# Statistical Analysis of the Weight and Center-of-Gravity Position of an Empty Container Ship
## 2 Materials and Method
### Research Method  
Statistical analysis methods were used to obtain mathematical relationships between weight indexes, weight light ship and center of gravity position and geometric parameters, propulsion power, speed, _TEU_ capacity or displacement for manned container ships.  
The process proceeded as follows:  
1. selection of substantively relevant parameters--affecting or related to the variable,
2. selection of the form of the estimation function,
3. selection of statistically significant parameters,
4. checking the accuracy of the fit.  
The general form of simple and multiple regression functions and statistics for evaluating their accuracy are known and reported in many publications, e.g., [34; 35]. It is also often used for finding mathematical relationships between ship parameters, [36; 37].  
The required approximation function had to meet the criteria of high accuracy and simplicity. Finding the approximation function in the form suitable for the quantity under study began with simple regression, where the predicted quantity depends on a single independent variable. The approximation relationships were first in the simplest form, that is, a class of linear functions (linear regression). When fit errors were too large, other solutions were sought in the group of nonlinear functions (polynomial, power, exponential functions). Simple regression was used to estimate the various approximated parameters and evaluate their variations depending on the parameters taken as independent variables. For the obtained functional relationships, the coefficient of determination R2, i.e., the ratio of explained variation to total variation, was considered to assess their accuracy. Also examined was the standard error of estimation, which informs of the average magnitude of deviations of the dependent variable values from the values calculated from the approximating function.  
Based on the analysis of the obtained simple regressions, to increase the accuracy of the predicted values, multiple regressions were developed (for two or more independent variables) starting with a linear and then non-linear multiple approximation function.  
Statistical verification of functional relationships in multiple estimation was based on the coefficient of determination R2 (goodness of fit), as well as the mean squared error and a scatter plot of predicted versus observed values (a scatter plot of values obtained from approximation versus benchmarks). Also tested were the significance of the parameters (independent variables) in the estimation function model and the Pearson correlation coefficient, which determines the level of linear dependence between the parameters.  
To search for formula equations and their coefficients, the computer program NdCurveMaster (version 8.2, SigmaLab, Mumbai, India, 2021) [38] was used, which usesheuristic curve-fitting and data analysis techniques and incorporates scientific machine learning-based algorithms such as random search. This program provides tools for evaluating the validity and usefulness of the resulting regression relationships.