Analysis of economic indicators of developing of small business using econometric models


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Эконометрик моделлардан фойдаланиб кичик бизнес ривожланишин таржимаси

The regression equation is the formula for the statistical relationship between variables. If this formula is linear, linear regression will be observed. The formula of the statistical relationship between two variables is called even regression, and the relationship among several variables is called multivariate regression.

The correlation index R is used to estimate the connection density among even factors. The correlation coefficient can be used to determine the density of linear connections. A negative value of the correlation coefficient r indicates that there is the inverse relationship among the phenomena [3].

We consider the regression analysis of a number of factors (X1, X2, X3) which affect the output factor (Y) which is produced by small businesses and private entrepreneurs on the basis of the data of the Regional Statistics Office. Regression analysis is performed on the basis of the following table data (Table 1):
Table 1

Analysis of factors which influence the volume of products which are produced by small businesses and private entrepreneurs in Karshi city




Years

Product volume which are produced by small businesses and private entrepreneurs(billion soums) Y


Investments in small business and private entrepreneurship (thousand soums) X1


Number of people which are worked in small business and private entrepreneurship X2


Number of small businesses and private entrepreneurship X3



2008

23.075852

8730152.7

11420

4220

2009

21.226537

21525265.5

10002

4549

2010

23.598471

93703785

10726

4634

2011

49.702919

43074637.2

10455

4622

2012

186.563885

71380052.8

11188

4251

2013

177.019929

43862007.1

10000

3994

2014

197.693541

62865012

11661

3461

2015

225.456267

115179625

13407

3213

2016

263.376348

167864643

14484

3175

2017

264.769629

370580627

15843

3442

2018

549.300749

280439243

16025

3835

2019

677.377468

393080957

20769

4489

* Compiled by the author on the basis of data from the Regional statistics department.

In the analysis of the data of Table 1, the volume of products which are produced by small businesses and private entrepreneurs is taken as (Y). Investments in small business and private entrepreneurship (thousand soums) X1, number of people engaged in small business and private entrepreneurship X2, number of small business and private entrepreneurship X3, are taken as influencing factors. On the basis of the data in the table, calculations are performed and the following regression analysis results are obtained. (Table 2):



Table 2

Results of regression analysis



Variable

Coefficient

Std. Error

t-Statistic

Prob.  

X1

-1.171542

6.09E-07

-0.192397

0.8522

X2

0.061955

0.025217

2.456905

0.0395

X3

0.004171

0.056597

-0.073698

0.9431

C

-55.7401

350.8470

-1.569744

0.1551

R-squared

0.826754

    Mean dependent var

221.5968

Adjusted R-squared

0.761786

    S.D. dependent var

206.8916

S.E. of regression

100.9779

    Akaike info criterion

12.32888

Sum squared resid

81572.24

    Schwarz criterion

12.49052

Log likelihood

-69.97329

    Hannan-Quinn criter.

12.26904

F-statistic

12.72568

    Durbin-Watson stat

1.609758

Prob(F-statistic)

0.002057









As we can see from the amount of coefficient of the analysis of results which are obtained in Table 2 that when the investment in small business and private entrepreneurship in Karshi city increased by 1%, it is led to increase the average volume of products which are produced by small business and private entrepreneurship by 1,2%, the number of people who work in small business and private entrepreneurship by 1% when increase in the volume of products which are produced by small businesses and private entrepreneurship other factors do not change, the increase in the number of small businesses and private entrepreneurship by 1% when the other factors do not change, increase in the volume of products which are produced by small businesses and private entrepreneurship by average of 0,006%.

When each factor which influences the volume of products which are produced by small businesses and private entrepreneurship in Karshi city, is analyzed individually, and the others are considered unchanged, the biggest influenced factor is considered the share of investment in small business and private entrepreneurship. In this case, we can express the regression equation which represents the correlation bond between the resulting factor with the influencing factors on the basis of data of Table 2 and using the method of "The smallest squares" as follows:
Y = 1,2 *X1 + 0,06*X2 + 0,004*X3 – 55 (1)
Thus, we can conclude on the basis of (1) mathematical model that we can achieve an increase of the volume of products which are produced by small businesses and private entrepreneurship in Karshi city through increasing the number of investments in small business and private entrepreneurship in Karshi, the number of people who work in small business and private entrepreneurship, the number of small business and private entrepreneurship.


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