Linear regression is a statistical method used to study the relationship between variables. It helps us understand how one thing changes based on another. This method is vital in learning about statistics. The researchers focus on the basic linear regression model, how the coefficients are determined, and the essential model assumptions. They also explore advanced models like the generalized linear model, hierarchical linear model, and multivariate regression model. These extensions build upon the foundation of the basic linear regression, allowing for a deeper understanding of relationships between variables.