Normal probability plot validation

To verify the adequacy of the developed models of solvent-resistance in THF, chloroform, and MEK, normal probability plots were evaluated. Typical normal probability plots of residuals should be close to a straight line as shown in Fig. 19.7 because the underlying error distribution is expected to be normal.47 This means that the normality assumption is valid for the proposed model. Residuals that were intensified in the middle of straight line indicated that data were normally distributed. Also, there were no outliers in the model as indicated by absence of significant deviations from the straight line. A combination of the normal distribution of the model residuals (Fig. 19.7) and the very high values of adjusted R2 demonstrated a good quality of the model. 

Fig. 9 shows the fitted and CV-predicted production values and the corresponding residual normal probability plots of models 1-3. By cross-validation, the model 2, i.e. y = bg +b X +bj2 i 2 the best one. Finally, Fig. 10 shows the contour plot of the best model, model 2. 

Fig. 9. Cross-validation of models 1-3. Left panel Production vs. the number of experiment black circles data blue triangles fitted values red pluses cross-validated leave-one-out prediction. Right panel Normal probability plots of the cross-validated leave-one-out residuals.

As described in Section 5, the latent variable methods provide outputs of residuals for X and Y as measures of the distance from the objects to the model. These residuals can be portrayed in many ways to detect outliers or trends. Some of the most used plots are predicted versus reference values for Y and the object residuals as normal probability plot or as Q- or F-residuals with critical limits. It is important to show both the calibration and validation residuals. It must be pointed out, however, that interpretation must be done based on the background information about the objects and patterns in the various plots. Automatic removal of outliers is not encouraged. 

Principal components analysis (PCA) reduces the volume of large data sets by combining correlated variables and maximizing variances to show patterns in the data. Usually, analysis of the variance (ANOVA) is used to prove that the null hypothesis, that there is no difference between the data sets, is not valid. Test results are compared with table values at a probability (normally 95%) that they will conform to that value. Data are plotted in such ways that different populations are visibly separate and the clustering within each set illustrates the degree of repeatability. 

The assumption of global kinetic control is probably valid for only a handful of catalytic reaction processes. Nevertheless, some typical simulation results of the model of catalyst deactivation under kinetic control are presented here in order to emphasize some of the unique percolation-type aspects of the problem. The overall plugging time 0p, i.e., the time at which the catalyst becomes completely deactivated is shown is Figure 1, where it is plotted versus Z, the average coordination number of the network of pores, (in industrial applications, of course, the useful lifetime of the catalyst is significantly smaller than 0p). Note that as Z increases, (higher values of Z mean a more interconnected catalyst pore structure) 0p increases, i.e., the catalyst becomes more resistant to deactivation. The dependence of normalized catalytic activity (r/rQ) ([Pg.176]

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