# Statistical Analysis of the Weight and Center-of-Gravity Position of an Empty Container Ship
## 3 Research Results  
### Results of Analyses from Simple Nonlinear Regression  
To estimate the weight light of a container ship, simple nonlinear regression methods were used in the first step, because the developed approximation formulas are easy to use and are a function of only one ship parameter: \(V\), \(TEU\), \(DWT\), \(J\), \(Nc\), \(Ne\). Statistical analysis using simple regression for light container ships was conducted for:  
* weight indices for each class (Table 1)--Formula (6), where the independent variables used include the parameter resulting from the definition for a given weight index (Table 1), \(LBH\), \(DWT\) and \(TEU\), \(J\), \(N_{C}\) and \(Ne\). * weight of the whole hull of weight light ship--Formula (7), where \(LBH\), \(DWT\) and \(TEU\) are independent variables,
* coordinates of the center of gravity of a light empty container ship--Formula (8), with \(LBH\), \(DWT\) and \(TEU\) taken as independent variables. The results of these analyses are presented in the form of functional relationships, including R\({}^{2}\) coefficients, and in graphs:  
* for indices \(C_{1}\)--\(C_{8}\) (classes 1-8), Formulas (9)-(24), Figures 5-20, (second set of container ships, Table 3),
* for the weight light ship \(WLS\), Formulas (25)-(27), Figures 21-23, (first set of container ships, Table 2),
* for the coordinates of the ship's center of gravity \(x_{CG}\), \(z_{CG}\), Formulas (28)-(33), Figures 24-29, (second set of container ships, Table 3). Index \(C_{1}\):  
\[C_{1}=0.1652\cdot LBH^{-0.054}\hskip 14.226378 ptR^{2}=0.1001 \tag{9}\]Figure 8: Dependence of the weight index \(C_{2}\) as a function of \(LB\) (the product of the length and breadth of the ship). Figure 6: Dependence of the weight index \(C_{1}\) as a on the ship’s deadweight tonnage _DWT_. Figure 7: Dependence of the weight index \(C_{1}\) on the number of \(TEU\) containers. The weight light ship _WLS_:  
\[WLS=3.321\cdot DWT^{0.7711}\quad\quad R^{2}=0.9110 \tag{25}\]  
Figure 23: Dependence of the total weight light ship _WLS_ as a function of _LBH_ (volume module). Figure 21: Dependence of the total weight light ship _WLS_ on the ship’s deadweight _DWT_. Figure 22: Dependence of the total weight light ship _WLS_ as a function of the number of _TEU_ containers. coordinates of the center of gravity of the whole ship \(x_{CG}\), \(z_{CG}\) (Figure 2):  
\[x_{CG}=2.6063\cdot DWT^{0.3267}\ \ \ \ \ R^{2}=0.8935 \tag{28}\]  
Figure 26: Dependence of the longitudinal coordinate of the center of gravity of the whole ship \(x_{CG}\) as a function of \(LBH\) (volume module). Figure 8:0 Dependence of the longitudinal coordinate of the center of gravity of the whole ship \(x_{CG}\) on the ship’s deadweight \(DWT\). Figure 8:1 Dependence of the longitudinal coordinate of the center of gravity of the whole ship \(x_{CG}\) as a function of the number of \(TEU\) containers. The estimation formulas obtained from simple regression (dependencies, among others, on parameters used in shipyards) for the \(C_{k}\) indices, Equations (9)-(24), Figures 5-20,  
Figure 8:2 Dependence of the vertical coordinate of the center of gravity of the whole ship \(z_{CG}\) as a function of the number of _TEU_ containers. Figure 8:3 Dependence of the vertical coordinate of the center of gravity of the whole ship \(z_{CG}\) on the ship’s deadweight _DWT_. Figure 8:4 Dependence of the vertical coordinate of the center of gravity of the whole ship \(z_{CG}\) as a function of _LBH_ (volume module). do not meet the expected accuracy of fit (low R\({}^{2}\) value). This is especially true for the \(C_{7}\) and \(C_{8}\) indices, where the degree of fit was below 0.4. These dependencies concern the weights with the smallest percentage share in the total weight of the ship (\(M_{7}\)-0.33\({}^{\circ}\); \(M_{8}\)-0.24\({}^{\circ}\)), so the error made in their determination will not have such a significant impact on the total weight.