## 3 Results and Discussion
### Variance Analysis of RMSEs  
A prerequisite of any data analysis is to survey the data. No data preprocessing was carried out in ref. [2]. Calculation of means, median, skewness, and kurtosis could help to judge the residua normal behavior. A simple matrix plot suggests serious outliers in the data (Figure 7):  
At least two outliers can be observed: \(1.534\times 10^{7}\) (Germany, compound model and genetic algorithm) and \(5.208\times 10^{7}\) (Italy, exponential model, and particle swarm optimization). After filtering the two outliers, a formal variance analysis (factorial ANOVA) can be completed for the RMSE data of Tables 3-10 of ref. [2]. Three factors can be decomposed: F1, countries (five levels: Italy (I), China (C), Iran (P), USA (U), Germany (G)); F2, models (eight levels; see abbreviations in the notations for Table 1); and F3, techniques of global optimum search algorithms (three levels: GA, PSO, and GWO, resolved in the notations of Table 1). One factor should be hidden as no repeated measurements are possible. The best candidate is F1 (countries) because the assumption is reasonable that the pandemic has similar trajectories in all five countries.  
Neither F2 nor F3 (nor their coupling F2*F3) is significant, but the intercept only. The interaction of F2 and F3 can be seen in Figure 8.  
Figure 8: Decomposition of models (in Figure 3) and global optimization methods. For abbreviations in \(x\) axis see the notations of Table 1.  
Figure 7: Matrix plot for global minimum search algorithms (RMSE values from data of Tables 3–10 in ref. [2]). Histograms are seen in the plots of the diagonal (\(y\) axes show the frequencies, whereas \(x\) axes the RMSE values), RMSE values can be found on the \(y\) and \(x\) axes alike for the off-diagonal plots. Blue circles stand for the points of RMSE values. GA, PSO, and GWO are abbreviations for optimization algorithms. The linear regression lines (red) are based on one (or two) outlier(s). The presence of outliers is obvious.  
The nonlinear models exhibit four more outliers at least. The _post hoc_ tests ([PERSON], [PERSON], and [PERSON]'s honest significant difference) show no significant differences between models and optimization algorithms either, because of the heavy outliers present. This calls for careful data preprocessing.  
However, it is interesting to know whether useful information can be obtained with wrong inputs or from inappropriate starting data. The quote \"garbage in, garbage out\" is commonplace in modeling: if the input data used to build a model is biased (blemish), the predictions are likely to be unreliable and deceptive. On the other hand, the history of science is full of brilliant discoveries from mistaken standpoints ([PERSON] miscalculated the distance, [PERSON]'s atomic model has unrealistic postulates, Transition State Theory (TST) assumes that reactions occur at equilibrium, but frequency of collisions is set to one, [PERSON]'s laws of inheritance were formulated whereas he neglected observations not to cover expectations deliberately, [PERSON]'s theory of special relativity assumes the luminiferous ether, an invisible substance, _etc._). Let us see whether wrong standpoints can lead to straightforward results.