ABSTRACT
In the empirical analysis of the relationships among variables, statistical methods play a central role. The null hypothesis introduces a number of linear constraints on the components of the parameters; therefore, it is said to be a linear hypothesis. Scatter plots of the transformed variables, showing a form of dependence closer to linearity and constant variability than for the original variables. Model extension, operates within parametric statistics, by enlarging a linear model so as to include some form of nonlinearity. Graphical diagnostics, is based on graphical methods which allow us to explore data only in a qualitative, albeit very useful, way. Nonparametric regression, takes an entirely new route. Decomposition is meaningful if the experimental units are essentially homogeneous and are given the treatment under the same conditions. In such a case, the observed differences among the treatment groups can safely be interpreted as being caused by the treatments themselves.
