# Statistical Analysis of the Weight and Center-of-Gravity Position of an Empty Container Ship
## 4 Analysis of the Test Results  
The search for functional relationships between the weight indices (C\({}_{1}\)-C\({}_{8}\)), the light ship weight (WSL) and the coordinates of the light ship centre of gravity (\(x_{\text{GC}}\), \(z_{\text{CG}}\)) and the design parameters, presented in Section 3.1, was performed using simple non-linear regression. The ship parameters \(P_{k}\), presented in Table 1, were used to develop the \(C_{k}\) indices. The parameters \(P_{k}\) for each class were in the past commonly used in shipyards to determine \(C_{k}\) indices. The number of ship crew \(J\) or the number of \(TEU\) containers were taken as independent variables in the simple regression of the weight indices \(C_{1}\)-\(C_{8}\), the weight light ship _WLS_ and the coordinates of the center of gravity (\(x_{\text{GC}},z_{\text{GC}}\)), which seems logical and correct. However, an analysis of these two parameters showed that the actual number of crewmembers \(J\) has little relation to the size of the ship (the number of crew is derived from the relevant regulations and not from the size of the ship). Also, the number of \(TEU\) containers (capacity) is not closely related to the size of the container ship (container ships can also carry empty containers, which has little effect on the \(DWT\) tonnage of the container ship). However, due to increasingly better ship design methods using optimization models, as well as increasing automation in ship operation, the parameters \(P_{k}\) in Table 1 for currently designed ships may not always be appropriate when developing regression formulas. This causes the resulting regression formulas for the \(C_{k}\) weight indices for each class (Table 1) to have very low accuracy (R\({}^{2}\) value). The low value of the coefficient of determination R\({}^{2}\) is also due to:  
* a small number of analyzed container ships (the analysis was conducted for built container ships, for which the weight values for each class were known, calculated on the basis of the technical and working documentation used for building the ship),
* analyzed container ships were built over 25 year period, the latest ones may have an improved design (less steel used in the construction),
* although the container ships were of the same type (Figure 2), they differed in operating speed and sailing range, which affects the weight of the engine room, the volume of fuel tanks, and thus the weight of the hull. Therefore, further research analyses were performed to determine \(P_{K}\) parameters other than those indicated in Table 1, to check whether a better fit of the R\({}^{2}\) index was possible. The results of calculating the weight light ship _WLS_ (25-27) or for the coordinates of of the resultant center of gravity of a light container ship \(x_{\text{CG}}\), \(z_{\text{CG}}\) (28-33) have become already much better--the value of the coefficient R\({}^{2}\) is already acceptable. In further studies, using multiple nonlinear estimation, other ship parameters were used than those indicated in Table 1.  
The results obtained from multiple regression are more accurate than in the case of simple regression. This is particularly visible for the weight indices \(C_{1}\)-\(C_{8}\). The collected, best results of regression analyses for both methods are presented in Table 4. Based on the R\({}^{2}\) index, it can be stated that the obtained formulas for multiple regression achieve high accuracy. For the functional dependencies obtained from multiple nonlinear regression, their qualitative and quantitative verification was carried out. The quantitative verification was carried out by comparing the results of ship weight calculations with measurements made for two container ships after their construction and performance of appropriate tests.