ABSTRACT
A linear model contains two parts, the fixed, or systematic part and the residual error. The formulation of the systematic part is discussed using quantitative and categorical predictors. Using theoretical knowledge of the underlying process is emphasized in the model formulation. In addition, it is pointed out that any curvilinear relationship between x and y-variables can be modeled by wise selection of the predictors. The starting assumptions about uncorrelated errors with constant variance are often insufficient, therefore modeling of inconstant error variance and correlation, due to temporal, spatial or grouped data structure, is discussed and demonstrated from the very beginning. Estimators of the of model parameters using ordinary and generalized least squares, and (restricted) maximum likelihood are defined and their properties are discussed. The graphical evaluation of the model fit and hypothesis testing are discussed and demonstrated with several examples. Prediction using a fitted model is discussed in two cases: when correlated data are not available and when correlated data are available. The latter case is demonstrated in the context of spatial data, which leads to methods known as kriging in the field of geostatistics. A total of 22 examples based on three different real-life data sets are included.
