Multivariate Linear Regression

Multivariate linear regression is an extension of simple linear regression to predict multiple dependent variables based on single predictor or independent variables. The goal of multivariate linear regression is to model the relationship between one feature (independent variables) and a response (dependent variable) by fitting a linear equation to observed data. The equation for a multivariate linear regression model can be represented as:

Y = β0+β1x1+β2x2+⋯+βnxn+ϵY=β0+β1x1+β2x2+⋯+βn**xn+ϵ

where:

• Y is the dependent variable (the variable being predicted),
• x1,x2,…,xnx1,x2,…,xn are the independent variables (predictors),
• β0β0 is the intercept,
• β1,β2,…,βnβ1,β2,…,βn are the coefficients of the independent variables, which represent the change in the dependent variable for one unit change in the predictor, holding all other predictors constant,
• ϵ is the error term, representing the difference between the observed and predicted values.

The coefficients (ββ) are determined during the model fitting process using methods such as the Least Squares method, where the goal is to minimize the sum of the squared differences between the observed and predicted values.

Multivariate linear regression is widely used in many fields such as economics, social sciences, and engineering for tasks like forecasting, trend analysis, and the examination of causal relationships between variables.

NOTE: Multivariate linear regression consider the data you have is single independent variable (feature) and multi dependent variables (target).