# Mathematical Modeling of the Manufacturing Sector's Dominant Part as a Base for Automation
## 3 Results
This allows a stimulating and instantaneous illustrative comparison as well as tracking the differences. For higher coherence, we demonstrate in Table 1 where the review of tested models and their results is initiated. Altogether, we tested seven mathematical models. The degree 6 and 7 polynomial models have the best results. These two variants are further considered. In Table 1, they are marked in dark. Even though the degree 8 and 9 polynomials get the better R-square results, this is because of the so-called higher degree polynomials problem. In general, distortion of the results is obtained by calculation over the R-square method, because when you increase the degree of a polynomial, the R-square increases, but the fit does not necessarily correspond to this R-square increase. The calculation of parameters is a step which is actually an integrated part of our modeling. The exact values are already given for the individual model types. As part of this step, the documentation [42] on behalf of our used tool can be reminded. The coefficients are calculated with 95% confidence of bounds. This implies that our model attempts to fit as close as possible to 95% of the determined data set. The remaining 5% may be redundant and the computation tool should ignore them if they are out of the function range. This set level is enough for our modeling to keep all relevant data, to get the sufficient scope to our model, and to receive the relevant fit together with the prediction. Describing our results, we move on to the next step--prediction. Execution of the prediction is the final step according to our designed methodology and constitutes the completion of the previous ones. As we stated above, the degree 6 polynomial model and the degree 7 polynomial model report the best outcomes. That is the reason why we test both of them within the prediction. Table 2 gives the prediction of bounds for the degree 6 polynomial as well as the degree 7 polynomial models. Regarding the difference between the degree 6 and 7 polynomials, the degree 7 polynomial has a better R-square value but a worse RMSE value. This is because the degree 7 polynomial fits our actual data better; nevertheless, the degree 6 polynomial is more suitable for predicting these data. The degree 7 polynomial sways what is further reflected in the degree 8 polynomial and the degree 9 polynomial, too. Therefore, these models are not suitable for prediction realization (see Table 1). Due to the mentioned swaying, the degree 7 polynomial is already basically a sinusoid. Such a state is improper for predicting our kind of data--it is impossible to go into negative numbers. At this spot, we track figures pertaining to the rows discussing predicted value with the most relevance (see Table 2). They represent the substantive values for our results. In Table 2, they are highlighted in dark. Thus, the prediction unsuitability of the degree 7 polynomial, despite a better R-square, can be clearly seen from Figure 6:1 \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model Type.** & **SSE** & **R-Square** & **Adjusted R-Square** & **RMSE** \\ \hline Linear fitting & 2.196 \(\times\) 10\({}^{12}\) & 0.8978 & 0.8808 & 4.277 \(\times\) 10\({}^{5}\) \\ Degree 4 polynomial & 2.855 \(\times\) 10\({}^{12}\) & 0.8671 & 0.8139 & 5.343 \(\times\) 10\({}^{5}\) \\ Degree 5 polynomial & 1.902 \(\times\) 10\({}^{12}\) & 0.9115 & 0.8623 & 4.597 \(\times\) 10\({}^{5}\) \\ Degree 6 polynomial & 1.637 \(\times\) 10\({}^{12}\) & 0.9238 & 0.8667 & 4.523 \(\times\) 10\({}^{5}\) \\ Degree 7 polynomial & 1.092 \(\times\) 10\({}^{12}\) & 0.9492 & 0.8984 & 3.949 \(\times\) 10\({}^{5}\) \\ Degree 8 polynomial & 7.503 \(\times\) 10\({}^{11}\) & 0.9651 & 0.9185 & 3.536 \(\times\) 10\({}^{5}\) \\ Degree 9 polynomial & 7.413 \(\times\) 10\({}^{11}\) & 0.9655 & 0.9034 & 3.85 \(\times\) 10\({}^{5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The overview of tested models with corresponding results. All analysis, modeling, and testing point to the degree 6 polynomial as our final model type.