# Statistical Analysis of the Weight and Center-of-Gravity Position of an Empty Container Ship
## 4 Analysis of the Test Results
The basic technical and operational parameters of both container ships are given in Table 5.  
The results of the verifications performed using data of the existing container ships (Table 5) are shown in Table 6 (weights for each class) and Table 7 (weight light ship and position of the center of gravity). \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Simple Regression** & \multicolumn{3}{c}{**Multiple Regression**} \\ \hline
**Formula** & \(\mathbf{R^{2}}\) & **Formula** & \(\mathbf{R^{2}}\) \\ \hline \(C_{1}=0.177\cdot TEU^{-0.092}\) & 0.2634 & \(C_{1}=0.0913757\cdot DWT^{0.1}-0.00304364\cdot(ln(TEU))^{2}\) & 0.9978 \\ \hline \(C_{2}=-2\cdot 10^{-5}LB+0.4037\) & 0.0849 & \(C_{2}=-1.17147\cdot 10^{7}\cdot DWT^{-2}+259.94\cdot TEU^{-0.9}-3.60709\cdot\) & 0.9828 \\ \hline \(C_{3}=0.40927\cdot TEU^{0.45}\) & 0.9569 & \(C_{3}=-0.241143\cdot(\ln(DWT))^{2}+0.891088\cdot TEU^{-1/10}\cdot LBH^{0.4}\) & 0.9762 \\ \hline \(C_{4}=0.0419\cdot N_{\text{C}}^{0.0345}\) & 0.0180 & \(C_{4}=\) & \(761505\cdot V^{-6}-1.22616\cdot 10^{6}\cdot N_{\text{C}}^{-2}+0.000588802\cdot V^{5} \cdot N_{\text{C}}^{-1.1}\) & 0.9913 \\ \hline \(C_{5}=0.0118\cdot e^{-1.10^{-5}\cdot LBH}\) & 0.6883 & \(C_{5}=0.00671665\cdot TEU^{1/8}-0.000422513\cdot DWT^{0.55}\) & 0.9779 \\ \hline \(C_{6}=4.2761\cdot Ne^{-0.576}\) & 0.3640 & \(C_{6}=1.30598\cdot 10^{9}\cdot J^{-8}+0.000355803\cdot J^{2.6}\cdot Ne^{-0.5}\) & 0.9606 \\ \hline \(C_{7}=-1\cdot 10^{-8}\cdot DWT+0.0007\) & 0.3795 & \(C_{7}=-33711.5\cdot LBH^{-1.8}+0.229357\cdot DWT^{-0.6}\) & 0.9493 \\ \hline \(C_{8}=-1\cdot 10^{-7}\cdot TEU+0.0005\) & 0.0910 & \(C_{8}=0.0614659\cdot LBH^{-1/2}-1.89401\cdot 10^{15}\cdot TEU^{-7}+\) & 0.8517 \\ \(0.0000307182\cdot LBH^{4}\cdot TEU^{-6}\) & & \\ \hline \(WLS=0.1022\cdot LBH+1216.9\) & 0.9197 & \(WLS=0.106819\cdot DWT+0.0585666\cdot LBH+78.816\cdot V\) & 0.9886 \\ \hline \(x_{\text{CG}}=1.3668\cdot LBH^{0.3567}\) & 0.9259 & \(x_{\text{GC}}=\) & \(0.917216\cdot L^{1.15}-0.000024495\cdot N_{\text{C}}^{1.3}+0.0000866675\cdot DWT ^{1.1}\) & 0.9989 \\ \hline \(z_{\text{CG}}=8.3298\cdot e^{3\cdot 10^{-6}\cdot LBH}\) & 0.7019 & \(z_{\text{GC}}=4.18089+0.000024958\cdot LBH+0.253695\cdot V\) & 0.9443 \\ \hline \end{tabular}
\end{table} 
Table 4: Functional relationships of the obtained regression analyses results and the coefficient of determination \(\text{R}^{2}\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Container Ship A [39].** & **Container Ship B [16].** \\ \hline \(L\) [m]. & 154.0 & 196.0 \\ \hline \(B\) [m]. & 25.30 & 32.26 \\ \hline \(H\) [m]. & 13.5 & 19.0 \\ \hline \(T\) [m]. & 10.5 & 10.0 \\ \hline \(DWT\) [t]. & 20,275 & 39,128 \\ \hline \(TEU\) [-]. & 1334 & 2700 \\ \hline \(V\) [kn]. & 19.1 & 21.0 \\ \hline \end{tabular}
\end{table} 
Table 5: Parameters of the container ships used for the verification of the regression formulas. The values of the weights \(M_{\mathrm{\xi}}\) (Table 1) for each class were determined from the transformation of relation (6). From the comparative analyses results, contained in Table 6, we can see that the accuracy of calculations of individual weight classes ranges from 4% to 26% compared to the measured values. The weight of the whole ship is mostly affected by the classes \(M_{1}\), \(M_{2}\) and \(M_{4}\). For these major classes, the calculation error from regression formulas oscillates between 6% and 12%. Table 7 shows the results of the accuracy of the calculation of the weight light ship _WLS_ and the coordinates of the center of gravity. For the weight _WLS_, the accuracy of the calculations is less than 1%, while for the position of the center of gravity it is less than 5%. These are exceptionally good results confirming very good approximations using multiple regression formulas. The developed method and the formulas obtained from multiple regression allow at the preliminary design stage to predict with high accuracy the weight _WLS_ of a light container ship and the position of the center of gravity.