Econometric analysis of increasing efficiency of industrial enterprises

: One of the main rules for the construction of multifactor econometric models is to determine the connection densities between the factors selected for the model, that is, to check the multicollinearity problem of the connection between the selected factors. He used the method of least squares to construct and analyze an econometric model between the volume of industrial output and its influencing factors. When the results of the built empirical model were analyzed based on the evaluation criteria of econometric models, the results of some criteria showed that the coefficients of the model were insignificant, and the result of the model was analyzed based on the criteria of re-evaluation by expressing the n-level regression equation. The built empirical model is analyzed economically, conclusions and suggestions are given.


Introduction
On a global scale, many scientific studies are being carried out on the purposeful use of modern methods in the management of enterprises, comprehensive assessment and forecasting of their economic potential based on integrated indicators, and increasing their economic potential.Also, due to the improvement of the modern accounting system, attention is being paid to the issues of ensuring the innovative development of enterprises, improving the methodology of modern evaluation of the innovative potential of enterprises, and applying methods of systematic analysis of the innovative and economic potential.Indeed, today's conditions, when "40.0% of the share of the industry in the gross domestic product (GDP) of developed countries, and more than 50.0% of the contribution of the service sector" [1] are required.
Systematic work is being carried out in Uzbekistan to ensure the effective use of economic potential in the activities of enterprises based on different ownership, to evaluate and forecast economic efficiency, to analyze finance and investment potential using econometric methods.Also, in 2017-2021, the Strategy of Actions for the further development of the Republic of Uzbekistan sets priorities such as "deepening structural changes, increasing the competitiveness of enterprises and increasing the export potential" [1][2][3][4][5][6][7][8][9][10].The effective performance of these tasks requires improvement of the use of modern econometric methods in the assessment of the economic potential of enterprises, econometric research and forecasting of increasing the efficiency of the economic potential.
Econometric modeling of industrial production processes in our country has been the subject of scientific interest in this regard.In particular, famous economists of our country T.Sh.Shodiev, N.M.Makhmudov, B.T. Salimov, S.K. Salaev, B.A. I.S. Abdullaev, A.T. In Kenjabaev's scientific works, modeling and forecasting of production, modeling of socioeconomic processes under complex environmental conditions, forecasting of small business development trends, factors and econometric models of sustainable socio-economic growth, modeling of the formation and development of agriculture and the rural labor market are deeply and widely researched [10].
As noted in numerous studies, the industry is considered as the "main support point" of economic growth [2][3][4][5][6][7][8].This opinion is based on the high possibility of using new combination of innovation and knowledge of the industry compared to other sectors of the economy, the ability to implement scientific and technical achievements and scientific developments, to provide the economy and production sectors with technologies, to modernize and diversify the economy, and to ensure the development of each branch of the national economy.
This opinion is based on the high possibility of using new combination of innovation and knowledge of the industry compared to other sectors of the economy, the ability to implement scientific and technical achievements and scientific developments, to provide the economy and production sectors with technologies, to modernize and diversify the economy, and to ensure the development of each branch of the national economy.is explained by the property of giving.
Industrial development is such a form of changes in it that it reflects integral, complex, irreversible, progressive, quantitative and qualitative changes of the economic system in a certain time and space, and it is "growth", "change", "cause and effect" appears in forms.
In order to select the influencing factors in forecasting the increase in the volume of industrial products in Kashkadarya region and build a multi-factor econometric model, it is necessary to pay attention to and implement the following processes: One of the main rules of building a multifactor econometric model is to determine the strength of the connection between the vectors to be selected for the model and to check the multicollinearity problem of the connection between the selected vectors.For this, correlation coefficients are calculated between factors, and when i x and i y variables take values n i ,..., 1  , the most common indicator that shows a linear relationship between x and y is the correlation coefficient, which is calculated as follows: (1) The value of the momentum of the equation is determined by the following ratio: and is called the covariance of the variables x and y is found as: Correlation analysis is based on determining correlation coefficients and evaluating their importance and reliability [3].
The multiple correlation coefficient for a linear relationship can be determined by the matrix of pairwise correlation coefficients [4]: Based on the data of Table 1, i.e., the number of people employed in industrial enterprises of the region, the volume of production of consumer goods in industrial enterprises of the region, the number of enterprises operating in the region with the participation of foreign investment, the export of industrial products of the region as influencing factors in the econometric analysis of the process of increasing the volume of industrial products in Kashkadarya region volume, the volume of import of industrial products in the region, and the volume of investments involved in the fixed capital of industrial enterprises of the region.We conduct an autocorrelation analysis to determine the absence of multicollinearity between these factors.

Results
In order to create a multi-factor econometric model of exogenous factors in the econometric modeling of the process of increasing the volume of industrial products in Kashkadarya region, the above-mentioned employees in the industry (X1) and enterprises with foreign investment (X3) were taken as influencing factors, but in the correlation matrix (Table 2) the analysis revealed a weak correlation, so these two factors were not used.All factors other than these are taken and examined to see how they behave in the model.We use the method of least squares to create and analyze an econometric model between the volume of industrial output and the factors affecting it.
A linear multifactor econometric model has the following form [5]: here: y -the resulting factor; In order to have multifactor econometric models of the object, several options are analyzed in the Eviews10 program and relevant results are obtained.Table 3 shows the empirical model for the process, and the results of the linear regression equation and its coefficients, using criteria for estimating this model and its parameters.
When the results of the built empirical model are analyzed based on the evaluation criteria of econometric models, the results of some criteria show that the coefficients of the model are insignificant, therefore, we found it appropriate to express the econometric model in the form of an n-level regression equation and analyze the model result based on the criteria of re-evaluation.
Therefore, we will determine the natural logarithm value of the given statistical data and build a hierarchical multifactorial empirical model.
The level multifactor econometric model looks like this: here: y -the resulting factor;   In the evaluation of the econometric model built for the development of the volume of industrial production in the Kashkadarya region, it was found that the calculated value of the DW criterion is less than 2. This indicates that autocorrelation from endogenous factor residuals is positive."Fisher's and Student's criteria were calculated and the calculated value was compared with the table values, as a result, its magnitude was determined from the table values" [4].We expressed them in the form of the following model: Usually, the coefficient of determination takes values in the interval [1].The closer the coefficient value is to 1, the stronger the relationship.In this case, the coefficient of determination equal to 0.957 means that there is a sufficiently strong relationship between these economic indicators in the model.
"In order to be able to compare models with different number of factors, and this number of factors does not affect the R2 statistic, a corrected coefficient of determination is usually used" [2].
In this case, the smoothed coefficient of determination is equal to the value of 0.976 and its closeness to R means that the change in the number of influencing factors of the model is acceptable.
"We use Fisher's F-criterion to determine the statistical significance of the constructed multifactor econometric model and its compatibility with the studied process.The actual value of the F-criterion is calculated using the following formula" [5]: here: 2 R -coefficient of determination; n -number of observations; m -number of factors.F-the actual value of the criterion is equal to Fhisob=67,639.If the actual value is greater than the value in the table, then the constructed multifactor econometric model is said to be statistically significant or adequate for the process being studied.
"We find the tabular value of the F-criterion.For this, we calculate m k  Based on the level of significance 05 , 0   and degrees of freedom" [4] k1=4 and k2=12-4-1=7, the table value of the F-criterion is F=4.39.
"Fcalc>Ftable satisfies the condition that the calculated value of F-criterion is statistically significant than the value in the table, and it can be used to forecast the industry for future periods" [4].
"The Student's t-test is used to check the reliability of the parameters and correlation coefficients of the multifactor econometric model (7).In this case, their value is compared with the values of random errors" [5].
. ; ; "By comparing the calculated (calculated) and table (table) values of Student's t-test, we accept or reject the N0 hypothesis.For this, we find the tabular value of the t-criterion based on the conditions of the selected reliability probability (  ) and degree of freedom ( ).Here -number of observations, m -number of factors" [5].
"The condition | hisob | >  zhad should also be satisfied for the calculated parameters in the multifactor econometric model for infrastructure services serving agriculture" [5].
If there is a positive autocorrelation in the residuals of the resulting factor, then the value of the calculated DW criterion will be d<2.The value of this calculated DW criterion is equal to 1.97.This indicates that there is positive autocorrelation from the resulting factor residuals.
"Analyzing the constructed empirical model, if the volume of production of consumer goods (that is, demand for consumer goods) in the region increases by 1%, the volume of industrial production will increase by 0.498%, if the export of industrial products in the region is increased by 1%, the volume of industrial production will increase by 0.471%, It was determined that if the volume of import of industrial products in the region is increased by 1%, the volume of industrial production will decrease by 0.065%, if the volume of investment in the fixed capital of industrial enterprises of the region is increased by 1%, the volume of industrial production will increase by 0.288%".

Conclusion
To increase the efficiency of industrial enterprises, various factor influencing forces are used.These factors characterize the development processes and growth trends of industrial enterprises in different ways.
Econometric modeling of the complex economic potential of industrial enterprises remains an effective tool for decision-making in sustainable development.In this case, it is appropriate to forecast the economic potential of the enterprise on the basis of the complex economic potential of the enterprise and the system of the accepted main target indicators of its evaluation mechanism.
"It is necessary to pay attention to the following main factors for the development of the economic potential of industrial enterprises in the Kashkadarya region, and their impact is as follows: if the volume of production of consumer goods (that is, the demand for consumer goods) in the region is increased by 1%, the volume of industrial production will increase by 0.498%, if the export of industrial products is increased by 1%, if the volume of industrial production increases by 0.471%, if the volume of import of industrial products in the region is increased by 1%, then the volume of industrial production may decrease by 0.065%, if the volume of investment in the fixed capital of industrial enterprises of the region is increased by 1%, then the volume of industrial production may increase by 0.288%".

Table 1 .
Volume of production of industrial products in Kashkadarya region and factors affecting it

Table 2 .
Correlation matrix between the volume of production of industrial products and factors affecting it in Kashkadarya region

Table 3 .
A linear regression equation built between the volume of industrial production in Kashkadarya region and the factors affecting it.

Table 4 .
The n-level regression equation built between the volume of industrial production in Kashkadarya region and the factors affecting it.