accurately reflect the primary purpose of PCA. The first option suggests a testing framework for hypotheses, which is not the primary function of PCA but instead relates more to inferential statistics. The third option implies that PCA is used specifically for monitoring stock prices, which is overly restrictive; PCA can be applied in various fields beyond finance. The last option refers to calculating average returns, which is a different statistical concept entirely and not related to the PCA method. Hence, the focus on orthogonal factor identification captures the essence of what PCA is fundamentally designed to achieve.