Linear regression analysis

Linear regression is one of the most broadly applied statistical techniques to investigate the linear relationship between one single dependent variable and one or more than one independent variable. It is also considered the foundation of statistical learning theory. In this entry, we illustrate the standard linear regression model, review regression coefficient estimation approaches, and discuss major assumptions underlying the linear regression model. In addition, we present three extensions of the linear regression model, including the generalized linear model (GLM), the hierarchical linear model (HLM), and multivariate regression model.