## 3 Results
### Explanation Examples: IRIS
The results of the classification process performed with the provided functional model are depicted in Figure 9.  
The classification model, although not perfect, achieves a relatively high accuracy of approximately 95%. The model exhibits a high degree of simplicity, utilizing merely two input variables and a single MIV, with the number of outliers limited to only seven. The model is interpretable and easy to understand for humans. The 95% CI for the model accuracy is (0.9200, 0.9867). Functional models can incorporate more MIVs. Now, let us introduce another MIV that estimates sepal area. The inputs are sepal.length and sepal.width  
\[SLmSW=sepal.length*sepal.width \tag{2}\]  
MIVs in the model can be derived not only from input parameters but also based on other MIVs. An example of such an MIV is the petal-sepal area ratio based on MIVs (1) and (2). \[PdS=PLmPW/SLmSW \tag{3}\]  
Utilizing the GE approach, the following rules were generated based on the MIV value defined by Equation (3):  
ifelse(PdS <= 0.2, \"setosa\", \"other\")  
ifelse((PdS <= 0.43) & (PdS >= 0.22), \"versicolor\", \"other\")  
ifelse(PdS >= 0.43, \"virginica\", \"other\")  
The rules come together to form the functional model shown in Figure 10.  
Figure 8: Functional model for iris classification with an MIV. Figure 9: Three-class classification using a functional model with \(MIV=peal.length*peal.width\). The outcomes of the classification executed using the given functional model are shown in \[PLmPW=petal.length*petal.width \tag{1}\]0  
The model shows slight improvement compared to the previous one. The number of outliers is reduced to six (accuracy improved to 96%). The 95% CI for the model accuracy is (0.9267, 0.9867). The model is more complex than its predecessor yet remains interpretable to humans. Furthermore, in order to statistically compare the functional models shown in Figure 8 (Model 1) and Figure 10 (Model 2), we performed analysis of variance (ANOVA) on 1000 bootstrap samples for both models, specifically examining their respective accuracies. The complete results of ANOVA are presented in \[PLmPW=petal.length*petal.width \tag{1}\]1 A low \(p\)-value (\(<2\times 10^{-16}\) ) indicates that there is a statistically significant difference in accuracy between the two tested models. The significant F value (96.75) suggests a strong model effect on accuracy. As ANOVA indicated significant differences between models, we performed [PERSON]'s Honestly Significant Difference (HSD) test. The adjusted \(p\)-value (effectively zero) indicates that the difference in mean accuracy between Model 1 and Model 2 is statistically significant. Model 2 has a higher mean accuracy than Model 1 by approximately 0.745%, with a 95% CI of (0.0060, 0.0089). \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Degrees of Freedom** & **Sum of Squares** & **Mean Square** & **F-Value** & \(p\)**-Value** \\ \hline Model 2 vs. Model 1 & 1 & 0.0278 & 0.027776 & 96.75 & \(<2\times 10^{-16}\) \\ Residuals & 1998 & 0.5736 & 0.000287 & & \\ \hline \end{tabular}
\end{table} 
Table 6: ANOVA results. Figure 10: Functional model for iris classification with multiple MIVs. Figure 11: Three-class classification using a functional model with multiple MIVs.