Linear Hypothesis: Regression (Basics)

Regression analysis is the study of how a response variable depends on one or more predictors. Usually, dependence is assumed to be through the mean, and we think of the mean or regression function as describing how the mean of the response depends on the predictors. Although some regression problems can be usefully summarized using nonparametric regression methods that make a minimum of assumptions, adding a few plausible assumptions allows using parametric models for regression that give elegant and simple results. The important class of linear regression models is described in this aritcle. These models are frequently used in practice, and can often lead to very useful results. Topics covered include both simple and multiple regression, the basic forms of the models, interpretation of estimates and parameters, testing ideas, including comparison of groups, and diagnostic methods.