ABSTRACT
The linear model is exceptionally well documented throughout the statistical literature. The theory is elegant, and applications in science, engineering, medicine, education, social science, commerce and industry abound. Accounts are included in introductory texts such as that of Kutner et al. (2004), the book devoted to regression by Draper and Smith (1998) and matrix algebra-based texts such as the classic books by Scheffé (1959), Searle (1971), Graybill (1976) and Rao (2001) and the more recent books by Ravishanker and Dey (2002) and Khuri (2010). The theory of the linear model falls naturally into two parts, that for the linear model of full rank and that for the linear model not of full rank. While certain concepts relating to these two forms of the linearmodel intersect, themodels neverthelessmerit
of Design and Analysis of
separate attention. The aim in this chapter, therefore, is to give concise accounts of each separately, emphasizing those aspects which have an impact on design and introducing some key concepts relating to the construction of optimal designs.
