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

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.