In PCA, which matrix contains the relationships between original variables and extracted components?

In PCA, which matrix contains the relationships between original variables and extracted components?

• A. Covariance matrix
• B. Correlation matrix
• C. Component matrix
• D. Factor loading matrix

Answer: (C)

In PCA, each component is formed as a linear combination of the original standardized variables, so the numbers that tell you how much each variable contributes to each component are the coefficients that form that matrix. The component matrix collects these coefficients, showing the relationships between the original variables and the extracted components. In other words, it tells you how strongly each variable is associated with each component. The covariance or correlation matrices describe relationships among the original variables themselves, not with the components, and the term “factor loading matrix” is more typical of factor analysis, whereas in PCA the analogous construct is the component (loading) matrix.

In PCA, each component is formed as a linear combination of the original standardized variables, so the numbers that tell you how much each variable contributes to each component are the coefficients that form that matrix. The component matrix collects these coefficients, showing the relationships between the original variables and the extracted components. In other words, it tells you how strongly each variable is associated with each component. The covariance or correlation matrices describe relationships among the original variables themselves, not with the components, and the term “factor loading matrix” is more typical of factor analysis, whereas in PCA the analogous construct is the component (loading) matrix.