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ALGORITHMIZATION AND PROGRAMMING OF ECONOMETRIC MODELS OF POPULATION
DEMAND FOR MEAT AND DAIRY PRODUCTS
Toshpulov Bekzod
Tashkent State University of Economics
ORCID: 0009-0006-2130-6713
Abstract.
In this article, the theoretical basis of the processes of using food resources in the
Republic of Uzbekistan is studied. Also, the issues of production and use of primary food products
delivered to the population were considered, and the meat and dairy products produced and
delivered to the population in 2001-2021 were analyzed economically. In studying and analyzing
the consumption of these products, numerical results were obtained by creating an econometric
model of this process. Based on the results, economic analyses, conclusions and proposals were
developed. Also, in this article, a program was created using the Python programming language
to perform correlation and regression analysis.
Keywords:
food safety, econometric model, correlation, regression, regression equation,
pair correlation, mean square deviation, dispersion.
АҲОЛИНИНГ ГЎШТ ВА СУТ МАҲСУЛОТЛАРИГА ТАЛАБИНИНГ ЭКОНОМЕТРИК
МОДЕЛЛАРИНИ АЛГОРИТМЛАШТИРИШ ВА ДАСТУРЛАШ
Тошпулов Бекзод
Тошкент давлат иқтисодиёт университети
Аннотация.
Ушбу мақолада Ўзбекистон Республикасида озиқ
-
овқат ресурсларидан
фойдаланиш жараёнларининг назарий асослари ўрганилган. Шунингдек, аҳолига етказиб
берилган бирламчи озиқ
-
овқат маҳсулотларини ишлаб чиқариш ва улардан фойдаланиш
масалалари кўриб чиқилиб, 2001
-
2021 йилларда ишлаб чиқарилган ва аҳолига етказиб
берилган гўшт ва сут маҳсулотлари иқтисодий таҳлил қилинган. Ушбу маҳсулотлар
истеъмолини ўрганиш ва таҳлил қилишда ушбу жараённинг эконометрик моделини
яратиш орқали сонли натижалар олинди. Олинган натижалар асосида иқтисодий
таҳлиллар, хулоса ва таклифлар ишлаб чиқилди. Шунингдек, ушбу мақолада Python
дастурлаш тили ёрдамида корреляцион ва регрессион таҳлилни амалга оширувчи
дастур яратилди.
Калит сўзлар
:
озиқ
-
овқат хавфсизлиги, эконометрик модель, корреляция,
регрессия, регрессия тенгламаси, жуфт корреляция, ўртача квадратик четланиш
,
дисперсия.
UOʻK:
519.636.03
655-663
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АЛГОРИТМИЗАЦИЯ И ПРОГРАММИРОВАНИЕ ЭКОНОМЕТРИЧЕСКИХ МОДЕЛЕЙ
СПРОСА НАСЕЛЕНИЯ НА МЯСНУЮ И МОЛОЧНУЮ ПРОДУКЦИЮ
Тошпулов Бекзод
Ташкентский государственный экономический университет
Аннотация.
В данной статье исследуются теоретические основы процессов
использования продовольственных ресурсов в Республике Узбекистан. Также
рассмотрены вопросы производства и использования первичных пищевых продуктов,
поставляемых населению, а также произведенные и поставленные населению
мясомолочные продукты в 2
001-
2021 годах проанализированы экономически. При
изучении и анализе потребления этих продуктов были получены численные результаты
путем создания эконометрической модели этого процесса. По результатам были
разработаны экономические анализы, выводы и предложения. Также в данной статье
создана программа с использованием языка программирования Python для проведения
корреляционного и регрессионного анализа.
Ключевые слова
:
пищевая безопасность, эконометрическая модель, корреляция,
регрессия, уравнение регрессии, парная корреляция, среднеквадратическое отклонение
,
дисперсия.
Introduction.
Currently, a number of important reforms are being carried out in our country to provide
the population with quality primary food products. In particular, if we look at the types of
primary food products, these are meat and meat products, milk and milk products, wheat, rice,
vegetables, fruits, sugar and dairy products. Also, when it comes to the lifestyle and health of
the population, the role of protein-rich meat and dairy products in these food products is
incomparable. Of course, the issue of regularly delivering products necessary for human health
to the population is a complex one. The reason is that in order to solve this problem, it is
necessary to produce the necessary amount of product per capita. This production process is
directly related to the development of animal husbandry. It is also necessary to determine the
amount of necessary production products, to determine the factors affecting it, and to perform
econometric modeling.
Therefore, a number of decisions and decrees have been issued in our country on the
development of animal husbandry and the study of the experiences of developed countries in
the use of modern technologies. In particular, the decision PQ-4243 of the President of the
Republic of Uzbekistan "On measures to further develop and support the livestock sector"
defines the following measures and priority tasks. Rapid development of the livestock sector
plays an important role in providing our people with cheap and high-quality meat and other
food products, especially in increasing the employment and income of citizens living in rural
areas. At the same time, the current state of affairs in the regions requires specific
comprehensive measures to support the enterprises of this sector, increase the feed base,
improve breeding, including the development of artificial insemination, and strengthening the
material and technical base of breeding farms. it is necessary to implement the measures.
Comprehensive support for entrepreneurial initiatives of our people in the development of
animal husbandry, wide introduction of scientific approaches and advanced modern
technologies in this sector, further stimulation of the production and processing of import-
substituting and exportable livestock products, and ultimately the welfare of the population In
order to improve and increase their income, the following priority tasks are defined.
Therefore, in order to fulfill these priority tasks and satisfy the population's demand for
high-quality meat and dairy products, it is necessary to carry out an analysis of these products
in relation to the population and determine the amount of resources that will be needed in the
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future. Based on these determined indicators, it is possible to clearly define strategies for the
development of the livestock sector. It is also necessary to use the elements of econometric
modeling in the study of this economic process. In this case, it will be possible to calculate
economic changes by determining correlation coefficients and creating a regression equation.
Literature review.
At present, consistent reforms are being carried out to further improve and develop the
infrastructure of agriculture and animal husbandry in our country. In particular, the decision of
the President of the Republic of Uzbekistan "On measures to further develop and support the
livestock sector" dated 18.03.2019 No. PQ-4243 defines priority tasks for the development of
this sector (Decision, 2019).
Consistent scientific research is being carried out by scientists from all over the world to
further develop the livestock sector. In particular,scientists Gorbatovsky in his scientific work
"Management of Fodder Production Reserves and Evaluation of Its Economic Efficiency"
discussed in detail the types of feed needed for livestock and its feed units. Also, in the
development of animal husbandry and increasing its economic efficiency, he cited models for
the development of feed rations using optimization methods (Greene, 2011). In addition,
Lenkov in his scientific works, instructions were given on the use of optimization models and
econometric models for economic mathematical modeling and forecasting of agricultural
activities (Gujarati, 2022).
We can cite significant scientific results of our country's scientists on solving these issues.
In particular, Saukhanov (2022) economic mathematical models and econometric models for
assessing the economic efficiency of agricultural development in the conditions of
Karakalpakstan and reducing transaction costs are proposed. In this scientific research work,
the results of these scientific works and the developed models were studied and analyzed.
Saidova, Rustamova, Tursunov's "Agrarian Policy and Food "Food Safety" (2016).
Economic analytical opinions are presented. Ishnazarov, Nurllaeva. In the work
"Introduction to Economics," the econometric analysis of economic processes methods and
techniques necessary for modeling and economic analysis Methodologies of use are given.
Along with this, Saukhanov in a number of scientific works on agriculture in the Aral Sea region
on growing and increasing the economic efficiency of agricultural products analytical data are
presented (Tashev et al., 2022).
Research methodology.
During this scientific research, empirical results were obtained using systematic analysis
of the opinions and recommendations of scientists of the world and our country, empirical
research methods, analytical synthesis methods, economic mathematical modeling and the
method of least squares in econometric modeling.
Analysis and discussion of results.
Due to the rapid increase in the population and limited opportunities for food production,
the issue of providing the population with quality food is becoming a major problem in many
countries. During the years of independence in Uzbekistan, great achievements were made in
this field, including the production of agricultural products doubled. Taking this into account
and taking into account the growing demand for meat and dairy products, it is necessary to
study the factors affecting it. Population growth in our republic leads to an increase in the
demand for meat and dairy products. The results of econometric analysis of food products are
necessary to study the impact of meat and dairy products on population growth and to fully
satisfy the demand (Kazievish, 2020; Juraev and Rakhimberdiev, 2022; Karimov et al., 2022).
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Statistical data on the production and use of food products in our country for 2000-2021
(Table 1 and Table 2) are presented. In the economic analysis of this economic process, we need
to create an econometric model using these statistical data.
In the analysis of this economic process, we need to separate statistical data into the
following variables. The mentioned issue is a multi-factor economic process, and we will
analyze it according to the statistical data of 2 types of primary food products for 2000-2021.
Here,
1
x
is the volume of meat products delivered to the population (thousand tons),
2
x
is the
volume of dairy products (thousand tons) and
i
y
is the growth rate of the population. In our
case, the influencing factors are defined in the interval
i
x
,
1,2
i
=
. In the economic analysis of
this economic process, we need to create an econometric model using these statistical data
(Rakhimberdiev et al., 2022).
Table 1
Indicators of meat and dairy products delivered to the population in 2000-2010
Years
Demographic change of the population
(thousand people)
Products
i
i
y
1
x
-Meat products (thousand
tons)
2
x
-Dairy
products
2000
24487,70
841,80
3632,50
2001
24813,10
853,50
3665,20
2002
25115,8 2
865,10
3721,30
2003
25427,90
936,70
4031,10
2004
25707,40
998,30
4280,50
2005
26021,30
1061,50
4554,90
2006
26312,70
1139,40
4855,80
2007
26663,80
1208,70
5097,50
2008
27072,20
1288,00
5426,30
2009
27533,40
1367,80
5802,50
2010
28001,40
1461,40
6169,00
Table 2
Indicators of meat and dairy products delivered to the population in 2011-2022
Years
Demographic change of the population
(thousand people)
Products
i
i
y
1
x
-Meat products (thousand
tons)
2
x
-Dairy
products
2011
29123,40
1564,20
6766,20
2012
29555,40
1672,90
7310,90
2013
29993,50
1787,80
7885,50
2014
30492,80
1906,30
8431,60
2015
31022,50
2033,40
9027,80
2016
31575,30
2172,50
9703,40
2017
32120,50
2286,80
10047,90
2018
32656,70
2430,50
10466,40
2019
33255,50
2473,60
10714,30
2020
33905,20
2519,60
10976,90
2021
34558,90
2635,10
11274,20
2022
35271,30
2642,30
11278,20
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Figure 1. Changes in meat and dairy products produced in 2000-2021
Source:
author's development.
In the analysis of the economic problem presented in Table 1, we need to create an
econometric model of the process presented in Figure 1. This issue should be brought to a
multi-factor econometric model. Based on the statistics presented in the table, we can see that
the process is linear. Then, in our case, we will perform an economic analysis by determining
the linear regression equation. The general view of the linear multifactor regression equation
is given as follows (Rakhimberdiev et al., 2022; Juraev et al., 2022).
1 1
2 2
y a b x
b x
= +
+
(1)
Where,
1
2
, ,
a b b
- regression equation parameters (Gujarati, 2009)
The least squares method is used to determine parameters
1
2
, ,
a b b
in this regression
equation. In that case, the regression equation parameters are calculated as follows in formulas
(2), (3), (4) (Arzieva et al., 2022; Rakhimberdiev, 2022).
1
2
1 2
1
1 2
1
2
1
yx
yx
x x
y
x
x x
r
r
r
b
r
−
=
−
(2)
2
1
1 2
2
1 2
2
2
1
yx
yx
x x
y
x
x x
r
r
r
b
r
−
=
−
(3)
1 1
2
2
a
y b x
b x
= −
−
(4)
where
y
,
1
x
,
2
x
-
1
2
, ,
y x x
- mean square deviations of quantities.
1
yx
r
,
2
yx
r
,
1
2
,
x x
r
-pair correlation coefficients,
The following formulas are used to calculate these values.
2
2
y
y
y
=
−
(5)
1
2
2
1
1
x
x
x
=
−
(6)
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2
2
2
2
2
x
x
x
=
−
(7)
1
1
1
1
yx
y
x
y x
y x
r
−
=
(8)
2
2
2
2
yx
y
x
y x
y x
r
−
=
(9)
1 2
1
2
1
2
1
2
x x
x
x
x x
x x
r
−
=
(10)
Numerical solutions of mean square deviations of quantities
1
2
, ,
y x x
and pair correlation
coefficients using equations (5)-(10) given above are presented as follows (Table 3).
Table 3
1
2
, ,
y x x
- mean square deviations of quantities and values of pair correlation
coefficients
1
x
2
x
y
1
yx
r
2
yx
r
1 2
x x
r
618,567451
2713,685257
3324,324825
0,995212652
0,993871648
0,999004961
Also, the correlation graphs of meat and dairy products with population demography are
presented in Figures 2-3.
Figures 2.Dependence of population
demography on meat products
Figures 3. Dependence of population
demography on Dairy products
Regression equation of population
demography dependence on meat
products:
y = 92,446x + 549,22
Regression equation of population
demography dependence on milk products:
y
= 404,65x + 2323,4
Correlation coefficient of
dependence of population demographics
on meat products:
R² = 0,9828
Correlation coefficient of dependence of
population demographics on milk products:
R² = 0,9783
Source:
author's development.
Using the values presented in Table 2, it is necessary to form a regression equation of the
form (1). To create a regression equation, first, (1) it is required to determine the parameters
1
2
, ,
a b b
from equations (2), (3), (4) in the regression equation. In this case, we will have the
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661
values
1
8,186482
b
=
,
2
0,646685
b
= −
,
20225,0845
a
=
. As a result, the following
multifactor regression equation is derived.
1
2
20225,0845 8,186482
0,646685
y
x
x
=
+
−
(11)
The effect of meat and dairy products on population demography is realized through this
result. It is possible to get an economic analytical result of the multifactor regression equation
that relates the factors to the demographics of the population. The parameter
1
8,186482
b
=
of the regression equation determined in the form (11) increases the annual demand for meat
products and increases the population by
818648,2
. Also, the
2
0,646685
b
=
parameter
indicates that the annual increase in the demand for dairy products will increase the population
by
646685
.
Algorithmization and programming of the correlation coefficient calculation
process.
Nowadays, computers and other computing tools are used in the research of most
scientific and technical processes in mathematical modeling and simulation modeling of
models. Programming tools are used to perform calculation processes using electronic
calculators. before implementing the programming process, it is necessary to create an
executable algorithm of the process. We make the block diagram of the correlation coefficient
calculation algorithm as follows Figure 4[18].
Figure 4. Block diagram of the correlation coefficient calculation algorithm
Currently, Python programming language is used for most of the problem solving and
programming. This programming language has several special functions for calculating the
correlation coefficient, as follows[10].
The statistics module in Python comes with many statistical functions that help analyze
numerical data. The
statistics.correlation()
method in Python is used to return Pearson’s
correlation coefficient between two inputs[14].
➢
Syntax:
statisticcs.corrrelation(x,y,/);
➢
Parameters
The
statistics.correlation()
method takes the x and y parameters which represent the x
and y values for which the correlation coefficient is to be determined.
➢
Return value
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The
statistics.correlation()
method returns the Pearson’s correlation coefficient for two
given inputs.
Let’s use the
statistics.correlation()
method to determine the Pearson’s correlation
coefficient for two inputs, x and y:
Figure 5. Program code for calculating the correlation coefficient in the Python
programming environment
Source:
author's development.
Conclusion and suggestions.
Currently, in the Republic of Uzbekistan, the issues of providing the population with
quality food products are considered urgent. For this purpose, it is important to determine the
level of food supply and economic analysis of the population in the republic. Therefore, in this
article, the size of the population of meat and dairy products delivered to the population of the
Republic of Uzbekistan and the demographic impact were studied. In this case, the correlation
between the milk and meat products produced in 2000-2022 and the demographics of the
population was determined. As a result, the correlation of population demographics with
respect to meat products is 0.98, which means that it has a strong relationship. the correlation
coefficient of 0.97 for dependence on dairy products is considered a strong connection. From
this, it follows that the importance of dairy and meat products among high-quality food
products in improving the lifestyle of the population is very high.
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