Introduction. The Caspian region is located at an important crossroads of the world’s roads, connecting the rich North with the poor South. This is a vast region, which is administered by five states with a population of more than 240 million people [4], with a unique global water basin, and its shelves with hydrocarbon reserves, bioresources, where 90% of the world’s sturgeon caviar reserves are concentrated [5]. Its development cannot but be influenced by global processes and changes taking place in the world. TInterstate relations between the countries of the region were already built as international ones. The most important geopolitical consequence of the penetration of world globalization processes into the region was the intensification of political and commercial confrontation for control over the vast energy resources of the Caspian region of eight newly independent states of Central Eurasia: Kazakhstan, Kyrgyzstan, Tajikistan, Turkmenistan, Uzbekistan (Central Asia subregion) and Armenia, Azerbaijan, Georgia (Caucasus subregion). Undoubtedly, the world centers of power represented by the USA, the European Union, China, and other countries of the AsiaPacific region have become no less influential players in the region. In addition, the huge reserves of oil and natural gas have attracted the attention of the world’s main “players” to the region. At present, there is a sharp struggle in the Caspian region both for control over its resources and over the ways of their transportation. This is due to the fact that the development of hydrocarbon resources can not only improve the economic and sociopolitical situation in the coastal states, but also significantly change the balance of power in the global oil and gas market. These factors determine the strategic direction of development of the situation in the region[5].
Main part. The Caspian countries, which have a large oil and gas potential for export activities, account for 46% of the world’s gas reserves[4].The Caspian countries is high compared to other countries: 33.5 trillion m3 in the Islamic Republic of Iran and 32.3 trillion m3 in Russia. Azerbaijan’s natural gas potential is 1.1 trillion m3, which is 1.3% of the total natural gas potential of the Caspian countries. According to the schedule, since the bulk of gas production comes from Iran, Russia and Turkmenistan, it is expected that the volume of gas exports in Azerbaijan and Kazakhstan will decrease in the prospective period. The Caspian region, which has hydrocarbon resources, has always attracted the international world as the center of attention of the countries of the world.
It should be noted that the export of crude oil and natural gas to Azerbaijan, Kazakhstan and Turkmenistan in the Caspian region had a positive impact on the growth of GDP of EU countries. While Azerbaijan and Kazakhstan receive their main energy income from the export of oil, the main source of income for Turkmenistan is the export of natural gas. The recent economic development of the Caspian countries, especially the Republic of Azerbaijan and the Republic of Kazakhstan, allowed them to move from the level of income below the average to the level of countries with the level of income above the average in 2006. The dependence between GDP, which is the main indicator of the level of economic wellbeing of the EU region, and the income from gas exports of Azerbaijan, Kazakhstan and Turkmenistan in the Caspian region can be assessed using regression analysis. For the purpose of the study, let us designate the volume of gas exports of Azerbaijan, Kazakhstan and Turkmenistan in value terms with X1, X2 and X3 as causal factors, as well as the Gross domestic product of the European Union region with Y as the result of the factor. Using the EViews12 software package, based on the value of gas exports from Azerbaijan, Kazakhstan and Turkmenistan for 20042020 and the statistical data of the European Union region for this period, we obtain the following result.
Dependent Variable: Y  
Method: Least Squares  
Date: 17/08/22 Time:12:59  
Sample (adjusted): 2004 2020  
Included observations: 17 after adjustments  
Variable

Coefficient

Std. Error

tStatistic

Prob.

X3

64,3592

52,22725

1,232292

0,0026

X2

538,2469

143,8802

3,740938

0,0485

X1

1777,443

650,091

2,734144

0,017

C

10306767

908889,3

11,33996

0

Rsquared 
0,627711

Mean dependent var 
13311118


Adjusted Rsquared 
0,541798

S.D. dependent var 
2724915


S.E. of regression 
1844512

Akaike info criterion 
31,89565


Sum squared resid 
4.42E+13

Schwarz criterion 
32,0917


Log likelihood 
267,113

HannanQuinn criter. 
31,91514


Fstatistic 
7,306359

DurbinWatson stat 
1,456035


Prob(Fstatistic) 
0,004061

Source: EМiews12 application was developed by the author based on the software package.
Based on the results obtained from the EViews application software package, the regression equation will be as follows:
As can be seen from the regression equation obtained from the software complex Eviews12, the coefficients of the free term and dependent variables, reflecting causal factors and factoreffect, are greater than their standard errors. This characterizes the statistical significance of the obtained result [3,p.310]. However, to ensure the adequacy of this result, it is necessary to check the statistical significance of the given coefficients.
Critical point of distribution of the student (tdistribution) (б=0.0005) will be [3, с. 312]. As you can see, the coefficients of variables X1, X2 and X3 are statistically significant, as and , .
According to the result of the package of application programs Eviews12, the coefficient of determination R^{2}=0.628 means that 62.8% of the variance of the corresponding regression equation is explained by the performance indicator, and 28.2% by the influence of other factors [2].
According to the Eviews12 application program, the change in the natural gas export of the Republic of Azerbaijan, Turkmenistan and Kazakhstan with GDP in the region of the European Union for 20022020 is determined by the following schedule.
Fig. 1. Changes in the natural gas export of the Republic of Azerbaijan, Turkmenistan and Kazakhstan and the World Economic Forum in the European Union region for 20022020.
Source: EViews12 application was developed by the author based on the software package
Since it is important to check the adequacy of the established model, this adequacy can be defined as one of the traditional methods using the Fisher criterion. Fstatistic (Fisher’s test) = 7.31
When the FFisher test is compared with the , it turns out that the FFisher test . This means that the regression equation as a whole is statistically significant, and model (1) is an adequate model.
The autocorrelation result in the model can be determined based on the Durbin Watson statistics in Table 1 obtained from the EViews12 application suite. As you can see from the table, DW is 1.456. In this case, the points of the Durbin Watson crisis for observing 3 explanatory variables m = 3 and n = 17 up to the significance level б= 0.05 will be as follows [3, p. 337].
there is no autocorrelation [2, 3]. This means that the regression equation as a whole is statistically significant, and the constructed model (1) is an adequate model. If we adjust the criterion of the normality of the histogram based on the regression analysis of the dependence of the influence of gas exports to Azerbaijan, Kazakhstan and Turkmenistan in the Caspian region on the GDP of the European Union region for the studied period, we will get the following result.
Fig. 2. Criterion normality histogram
Source: Developed on the basis of the EViews12 software complex.
The regression equation obtained according to the package of application programs EViews12, annual values and standard errors of GDP of the countries of the European Union, as well as a number of characteristics of using the equation for the purposes of forecasting are presented in the graph below (3).
Fig. 3. Characteristics of UDM in the Republic of Azerbaijan for forecasting.
Source: Values and standard errors of GDP of EU countries by years and predictive characteristics of the model
As can be seen from the graph, the values of GDP of the EU countries by year, standard errors and characteristics of the model for forecasting determine the prognostic suitability of the model for the prospective period.
In the result of the research for the equation of linear regression (1) shown above, it is possible to determine how much the result factor changes due to the cause factor by calculating the elasticity coefficient. The calculated elasticity coefficients according to the constructed model will be as follows[3, 137].
The result. As a result of the study, the following results were obtained:
 The Caspian countries, which make up 46% of the world’s gas reserves, form the basis of natural gas consumption in the EU countries and play an important role in increasing the GDP of these countries;
 there is a high correlation between the GDP of the EU countries and natural gas exports of the Caspian countries, expressed by the linear regression equation Y = 1777.443*X1 +538.249*X2 +64.359*X3 + 10306767.163;
 in the research work, tests of the normality of histograms between the GDP of the EU countries and the export of natural gas of the Caspian countries were carried out in the Eviews12 application software package and the adequacy of the model was tested based on statistical characteristics;
 in a research study in the Eviews12 application package, the predictive suitability of the model was determined based on annual values, standard errors and model characteristics for forecasting the countries of the European Union. Using the predictive characteristics of the model, it is possible to determine the forecast prices of GDP for the prospective period, taking into account the impact of natural gas consumption in the EU countries on GDP.
 As a result of the study, it was found that a 1% increase in gas exports to the European Union in the Caspian region of the Republic of Azerbaijan leads to an increase in the GDP of the European Union region by 0.024%. An increase in gas exports to the European Union by the Republic of Kazakhstan by 1% leads to an increase in the GDP of the European Union region by 0.012%, and an increase in gas exports to the European Union by the Republic of Turkmenistan by 1% leads to an increase in the GDP of the European Union region by 0.24%.
References
 Zhiltsov S.S. (2013). Caspian Sea. Encyclopedia. M.: Oriental book (EastWest, Ant), 560 p. (2013)
 Yadigarov T.A. Econometric assessment of the level of development of balanced foreign economic relations in conditions of uncertainty// Finance: Theory and Practice, 2022 (№ 1), P.7990
 Yadigarov T.A. (2019a). Operations Research and Econometric Problem Solving in MS Excel and Eviews Software Packages: Theory and Practice (Monograph). Baku, Europe Publishing House, 352 p.
 BP Statistikal Review of World Energy 202170th editon
 https://ec.europa.eu/eurostat/statisticsexplained/index.php?title=RussiaEU_%E2%80%93_international_trade_in_goods_statistics