Empirical modeling of craftsmanship development using digital technologies in the region

Ytx - development of craft products in the region (in billion soums)
Y1
As - total population of the region (thousands of people)	X1
Shi - personal consumption of the population of the region (in billion soums)	X5
Ii - social consumption of the population of the region (in billion soums)	X6
Km - capital resources of the region's population (in billion soums)	X7

^{Based on the craft industries and factors affecting them in Table 1, we created the following functional view. A functional view of the empirical models constructed for each branch of regional handicrafts}

Ytx^– development of craft products in the region

<sup>We used statistical data from 2003 to 2022 to create multi-factor empirical models for the population of Kashkadarya region through handicraft industries and factors affecting them.
Table 2


Share of handicrafts in GNI in real terms</sup>

Years		Kkbt - Handicrafts (in billion soums)	Kbtks - Registered Craftsman number of enterprises (units)	Employment - the total share of the population employed in crafts (percentage)	Kbtyt - Newly established craft enterprises (together)	Kbttug - Finished k/b (unit)
1	2003	1368.85965	10504	60.4	1457	478
2	2004	1198.10606	11547	65.2	1541	458
3	2005	1076.32399	12457	66.1	1674	650
4	2006	1837.62626	14457	67.1	1798	745
5	2007	2364.80331	15871	67.4	1876	879
6	2008	2234.80392	17587	68.1	1985	987
7	2009	2702.78552	18425	70.2	2854	1441
8	2010	2675.8	19547	74.1	3002	1345
9	2011	3225.76132	20767	76.1	3202	1428
	2012	3251.17605	20529	77	1438	1728
10	2013	2893.87755	20430	77.9	1652	1832
11	2014	2932.34802	17492	78.4	1578	4561
12	2015	3496.86869	15890	79.3	1620	3242
13	2016	3743.24199	15180	79.9	1743	2496
14	2017	5730.96072	14969	80	1980	1652
15	2018	5574.91608	16752	80.2	2365	592
16	2019	5571.66752	20921	78.5	5154	1005
17	2020	5565.34039	26088	78.1	5742	567
18	2021	6202.82404	32584	78.5	9463	2967
19	2022	6456.76048	38985	78	8551	2158

One of the main rules for building a multifactor empirical model is to determine the density of connections between the factors selected for the model, that is, to check the problem of multicollinearity between the selected factors. For this, correlation coefficients are calculated between factors, and variables In accepting values, the most common metric that shows a linear relationship between x and is the correlation coefficient. It is calculated as follows:
(1)
(1) is in the form of Eq value is determined by the following ratio:
(2)
and is called the covariance of the variables and is found as:
(3)
The correlation matrix between the influencing factors for the development of the craft network in Kashkadarya region was calculated in the Eviews 9 program.
We use the method of least squares to construct and analyze the empirical model.
A linear multifactor econometric model looks like this:
(4)
Here: - the resulting factor; - influencing factors.
(4) to find the unknown parameters a0, a1, a2, ..., an in the model, the following system of normal equations is created:
(5)
The level multifactor econometric model looks like this:
(6)
Here: - the resulting factor; - influencing factors.
If we substitute natural logarithm in the model (6), then we will have the following form:
. (7)
(7) in the model , if we make the designations, then we will have the following appearance:
. (8)
(8) to find the unknown parameters in the model, the following system of normal equations is constructed:
(9)
If this system of normal equations (9) is analytically solved by several methods of mathematics, then the values ​​of the unknown parameters are found.
<sup>In order to have multifactorial empirical models of their processes, several options were calculated in the Eviews 9 program and appropriate results were obtained.



1- table</sup>

A correlational analysis of craft

Covariance Analysis: Ordinary
Date: 08/17/23 Time: 14:52
Sample: 2003 2022
Included observations: 20
Covariance
Correlation
t-Statistic
Probability	Y7	X1	X2		X3		X4
Y7	2872768.
Correlation	1.000000
t-Statistic	-----
Probability	-----
X1	8149341.	44837454
Correlation	0.718045	1.000000
t-Statistic	4.377044	-----
Probability	0.0004	-----
X2	8051.196	20211.99	36.19288
Correlation	0.789584	0.501738	1.000000
t-Statistic	5.459084	2.460863	-----
Probability	0.0000	0.0242	-----
X3	2829996.	13912216	4909.891		5299745.
Correlation	0.725284	0.902502	0.354514		1.000000
t-Statistic	4.469634	8.890473	1.608547		-----
Probability	0.0003	0.0000	0.1251		-----
X4	454425.2	2089913.	3558.256		371093.9		1106880.
Correlation	0.254837	0.296659	0.562180		0.153217		1.000000
t-Statistic	1.118095	1.317947	2.884021		0.657811		-----
Probability	0.2782	0.2040	0.0099		0.5190		-----

^{If there is no autocorrelation in the residuals of the resulting factor, then the value of the calculated DW criterion will be around 2.
2- table}

Dependent Variable: Y7
Method: Least Squares
Date: 08/17/23 Time: 14:53
Sample: 2003 2022
Included observations: 20
Variable	Coefficient	Std. Error		t-Statistic		Prob.
X1	-0.060653	0.054870		-1.105395		0.2864
X2	222.3343	31.25380		7.113832		0.0000
X3	0.512540	0.147878		3.465971		0.0035
X4	-0.361500	0.162572		-2.223636		0.0420
C	-12788.44	2017.159		-6.339828		0.0000
R-squared	0.898779	There is a mean dependent				3505.243
Adjusted R-squared	0.871787	SD dependent				1738.956
SE of regression	622.6660	Akaike info criterion				15.91822
Sum squared resid	5815694.	Schwarz criterion				16.16715
Log likelihood	-154.1822	Hannan-Quinn criterion.				15.96681
F-statistic	33.29762	Durbin-Watson stat				1.572172
Prob(F-statistic)	0.000000

^{It was found that the value of the DW criterion calculated by the empirical models built for the craft is higher than the table value. This indicates that there is no autocorrelation in the resulting factor residuals. Fisher's and Student's tests were calculated and the calculated value was compared with the table values, and their magnitude was determined from the table values.}

Scaled Coefficients
Date: 08/17/23 Time: 14:53
Sample: 2003 2022
Included observations: 20
		Standardized	Elasticity
Variable	Coefficient	Coefficient	at Means
X1	-0.060653	-0.239621	-0.329618
X2	222.3343	0.789165	4.695337
X3	0.512540	0.696154	0.443598
X4	-0.361500	-0.224393	-0.160942
C	-12788.44	NO	-3.648375

^{An empirical model constructed for crafting}