Simple linear regression is a statistical method within the domain of inferential statistics that models the relationship between a single continuous dependent variable and one independent predictor using a deterministic linear function defined by an intercept ($\alpha$) and a slope coefficient ($\beta$). The core theoretical mechanism involves estimating these parameters to minimize the sum of squared residuals (errors), thereby deriving an equation where predictions are functions of standardized deviations in variables correlated through specific formulas involving standard deviations. This concept serves as the foundational theory for general linear models, establishing the mathematical framework necessary before advancing to multiple regression analyses or more complex hypothesis testing procedures regarding statistical significance and error distribution assumptions.
Simple linear regression is a statistical method within the domain of inferential statistics that models the relationship between a single continuous dependent variable and one independent predictor …