Mehrvarianzenregression

Mehrvarianzenregression, also known as multivariate regression, is a statistical technique used to model the relationship between one dependent variable and two or more independent variables. It extends the concept of simple linear regression, which involves only one independent variable, by allowing for a more complex analysis of how multiple factors influence an outcome. The goal of multivariate regression is to find the best-fitting linear equation that describes this relationship.

In a multivariate regression model, the dependent variable is predicted as a linear combination of the independent variables, each multiplied by a corresponding coefficient. These coefficients represent the strength and direction of the relationship between each independent variable and the dependent variable, holding all other independent variables constant. For example, in predicting house prices, multivariate regression could use variables like square footage, number of bedrooms, and location to estimate the price.

The process of multivariate regression involves estimating these coefficients by minimizing the sum of the squared differences between the observed and predicted values of the dependent variable. Common methods for estimation include ordinary least squares (OLS). Key assumptions for the validity of multivariate regression results include linearity, independence of errors, homoscedasticity (constant variance of errors), and normality of errors. Violations of these assumptions can affect the reliability of the model's predictions and inferences. Multivariate regression is widely applied in fields such as economics, social sciences, engineering, and medicine to understand complex phenomena and make predictions.