## 2 Methods
### Mathematical Model
& 1 & \(-\)1 & \(-\)1 & \(-\)1 & 55 & 55 & 50 & 50 & 50 & 55 & 60 & 55 & 50 & 50 \\ \hline
9. & \(-\)1 & 1 & 1 & 1 & 85 & 80 & 85 & 80 & 80 & 85 & 80 & 85 & 80 \\ \hline
10. & \(-\)1 & 1 & 1 & \(-\)1 & 75 & 70 & 80 & 75 & 75 & 80 & 85 & 80 & 80 & 70 \\ \hline
11. & \(-\)1 & 1 & \(-\)1 & 1 & 70 & 65 & 70 & 60 & 65 & 70 & 70 & 65 & 60 & 65 \\ \hline
12. & \(-\)1 & 1 & \(-\)1 & \(-\)1 & 45 & 50 & 45 & 50 & 55 & 50 & 45 & 45 & 50 & 50 \\ \hline
13. & \(-\)1 & \(-\)1 & 1 & 1 & 50 & 60 & 65 & 60 & 55 & 60 & 65 & 55 & 55 & 65 \\ \hline
14. & \(-\)1 & \(-\)1 &The following models were obtained:  
Y. Linear model. General view of the formula for evaluating the coefficients of the regression model:  
\[\text{Y}=\text{z}^{*}\text{a}+\text{e}, \tag{9}\]  
where a is the matrix of expert assessments,  
y is the vector of errors. Y is the size vector of expert assessments obtained using the robust method. Regression statistics using a linear model are presented in Table 7.  
The following models were obtained:  
Y. Linear model. General view of the formula for evaluating the coefficients of the regression model:  
\[\text{Y}=\text{z}^{*}\text{a}+\text{e}, \tag{10}\]  
where a is the matrix of expert assessments,  
y is the vector of errors. Y is the size vector of expert assessments obtained using the robust method. Regression statistics using a linear model are presented in Table 7. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**No. of** & \(\text{Z}_{1}\) & \(\text{Z}_{2}\) & \(\text{Z}_{3}\) & \(\text{Z}_{4}\) & \(\text{Y}\) \\ \hline
6. & 1 & –1 & 1 & –1 & 54.37 \\ \hline
7. & 1 & –1 & –1 & 1 & 70.62 \\ \hline
8. & 1 & –1 & –1 & –1 & 52.5 \\ \hline
9. & –1 & 1 & 1 & 1 & 81.88 \\ \hline
10. & –1 & 1 & 1 & –1 & 76.88 \\ \hline
11. & –1 & 1 & –1 & 1 & 66.25 \\ \hline
12. & –1 & 1 & –1 & –1 & 48.12 \\ \hline
13. & –1 & –1 & 1 & 1 & 59.37 \\ \hline
14. & –1 & –1 & 1 & \(-1\) & 46.87 \\ \hline
15 & –1 & –1 & –1 & 1 & 45 \\ \hline
16 & –1 & –1 & –1 & \(-1\) & 27.5 \\ \hline
17. & 1 & 0 & 0 & 0 & 53.75 \\ \hline
18. & –1 & 0 & 0 & 0 & 45.62 \\ \hline
19. & 0 & 1 & 0 & 0 & 67.5 \\ \hline
20. & 0 & –1 & 0 & 0 & 56.25 \\ \hline
21. & 0 & 0 & 1 & 0 & 60.62 \\ \hline
22. & 0 & 0 & \(-1\) & 0 & 49.87 \\ \hline
23. & 0 & 0 & 0 & 1 & 61.25 \\ \hline
24. & 0 & 0 & 0 & \(-1\) & 53.75 \\ \hline
25. & 0 & 0 & 0 & 0 & 58.12 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: _Cont._ \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{2}{c}{Regression statistics} \\ \hline Multiple R & 0.879488 \\ \hline R-Square & 0.773499 \\ \hline Normalized R-Square & 0.728199 \\ \hline Standard error & 7.191446 \\ \hline Observations & 25 \\ \hline Analysis of variance \\ \hline Regression & 4 & 883.0661097 & 17.07500251 & 3.10424 \(\times\) 10\({}^{6}\) \\ \hline Remainder & 20 & 51.71689486 \\ \hline Total & 24 \\ \hline Coefficients & \(\kappa\)-statistics & \(p\)-value \\ \hline \(Y\)-intersection & 60.3684 & 41.97236579 & 5.6264 \(\times\) 10\({}^{21}\) \\ \hline Variable X 1 & 5.937222 & 3.502703176 & 0.002241053 \\ \hline Variable X 2 & 8.681667 & 5.121806169 & 5.19784 \(\times\) 10\({}^{5}\) \\ \hline Variable X 3 & 7.125 & 4.203440463 & 0.000437187 \\ \hline Variable X 4 & 5.903333 & 3.482710204 & 0.002347197 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Regression statistics obtained using the linear model. The following dependence was obtained:  
\[Y=60.37+5.94\;{\rm z_{1}}+8.68\;{\rm z_{2}}+7.125\;{\rm z_{3}}+5.90\;{\rm z_{4}}-4. 41\;{\rm z_{1}}^{2}+7.78\;{\rm z_{2}}^{2}++1.15\;{\rm z_{3}}^{2}+3.40\;{\rm z_{4}} ^{2}. \tag{10}\]  
With a confidence probability of 0.95 (\(p\)-value is less than 0.05) all coefficients are significant (according to Student's test). The coefficient of determination of the model is 0.879, which confirms its high adequacy. It should be noted that the closer the coefficient of determination to 1, the better the model approximates the data. 1.