Demonstrating the Mechanics of Principal Component Analysis via Spreadsheets

Abstract

Principal component analysis (PCA) is a popular multivariate statistical method that is used for dimensionality reduction. When teaching PCA in a marketing research or business analytics course, the mechanics of the analysis are often not communicated to the students. Students observe computer output that contains information pertaining to eigenvalues, component loadings, and rotated loadings, yet an understanding of how these numbers were obtained is lacking. This paper presents an Excel workbook that demonstrates the mechanics of PCA, which include (1) the construction of the correlation matrix from the raw data, (2) the extraction of eigenvalues and eigenvectors from the correlation matrix and the computation of the component loadings, and (3) the rotation of the component loadings to improve interpretability.