Diagnostic tests of the fitted model. Residual plots

Diagnostic test of the fitted model. Residual plots 

That a fitted model has been shown to be significant according by means of an analysis of variance is not sufficient. Sometimes a rather sloppy attitude in this respect can be found in published works. To be trustworthy, a model must withstand all diagnostic tests which could jeopardize the model. It is important that the experimenter should not fool himself/herself and draw conclusions which are not 

Another diagnostic test which always should be made is to plot the residuals in each experimental point against the predicted response from the corresponding experiment. An adequate model should give a plot in which the points show a random scatter such that the upper and lower bonds of the pattern in the plot form two parallel horizontal lines at approximately equal distances from the zero line. The corresponding plot of the residuals in the Willgerodt-Kindler study is shown in Fig. 6.12. The plot is satisfactory. 

However, plots of residuals can show different anomalous features, which indicate that the model is poor  

If the upper and lower bonds diverge and the pattern of the residuals in the plot is funnel-like, (Fig. 6.11a), it is an indication that the error is different in different parts of the experimental domain. In such cases, the assumption of a constant error variance is violated. To overcome this difficulty and to obtain a fairly constant error distribution, the metric of the response variable should be changed through some transformation, and the modell refitted to the transformed response. How this can be done is discussed in Chapter 12. 

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