Multivariánsak

Multivariánsak (plural) refer to objects or analyses that involve more than one variable. In statistics, multivariáns analízis studies the relationships among several variables simultaneously, rather than examining each variable in isolation. Data are represented as vectors of measurements for each observation, and the aim is to understand their joint structure and interdependencies.

A central concept in multivariánsok is the covariance or correlation matrix, which summarizes how pairs of variables vary together. Many methods rely on the eigenstructure of such matrices to reduce dimensionality or to uncover latent relationships. Dimensionality reduction and data visualization are common goals, allowing complex multivariate data to be interpreted more easily.

Common multivariate techniques include Principal Component Analysis (PCA) for reducing dimensionality while preserving variance, Factor Analysis for uncovering latent constructs, Canonical Correlation Analysis for relationships between variable sets, MANOVA for testing mean differences across groups on several dependent variables, Multivariate Regression for predicting multiple outcomes, Discriminant Analysis for grouping observations, and Cluster Analysis for identifying natural data clusters. These methods can be descriptive, inferential, or predictive, and they often complement univariate approaches.

Applications span psychology, biology, economics, environmental science and finance, where multiple measurements interact and inform decisions. Typical considerations include adequate sample size relative to the number of variables, assumptions about linear relationships and, for some methods, multivariate normality, as well as concerns about interpretability and the risk of overfitting in high-dimensional settings.