Multivariate linear regression is a statistical method used to model and analyze the relationship between multiple independent variables and a dependent variable. It is an extension of simple linear regression, which only considers one independent variable.
Multivariate linear regression is typically used when there are multiple independent variables that may influence a dependent variable. It is commonly used in fields such as economics, social sciences, and business to study the relationship between several factors and a specific outcome.
The main difference between multivariate linear regression and simple linear regression is the number of independent variables. Simple linear regression only considers one independent variable, while multivariate linear regression considers two or more. This allows for a more complex and nuanced analysis of the relationship between variables.
The assumptions of multivariate linear regression include linearity, independence of errors, normality of errors, homoscedasticity (equal variance) of errors, and absence of multicollinearity (high correlation) among the independent variables.
The accuracy of a multivariate linear regression model is typically evaluated by examining the coefficient of determination (R-squared), which indicates the proportion of the variation in the dependent variable that is explained by the independent variables. Other metrics, such as the root mean square error (RMSE) and adjusted R-squared, may also be used to assess the model's performance.