ABSTRACT
Linear models are important statistical models in both theoretical and applied areas of statistics. Linear models include linear regression models, analysis of variance models, analysis of covariance models, and variance components models. These models have extensive applications in many fields. The chapter presents the linear models through a general mathematical definition accompanied with some real examples. For each linear model, various assumptions on the structure of random errors will be discussed based on its practical interest. The chapter not only provides the readers, who are interested in theoretical development, some practical background in the application of linear models in real world problems, but also explores the relationship among these linear models. It explains some statistical inferences such as parameter estimation, confidence interval and hypotheses testing of linear models. In practice, statistical models for many experimental designs can be expressed in terms of an analysis of variance model.
