Multivariabele

Multivariabele is a term used in mathematics and statistics to describe situations, models, or analyses that involve more than one variable. In mathematics, a multivariable (also called multivariate) function takes several input variables and maps them to a single output or to several outputs, often written as f(x1, x2, ..., xn).

In statistics and data analysis, multivariate approaches study multiple dependent variables together, recognizing their interrelationships rather than treating each variable separately. In multivariate statistics, data are represented as vectors X = (X1, X2, ..., Xn). The joint distribution, covariance or correlation structure, and conditional relationships among components are central concepts. Common tools include the covariance matrix, principal component analysis, factor analysis, multivariate regression, MANOVA, discriminant analysis, canonical correlation analysis, and multivariate time series methods.

Applications span many fields: natural and social sciences, engineering, finance, and machine learning. They enable modeling of complex phenomena where variables influence one another, such as modeling multiple physiological measurements, financial risk factors, or image and signal data in high dimensions.

Related mathematical areas include multivariate calculus, multivariate normal distributions, and vector-valued functions. The field emphasizes interpretability of relationships, dimensionality reduction, and methods for handling high-dimensional data, correlation, and potential multicollinearity.