## 3 Materials and Methods  
Using a distribution network model, the authors conducted computer simulations for various alternatives, the effects of which formed the basis for developing a regression model. The assumption was that deliveries to warehouses (distributions centers) are performed on a daily basis, immediately after production. First of all, in order to develop the regression model, simulations had to be carried out (using the model mentioned above) to find the relationship between the following variables:  
The dependent variable is:  
\(\underline{\text{y--Average Stocks in the Distribution Centers. }}\)  
The independent variables are:  
\(\underline{\text{x}_{1}}\)--Yearly sales;  
\(\underline{\text{x}_{2}}\)--Standard deviation of average sales in one warehouse;  
\(\underline{\text{x}_{3}}\)--No. of distribution centers;  
\(\underline{\text{x}_{4}}\)--Customer service level in distribution centersThe significant scientific novelty of this article is the presentation of a new methodology that, through calculations from a computer simulation model, allows for the development of a simplified multiple regression model for calculating average inventory levels. Multiple regression is a statistical method of which the main aim is to quantify the relationship between multiple independent variables and the dependent variable [48]. Even if there is no direct relationship between the variables, one can seek to link them by means of a mathematical equation that, under certain assumptions, allows one to predict quantities determined on the basis of knowledge of other variables. Regression is one of the most commonly used methods when applied to problem solving in technical sciences, economics, and management [49]. The concept of the developed methodology is presented in Figure 1.  
The concept is based on the assumption that from the results obtained by a complex simulation model, which takes into consideration a large number of variables as well as random factors, it is possible to obtain a simpler formula to be used in practice by managers. Such a model (formula) allows one to obtain the answer to what should be the average level of stocks under given conditions, which would allow managers to easily implement it in practice. When analyzing real phenomena and processes, even in relatively simple situations, we are not able to explain them fully. Therefore, when describing interdependencies between them, we usually use some simplified models of real interdependencies. By \"model\" we can, therefore, mean a useful form of presentation of empirical data. When approaching the process of building a model, we have to accept a certain compromise between oversimplifying reality and wanting to include too much detailed data. One of the ways to describe such interdependencies can be the well-known method of multiple regression, which is used in this paper. In this paper, the regression approach was used to explain the result of changes in the independent variables (x\({}_{1}\) to x\({}_{4}\)) on the dependent variable (y). Two analyses were conducted separately for two types of demand modeling in the simulation model: the model using the Gaussian distribution and the model using the Gamma distribution; these are the two most commonly used models in the literature for demand analysis [50]. For the model using the Gamma distribution, all four independent variables were found to be  
Figure 1: Conceptual framework scheme of simulation modeling with a regression module for finding average stocks in the distribution centers. statistically significant. Table 1 shows significance tests with effect sizes, \(p\)-value, and \(t\)-test for variables x\({}_{1}\), x\({}_{2}\), x\({}_{3}\), and x\({}_{4}\). From Table 1, one can observe that all variables in the regression analysis are statistically significant; the \(p\)-values are distinctly smaller than 0.05. Additionally, an assessment of the significance of the structural parameters was carried out.