ows its true colors as a textbook. So this is where the review jumps into more mathematically English as well.
Many types of statistical analysis are based on linear models of single variables. This class of analyses includes :
simple and multiple linear regression
mixed model analysis of variance
In matrix terminology, the general linear model can be written as y = Xb + e where :
X is a matrix of known coefficients,
b is a vector of unknown populations parameters, and
e is a vector of random residuals.
For regression analysis, b is a collection of unknown partial regression coefficients and X is a matrix of (known) values of predictor variables. For analysis of variance, b is a collection of unknown treatment effects and X is a matrix of known classification (or indicator) variables. For analysis of covariance, b includes both treatment effects and regression coefficients, and X includes both predictor variables and indicator variables. In all three cases, e is a list of random residuals assumed to have means of zero. Varying assumptions are made about the variance-covariance structure of the residual effects. Depending upon the latter assumptions, the unknown population parameters may be estimated by:
ordinary least squares (OLSE)
weighted least squares (WLSE)
generalized least squares (GLS)
Mixed model analysis is a more recent development that applies particularly to research involving factors whose levels can be controlled by the researcher (fixed) as well as factors whose levels are beyond the researcher's control (random).
Since many, if not most, analyses of experimental data involve some mixed model aspect, there is an apparent need for teaching consistent analysis procedures directed toward appropriate model selection and interpretation based on the physical situation. The needed approach to linear models should be general enough ...