Multivariate statistical analysis comprises a family of quantitative methods for simultaneously modeling and interpreting relationships among multiple dependent and/or independent variables. It includes techniques such as multivariate regression, principal component analysis, factor analysis, canonical correlation, discriminant analysis, and multivariate analysis of variance (MANOVA). These methods account for covariance structures, control familywise error across correlated outcomes, and enable dimensionality reduction, classification, clustering, and latent structure discovery. Assumptions typically involve multivariate normality, linearity, homoscedasticity, and independence of observations, with inference based on matrix algebra, eigen-decomposition, and likelihood-based or resampling-based estimation and hypothesis testing.
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