Multivariate regression is a statistical technique used to explore the relationship between multiple independent variables and a single dependent variable. It is an extension of simple linear regression, which involves only one independent variable.
In multivariate regression, the goal is to identify how each independent variable contributes to the variation in the dependent variable, while controlling for the effects of other independent variables. The technique is commonly used in many fields such as economics, social sciences, and engineering, among others.
The equation for multivariate regression is:
Y = β0 + β1X1 + β2X2 + … + βnXn + ε
where Y is the dependent variable, X1, X2, …, Xn are the independent variables, β0 is the intercept, β1, β2, …, βn are the regression coefficients that represent the impact of each independent variable, and ε is the error term.
Multivariate regression can help to identify which independent variables have a significant impact on the dependent variable and how they are related to each other. It can also be used to predict the value of the dependent variable based on the values of the independent variables.