# Mathematical Modeling of the Manufacturing Sector's Dominant Part as a Base for Automation
## 3 Results
Degree 4 polynomial (Linear model Poly4):  
Figure 1:8  
where x is normalized by mean 2011 and std 4.472, the coefficients (with 95% confidence bounds) are  
Figure 1:9  
Figure 3:0  
Figure 3:1  
Figure 3:2  
Figure 3:3  
and efficacy of fit is represented by  
Figure 3:4  
Figure 3:5  
Figure 3:6  
Figure 3:7  
Degree 5 polynomial (Linear model Poly5):  
Figure 3:8  
where x is normalized by mean 2011 and std 4.472, coefficients (with 95% confidence bounds) are  
Figure 3:9  
Figure 2:0  
Figure 2:1  
Figure 2:2  
Figure 2:3Figure 2:4  
and efficacy of fit is represented by  
Figure 2:5  
Figure 2:6  
Figure 2:7  
Figure 2:8  
Degree 6 polynomial (Linear model Poly6):  
Figure 2:9  
Where x is normalized by mean 2011 and std 4.472, the coefficients (with 95% confidence bounds) are  
Figure 4:0  
Figure 4:1  
Figure 4:2  
Figure 4:3  
Figure 4:4  
Figure 4:5  
Figure 4:6  
and efficacy of fit is represented by  
Figure 4:7  
Figure 4:8  
Figure 4:9  
Figure 5:0  
Degree 7 polynomial (Linear model Poly7):  
Figure 5:1  
where x is normalized by mean 2011 and std 4.472, coefficients (with 95% confidence bounds) are  
Figure 5:2  
Figure 5:3  
Figure 5:4  
Figure 5:5  
Figure 5:6  
Figure 5:7  
Figure 5:8  
Figure 5:9  
Figure 6:0R-square = 0.9492 (52) Adjusted R-square = 0.8984 (53) RMSE = 3.949 \(\times\) 10\({}^{5}\) Degree 8 polynomial (Linear model Poly8): f(x) = p1 \(\times\) x\({}^{8}\) + p2 \(\times\) x\({}^{7}\) + p3 \(\times\) x\({}^{6}\) + p4 \(\times\) x\({}^{5}\) + p5 \(\times\) x\({}^{4}\) + p6 \(\times\) x\({}^{3}\) + p7 \(\times\) x\({}^{2}\) + p8 \(\times\) x + p9 (55) where x is normalized by mean 2011 and std 4.472, the coefficients (with 95% confidence bounds) are p1 = \(-\)8.279 \(\times\) 10\({}^{5}\) (\(-\)2.054 \(\times\) 10\({}^{6}\), 3.981 \(\times\) 10\({}^{5}\)) p2 = \(-\)7.435 \(\times\) 10\({}^{5}\) (\(-\)1.615 \(\times\) 10\({}^{6}\), 1.279 \(\times\) 10\({}^{5}\)) p3 = 4.363 \(\times\) 10\({}^{6}\) (\(-\)1.565 \(\times\) 10\({}^{6}\), 1.029 \(\times\) 10\({}^{7}\)) p4 = 3.727 \(\times\) 10\({}^{6}\) (\(-\)1.304 \(\times\) 10\({}^{4}\), 7.467 \(\times\) 10\({}^{6}\)) p5 = \(-\)7.288 \(\times\) 10\({}^{6}\) (\(-\)1.629 \(\times\) 10\({}^{7}\), 1.709 \(\times\) 10\({}^{6}\)) p6 = \(-\)5.542 \(\times\) 10\({}^{6}\) (\(-\)1.021 \(\times\) 10\({}^{7}\), \(-\)8.787 \(\times\) 10\({}^{5}\)) p7 = 4.06 \(\times\) 10\({}^{6}\) (\(-\)5.507 \(\times\) 10\({}^{5}\), 8.67 \(\times\) 10\({}^{6}\)) p8 = 3.356 \(\times\) 10\({}^{6}\) (1.707 \(\times\) 10\({}^{6}\), 5.004 \(\times\) 10\({}^{6}\)) p9 = 2.553 \(\times\) 10\({}^{6}\) (1.982 \(\times\) 10\({}^{6}\), 3.124 \(\times\) 10\({}^{6}\)) and efficacy of fit is represented by SSE = 7.503 \(\times\) 10\({}^{11}\) R-square = 0.9651 Adjusted R-square = 0.9185 RMSE = 3.536 \(\times\) 10\({}^{5}\) Degree 9 polynomial (Linear model Poly9): f(x) = p1 \(\times\) x\({}^{9}\) + p2 \(\times\) x\({}^{8}\) + p3 \(\times\) x\({}^{7}\) + p4 \(\times\) x\({}^{6}\) + p5 \(\times\) x\({}^{5}\) + p6 \(\times\) x\({}^{4}\) + p7 \(\times\) x\({}^{3}\) + p8 \(\times\) x\({}^{2}\) + p9 \(\times\) x + p10 where x is normalized by mean 2011 and std 4.472, the coefficients (with 95% confidence bounds) are p1 = \(-\)2 \(\times\) 10\({}^{5}\) (\(-\)2.287 \(\times\) 10\({}^{6}\), 1.887 \(\times\) 10\({}^{6}\)) p2 = \(-\)8.279 \(\times\) 10\({}^{5}\) (\(-\)2.23 \(\times\) 10\({}^{6}\), 5.746 \(\times\) 10\({}^{5}\)) p3 = 3.188 \(\times\) 10\({}^{5}\) (\(-\)1.081 \(\times\) 10\({}^{7}\), 1.145 \(\times\) 10\({}^{7}\)) p4 = 4.363 \(\times\) 10\({}^{6}\) (\(-\)2.418 \(\times\) 10\({}^{6}\), 1.114 \(\times\) 10\({}^{7}\)) p5 = 1.883 \(\times\) 10\({}^{6}\) (\(-\)1.783 \(\times\) 10\({}^{7}\), 2.16 \(\times\) 10\({}^{7}\)) p6 = \(-\)7.288 \(\times\) 10\({}^{6}\) (\(-\)1.758 \(\times\) 10\({}^{7}\), 3.004 \(\times\) 10\({}^{6}\)) p7 = \(-\)4.383 \(\times\) 10\({}^{6}\) (\(-\)1.761 \(\times\) 10\({}^{7}\), 8.847 \(\times\) 10\({}^{6}\)) p8 = 4.06 \(\times\) 10\({}^{6}\) (\(-\)1.214 \(\times\) 10\({}^{6}\), 9.333 \(\times\) 10\({}^{6}\)) (\(\rm 777\)) p9 = 3.163 \(\times\) 10\({}^{6}\) (4.111 \(\times\) 10\({}^{5}\), 5.916 \(\times\) 10\({}^{6}\)) (\(\rm 788\)) p10 = 2.553 \(\times\) 10\({}^{6}\) (1.9 \(\times\) 10\({}^{6}\), 3.207 \(\times\) 10\({}^{6}\)) and efficacy of fit is represented by SSE = 7.413 \(\times\) 10\({}^{11}\)R-square = 0.9655 (81) Adjusted R-square = 0.9034 (82) RMSE = 3.85 \(\times\) 10\({}^{5}\)  
We find it interesting to present a graphical representation for the degree 4 polynomial (Figure 3) and similarly the degree 9 polynomial (Figure 4).