# Mathematical Modeling of the Manufacturing Sector's Dominant Part as a Base for Automation
## 2 Materials and Methods
### Data and Methods  
The research is grounded in the collection, selection, analysis, and consecutive usage of eligible data for mathematical modeling purposes. The data come from a public and a freely available source: The World Integrated Trade Solution (WITS) [41]. The stated solution offers access to manifold international data with the possibility of sorting them by certain criteria. Various options can be discovered through this software in the form of numerous classifications, statistics, special analyses, development trends, or outputs involving a mixture of different filters. However, we find the pure data the best fundament for our research. Our work is thus based only on straight numbers. Anyway, we consider such options very helpful and do not exclude their usage in future investigations. Another great advantage, and powerful reason to utilize the described solution, is data guarantee. Data are compiled and summed under the patronage of several global organizations (e.g., the World Bank [42] and the World Trade Organization [43]) which represent the elite in the given issue. This creates an extensive, useful, and reliable database.  
Reflecting on the proposed methodology and stated elements that are required for mathematical modeling, the pick is made as follows:  
* Country: Lithuania
* Sector: Machinery, electrical machinery and parts (Mach and Elec)
* Indicator: Export
* Period: From 2004 to 2018  
The regarded figures appertain to Lithuanian exports to the world. In other words, all countries with an export trade partnership with Lithuania are included; international merchandise trade cooperation is included. Exports are reported in thousands of US dollars. The time interval taken into account in the analysis incorporates 2004 and 2018, inclusively. In summary, it is a 15-year period. The WITS database provides data before 2004; however, we reject them for a certain reason. Lithuania became a member of the European Union in 2004 [44]. Therefore, from this year all data are comparable. The same methodology and methods were used in data collection, sorting, and processing, which was not exactly the same before. Each country had its own partially adjusted procedures. Data for 2018 are the latest up-to-date, complete, and available ones.  
The decision about the implementation of mathematical modeling as the most suitable variant is our first one. This is followed by the selection of the model type. After studying the scientific literature and contemplating our research conditions, data, and specifics, we apply polynomials [45]. We assume that the polynomial approximation is an excellent method for building our model. Our research case corresponds to the polynomials in numerical analysis. The concretization of the investigation method (in our case, a closer specification of the polynomial degree that is de facto related to the choice of separate function) occurs later within the testing realization. We consider this fact to be a plus because it allows a wider space for research itself and its more natural development. The whole direction of developing the model is not strictly defined in advance and can therefore be developed more appropriately.  
Several software packages exist serving the mathematical design of the model. In our paper, the preferred one is Matlab [46]. In our opinion, the range of possibilities, accompanied by shipshape tools and graphical figurations, is unrivaled. From a wide scale of utilities, we adopt the Matlab Curve Fitting Tool [47]. The toolbox presents an app function for fitting curves and surfaces to data. Thus, we chose the polynomial model type with a Curve Fitting Tool when we looked for the most suitable degree of polynomial.