Society of Actuaries (SOA) PA Practice Exam

What is a primary outcome of applying PCA?

1. The generation of a new dataset with more variables

2. The extraction of the original dataset's features

3. The creation of a linear combination of original variables

4. The classification of data into unsupervised groups

The correct answer is: The creation of a linear combination of original variables

The primary outcome of applying Principal Component Analysis (PCA) is the creation of a linear combination of the original variables. PCA works by transforming the original correlated variables into a new set of uncorrelated variables known as principal components. These principal components are essentially linear combinations of the original variables, designed to capture the maximum variance within the data. In this process, the first principal component will account for the most variance, followed by the second principal component, which accounts for the second highest amount of variance, and so on. This transformation allows for a simplified representation of the data, often leading to dimensionality reduction, which can be particularly beneficial in making data analysis more manageable and interpretable. The other options do not accurately reflect the main outcome of PCA. For example, generating a new dataset with more variables contradicts the general purpose of PCA, which is aimed at reducing the number of dimensions. The extraction of the original dataset's features might imply isolating attributes without transformation, which PCA does not do; it combines them instead. Lastly, while unsupervised classification refers to clustering or grouping data, PCA itself is not designed for that purpose; it is primarily a method for transforming existing data.