Principal Component Analysis (PCA) is a commonly employed statistical method in data analysis for reducing dimensionality. The initial step involves standardizing the data to ensure that each attribute contributes uniformly to the analysis. Subsequently, PCA calculates a covariance matrix to understand the correlations among variables, enabling the identification of directions with the highest variance within the data.

The next stage entails determining eigenvalues and eigenvectors. These eigenvalues aid in the selection of the principal components, with the first few components typically capturing the majority of the variance. Consequently, a significant portion of the original data is retained as it gets transformed into a new, lower-dimensional space. This transformation simplifies analysis and visualization while preserving much of the original data. This technique proves highly effective in reducing extensive datasets with numerous variables into more manageable forms while maintaining a substantial level of information retention.