Chapter 8Linear model and its extensions
Linear model is arguably the most popular statistical model. It combines tractable theory with flexibility – many data analyses can be reduced to a linear model. The simple linear regression model was studied earlier in Section 6.7 and we strongly recommend the reader review the material. This chapter discusses the multiple linear model, sometimes called multivariate or linear regression with multiple predictors, sometimes called independent or explanatory variables. Matrix formulation is a primary method of statistical treatment in this chapter – we recommend the reader consult the Appendix, as well as Section 3.10.
The chapter is organized in the following way: First, we formulate general properties of linear model and then illustrate its applications with real‐life examples. Next, we extend the linear model to study tabular data using the ANOVA model, and finally discuss the generalized linear model when the dependent variable is binary (logistic regression) or count (Poisson regression).
8.1 Basic definitions and linear least squares
Multiple linear model (regression) relates the dependent variable, 
to several independent variables (or predictors) 
in a linear fashion as
where codes the th observation. The matter of concern ...
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