# Statistical Analysis of the Weight and Center-of-Gravity Position of an Empty Container Ship
## 3 Research Results
### Results of Analyses from Multiple Nonlinear Regression  
In further studies, multiple estimation was used and other ship parameters were used than those indicated in Table 1--such as the basic dimensions of the ship \(L\), \(B\), \(H\), the block coefficient \(C_{B}\) and the speed \(V\), which is a parameter assumed by the shipowner, determined at the preliminary design stage. The best results of the analyses performed are presented in the form of functional dependencies, Formulas (34)-(44) with the determination coefficient R\({}^{2}\) and in Figures 30-40 presenting the dispersion of observed values (measured data) in relation to the predicted values (calculated from the developed regression dependencies).  
\[C_{1}=0.0913757\cdot DWT^{0.1}-0.00304364\cdot(ln(TEU))^{2}\ \ \ \ \ R^{2}=0.9978 \tag{34}\]  
\[C_{2}=-1.17147\cdot 10^{7}\cdot DWT^{-2}+259.94\cdot TEU^{-0.9}-3.60709\cdot 10^{ 9}\cdot(LB)^{-3}\ \ \ \ \ R^{2}=0.9828 \tag{35}\]  
Figure 30: Scatter of predicted versus observed values for the index \(C_{1}\) determined from the dependencies in the form \(C_{1}=\) f(_DWT, TEU_)—Equation (34).  
Figure 34: Scatter of predicted versus observed values for the index \(C_{5}\) determined from the dependencies in the form \(C_{5}=\text{f}(DWT,\,TEU)\)—Equation (38).  
Figure 33: Scatter of predicted versus observed values for the index \(C_{4}\) determined from the dependencies in the form \(C_{4}=\text{f}(V,\,N_{C})\)—Equation (37).  
Figure 35: Scatter of predicted versus observed values for the index \(C_{6}\) determined from the dependencies in the form \(C_{6}=\mathfrak{f}(Ne,J)\)—Equation (39).  
\[C_{7}=-33711.5\cdot LBH^{-1.8}+0.229357\cdot DWT^{-0.6}\quad R^{2}=0.9493 \tag{40}\]  
Figure 36: Scatter of predicted versus observed values for the index \(C_{7}\) determined from the dependencies in the form \(C_{7}=\mathfrak{f}(DWT,LBH)\)—Equation (40).  
\[x_{GC}=0.197216\cdot L^{1.15}-0.0000244495\cdot N_{C}^{1.3}+0.0000866675\cdot DWT^{1.1 }\quad R^{2}=0.9989 \tag{43}\]  
Figure 38: Scatter of predicted versus observed values for weight light ship \(WLS\) determined from the dependencies in the form \(WLS=\text{f}(DWT,LBH,V)\)—Equation (42).  
Figure 37: Scatter of predicted versus observed values for the index \(C_{8}\) determined from the dependencies in the form \(C_{8}=\text{f}(TEU,LBH)\)—Equation (41).  
The obtained approximation formulas using multiple nonlinear regression are characterized by a much higher fit coefficient R\({}^{2}\) than from simple regression. This was influenced by the use of other ship parameters than those previously used, presented in Table 1.  
Figure 40: Scatter of predicted versus observed values for the vertical position of the center of gravity of the whole ship \(z_{CG}\) determined from the dependencies in the form \(z_{CG}=\) f(\(LBH\), \(V\))—Equation (44).  
Figure 39: Scatter of predicted versus observed values for the longitudinal position of the center of gravity of the whole ship \(x_{CG}\) determined from the dependencies in the form \(x_{CG}=\) f(\(L\), \(N_{C}\), \(DWT\))—Equation (43).