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DOI: https://doi.org/10.34069/AI/2024.74.02.21
How to Cite:
Gazuda, S., Erfan, V., Gazuda, M., Hertseh, V., & Zavadska, O. (2024). Modeling the impact of the agricultural sector on the
development of the regional economic systems. Amazonia Investiga, 13(74), 248-263. https://doi.org/10.34069/AI/2024.74.02.21
Modeling the impact of the agricultural sector on the development
of the regional economic systems
Modelando el impacto del sector agrícola en el desarrollo de los sistemas económicos regionales
Received: January 4, 2024 Accepted: February 21, 2024
Written by:
Serhiі Gazuda1
https://orcid.org/0000-0001-8148-6783
Vitalii Erfan2
https://orcid.org/0000-0002-8580-378X
Mykhailo Gazuda3
https://orcid.org/0000-0003-3947-5997
Viktoriia Hertseh4
https://orcid.org/0000-0003-4613-2829
Olena Zavadska5
https://orcid.org/0000-0001-8786-9005
Abstract
The purpose of the article is to study the role of
the agricultural sector in the development of
regional economic systems. The article uses
general scientific and specific research methods,
including: abstraction, analysis and synthesis,
generalization, statistical and comparative
analysis, dialectical and graphic. Within the
framework of the study, it is proposed to
investigate the impact of the agricultural sector
on the regions’ development using the
correlation-regression analysis method. The use
of the specified methodology made it possible to
simulate the regularity of the influence of the
volume of agricultural products sold on the gross
regional product.
The authors investigated the challenges faced by
the agricultural sector since the full-scale
invasion of Russia on the territory of Ukraine,
among which the following are highlighted: the
danger of the farmers’ work, limited access to
land plots, equipment, fuel and fertilizers,
1
PhD in Economics, Associate Professor, Department of Economics, Entrepreneurship and Trade, Uzhhorod National University,
Uzhhorod, Ukraine.
2
PhD in Economics, Associate Professor, Department of Economics, Entrepreneurship and Trade, Uzhhorod National University,
Uzhhorod, Ukraine.
3
Doctor of Economics, Professor, Department of Economics, Entrepreneurship and Trade, Uzhhorod National University, Uzhhorod,
Ukraine.
4
PhD in Economics, Senior Lecturer, Transcarpathia Institute of Postgraduate Pedagogical Education, Uzhhorod, Ukraine.
5
PhD in Economics, Associate Professor, Department of Entrepreneurship, Trade and Logistics, Lutsk National Technical University,
Lutsk, Ukraine.
Gazuda, S., Erfan, V., Gazuda, M., Hertseh, V., Zavadska, O. / Volume 13 - Issue 74: 248-263 / February, 2024
Volume 13 - Issue 74
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minefields of agricultural land, crop decline,
significant economic losses, insufficient
resources, destroyed or damaged agricultural
enterprises. The share of regions in agricultural
production was analyzed, the leader and the
outsider regions were distinguished. The study
analyzed the impact of the agricultural sector on
the development of the Carpathian Economic
Region of Ukraine, which includes the Lviv,
Chernivtsi, Transcarpathian and Ivano-Frankivsk
regions. The results of the study demonstrate a
significant relationship between the parameters
of the volume of agricultural products sold and
the gross regional product in Lviv (0.8801),
Chernivtsi (0.8962), Transcarpathian (0.9674)
and Ivano-Frankivsk (0.8985) regions. Also, the
results of the calculations prove that the defined
regression model is significant and corresponds
as closely as possible to the real functioning
model for all four regions.
Keywords: agricultural sector, agriculture,
agricultural business, region, regional economic
system, branding of agricultural regions.
Introduction
The agricultural sector plays a significant role in
the development of Ukraine’s economy and its
regions. There are regions in which the
agricultural sector is developing so rapidly and
successfully that it creates a regional brand.
Ukraine provides not only the domestic market
with food products, but also demonstrates
successful exports in this direction. It should be
noted that the agricultural sector is the main
source of employment for the rural population
and contributes to the development of rural areas.
The agricultural sector has a positive impact on
the health of the population due to the production
of environmentally friendly products. The
majority of modern agricultural enterprises
implement innovative technologies, which
contribute to increasing the efficiency of
management, reducing costs and increasing the
yield of crops. This increases the competitiveness
of the Ukrainian agricultural sector on the world
market. However, since the full-scale invasion of
Russia on the territory of Ukraine, the
agricultural sector has faced numerous
challenges and extremely difficult operating
conditions. Among the main problems, it is
appropriate to single out: dangerous of farmers’
work, limited access to land plots, equipment,
fuel and fertilizers, minefields of agricultural
lands, reduced harvest, significant economic
losses, insufficient resources, destroyed or
damaged agricultural enterprises, etc. However,
despite the listed problems, agricultural
enterprises, due to the support of international
partners, are trying to function and provide the
population with high-quality and affordable
products. This once again proves the important
role of the agricultural sector in the economy of
the country and its regions.
The purpose of the article is to study the role of
the agricultural sector in the regional economic
systems’ development.
Literature review
Many domestic and foreign scientists’ study
various aspects of agriculture development. Let's
consider some of them. The potential of
agriculture in contributing to the integrated
development of the regional rural economy was
analyzed within the scope of the study
(Loizou Efstratios et al., 2019). Scientists prove
the importance of agriculture and its significant
role in the economic growth of the region. The
results of the authors' research in four mountain
regions of Switzerland (Flury et al., 2008)
demonstrate the importance of agriculture in the
regional economy. The article proves that the
role of agriculture is determined not only by
direct employment and created added value, but
also by its impact on the rest of the economy. In
support of study (Bansah et al., 2023), it is
pertinent to note that small-scale agriculture is
largely rain-fed, and erratic rainfall and rising
250
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temperatures significantly affect crop production
and farmers' incomes.
The authors' study (Pradeleix et al., 2023)
analyzed the potential impact of irrigated
farming systems on the environment. The authors
assessed the impact of the agricultural region
under current conditions, and considered two
perspective scenarios. According to the authors
(Wanghai et al., 2023), agricultural production
depends on a variety of natural conditions in the
arid areas of northwest China. The authors note
the lack of coordination between agricultural
production and the ecological environment as
one of the urgent problems. Scientists have
studied the peculiarities of the development of
modern agriculture with the aim of balancing
ecological constraints and efficient use of
resources. Scientific work (Cervelli et al., 2023)
is devoted to the study of the analysis of spatial
policy and purposeful processes of landscape
planning and land use in the context of the
development of the agricultural sector. The
authors of the article offer approaches to
landscape planning and modern solutions to
environmental problems. Within the framework
of article (Aidat et al., 2023), the system of
greenhouse production, its significant
advantages for production in terms of quality and
quantity, creating a very important socio-
economic dynamic in the respective regions, is
investigated. According to the authors (Sutradhar
et al., 2023), assessment of regional differences
and recognition of underdeveloped areas are an
important aspect of achieving sustainable
regional development in agriculture. Scientists
evaluate the spatial distribution of agricultural
development and investigate the factors
responsible for this variability.
Article (Verma et al., 2023) argues that
agriculture, forestry and other land use is one of
the most important sectors for food security. To
reduce greenhouse gas emissions in the
agricultural sector, the authors of the study
propose to develop cost-effective mitigation
strategies and adaptation measures through
investments for adequate land and environmental
management.
The result of the article (Zhang et al., 2023) is to
prove that the green development of agriculture
and rural areas and economic growth are the
main challenges that are common in developing
countries. According to the authors, in the future
it is vital to promote the transformation of the
agricultural sector, while reducing the risk of
deterioration of the coordinated relationship with
economic growth. The main goal of the article
(Zafeiriou et al., 2023) is to investigate the
relationship between the use of pesticides in
agriculture per hectare of arable land and GDP
per capita in rural areas for twenty-five EU
countries. The authors are convinced that it is
advisable to take measures related to the
education of farmers, which will contribute to
increasing their awareness of environmental
issues. Fully supporting the results of research
(Muhammedov et al., 2023; Butko et al., 2019),
we would like to note that the role of agriculture
in ensuring food security, as well as creating jobs
and generating income from exports makes the
analysis of the impact of this industry on the
socio-economic development of the country
particularly relevant. The authors are convinced
that effective management of resources,
productivity improvement, creation of new jobs,
product promotion and production expansion are
important areas of the future development of the
agricultural sector.
However, despite significant results in this
direction of research, the issue of economic and
mathematical modeling of the impact of
agriculture on the Ukraine’s regions
development requires further research and
analysis.
Methodology
The article uses general scientific and specific
research methods, including: abstraction,
analysis and synthesis, generalization, statistical
and comparative analysis, dialectical and
graphic. Within the framework of the study, it is
proposed to investigate the impact of the
agricultural sector on the regions’ development
using the method of correlation and regression
analysis. The use of the specified methodology
will allow modeling the regularity of the impact
of the volume of agricultural products sold on the
gross regional product. Based on the analysis of
the available statistical information, it should be
noted that the outlined influence at the regional
level can be described using the construction of
one-factor models, and for their accuracy we
consider it appropriate to use the cubic type. The
stages of calculations are presented in Fig. 1.
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Figure 1. Stages of implementation of economic and mathematical modeling of the impact of agriculture
on the regions development.
Source: systematized by the authors.
+
+
+
+
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So, the specified methods and the presented
phasing of the scientific research made it possible
to analyze the development of the agricultural
sector and investigate the impact on the regional
economic systems’ development.
Results and discussion
The agricultural sector has a great impact on the
regional economy, providing a significant share
of the country's gross domestic product and
export potential. The cultivation of various
agricultural products in Ukraine allows to
provide the population with high-quality and
affordable food products and contributes to
ensuring the country's food security. If we
analyze the share of regions in agricultural
production, the leading regions include Vinnytsia
(8.3%), Dnipropetrovsk (6.2%), Poltava (5.9%),
Kyiv (5.7%), Khmelnytsky (5.6%), Kirovograd
and Kharkiv (5.2%) regions. The regions with the
smallest share in agricultural production are:
Transcarpathian (1.1%), Chernivtsi (1.6%),
Luhansk (1.9%) and Ivano-Frankivsk (2.0%)
regions (Fig. 2).
Figure 2. Share of regions in the agricultural production.
Source: calculated on the basis (State Statistical Service of Ukraine).
Within the framework of the study, we analyze
the impact of the agricultural sector on the
development of the Carpathian Economic Region
of Ukraine, which includes the Lviv, Chernivtsi,
Transcarpathian and Ivano-Frankivsk regions.
The initial data for calculations, namely the
volume of the gross regional product (GRP) and
the volume of realized agricultural products (AP)
for the period 2012-2021 are given in the Table
1.
Table 1.
Dynamics of the gross regional product and the volume of agricultural products sold in the Carpathian
Economic Region.
Year
Chernivtsi region
Transcarpathian region
Ivano-Frankivsk region
Lviv region
GRP, mln $
AP, mln $
GRP, mln $
AP, mln $
GRP, mln $
AP, mln $
GRP, mln $
AP, mln $
2012
1633.5
169.6
2655.6
329.5
4005.7
250.9
7687.6
357.7
2013
1685.9
142.3
2622.5
321.4
4068.1
266.5
7760.9
393.0
2014
1753.9
191.5
2811.2
327.7
4387.3
399.7
8499.2
755.6
2015
1107.5
135.9
1732.6
103.7
2744.1
263.7
5666.7
447.0
2016
558.2
45.0
851.2
22.4
1350.9
100.7
3018.2
157.9
2017
820.1
61.7
1234.9
35.4
1830.9
159.5
4226.9
241.1
2018
849.9
58.8
1314.7
32.9
1966.4
150.4
4443.0
284.5
2019
1135.5
59.4
1671.4
45.6
2362.5
171.1
5843.6
316.9
2020
1369.4
104.5
1885.2
57.3
2747.7
222.7
7180.9
368.4
2021
1406.4
76.7
1948.6
50.2
3083.7
176.9
7641.6
417.3
Source: calculated on the basis (State Statistical Service of Ukraine (n/f)).
0
1
2
3
4
5
6
7
8
9
Vinnytsia
Volyn
Dnipropetrovsk
Donetsk
Zhytomyr
Transcarpathian
Zaporozhye
Ivano-Frankivsk
Kyiv
Kirovograd
Luhansk
Lviv
Mykolayiv
Odessa
Poltava
Rivne
Sumy
Ternopil
Kharkiv
Kherson
Khmelnytsky
Cherkasy
Chernivtsi
Chernihiv
8,3
2,4
6,2
2,9
4,1
1,1
4
2
5,7 5,2
1,9
3,6 4,1 4,7
5,9
2,5
43,9
5,2 4,3
5,6 6
1,6
4,8
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The analysis of the impact of the volume of
agricultural products sold on the gross regional
product for the Lviv region is carried out as
follows. The value of auxiliary values necessary
for calculations is presented in the Table 2.
Table 2.
Results of calculations of auxiliary values (Lviv region)
Source: calculated by the authors
32 ;
4 3 2 ;
5 4 3 2 2 ;
6 5 4 3 3 .
823422412 1628666 3742 10 61960,
476158886678 823422412 1628666
a x b x c x nd y
i i i i
a x b x c x d x x y
i i i i i i
a x b x c x d x x y
i i i i i i
a x b x c x d x x y
i i i i i i
а b с d
аb
+ + + =
+ + + =
+ + + =
+ + + =
+ + =
+
++ 3742 25206312,
305408361016852 476158886678 823422412 1628666 11744315758,
1209965715303667230 305408361016852 476158886678 823422412 6274054684980.
сd
а Ь с сі
а b с d
+=
++
+
=
+ + =
+
823422412 1 628666 3742 1 0
476158886678 823422412 1 628666
= 3742 2,305
305408361016852 476158886678 823422412 1 628666
209965715303667230 305408361016852 476158886678 823422412
=9383239206676 30;е+
Solving the system of linear equations by Kramer's method:
61960 1 628666 3742 1 0
25206312 823422412 1 628666 3742
11
а= 1,0533228241132923 26
744315758 476158886678 823422412 1 628666
6274054684980 305408361016852 476158886678 823422412
е
а
а
+=
= 1,0533228241132923 26 0;
2,3059383239206676 30
е
е
=
+
+
823422412 61960 3742 1 0
476158886678 25206312 1 628666 3
b= 742 1,9293163646730278
305408361016852 1 1744315758 823422412 1 628666
209965715303667230 6274054684980 476158886678 823422412
е−= 29
1,9293163646730278 29 0,0837;
2,3059383239206676 30
е
bе
b
+
−
−= =
+
+
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823422412 1 628666 61960 1 0
476158886678 823422412 25206312
c= 3742 1,2365
305408361016852 476158886678 1 1744315758 1628666
209965715303667230 305408361016852 6274054684980 823422412
=
;
180089518777 32
1,2365180089518777 32
2,3059383 ,
2392 5
06 6
67 3 23
6 30 2
е
е
е
c
c
= =
+
+
+
823422412 1 628666 3742 61960
476158886678 823422412 1 628666
d= 25206312
305408361016852 476158886678 823422412 1 1744315758
209965715303667230 305408361016852 476158886678 6274
9,23408658
.
055352 33
054684980
9,23408658055352 33 4004,4812
2,3059383239206676 30
d
d
е
е
е
−
+
=
+
−
=
+
−=
So, the cubic one-factor regression equation,
which describes the influence of the volume of
agricultural products sold on the gross regional
product (GRP) of the Lviv region, will be:
GRP= – 0.0837AP2 + 53.6232AP – 4004.4812,
GRP – gross regional product of Lviv region;
AP - volume of agricultural products sold in Lviv
region.
Fig. 3 shows the dependence between two
indicators, namely the influence of the volume of
agricultural products sold on the gross regional
product of the Lviv region.
Figure 3. Graphic representation of the influence of the volume of agricultural products sold on the gross
regional product of the Lviv region.
Source: developed by the authors.
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Table 3.
The value of auxiliary values for evaluating the significance of correlation parameters (Lviv region)
Source: calculated by the authors
The correlation coefficient:
2
2.
6867918,6658
6
()
18
1 0,8801
(3
)04 481
ii
i
yy
Ryy
−
= − = −
−
The determination coefficient:
22
0,8801 0,7746.R=
Fisher's F-test:
‒ critical (tabular)
12
( , , ) (0,05,3,6) 4,7571.
tabl
F F a k k F= =
‒ factual
22
faсt 21
0,7746 6 6,8716.
1 1 0,7746 3
k
R
FRk
= =
−−
where k1 = m = 3, k2 = n – m – 1 = 12– 3 – 1 =
8, (a=0.05)
m – the number of parameters in the variables of
the regression equation.
Next, for the analysis of the influence of the
volume of agricultural products sold on the gross
regional product, we take the Chernivtsi region.
The value of the auxiliary values necessary for
calculations is presented in Table 4.
Table 4.
Results of calculations of auxiliary values (Chernivtsi region)
Source: calculated by the authors
32 ;
4 3 2 ;
5 4 3 2 2 ;
6 5 4 3 3 .
;19527793 133487 1045 10 12321
3095098343 19527793 133487 104
a x b x c x nd y
i i i i
a x b x c x d x x y
i i i i i i
a x b x c x d x x y
i i i i i i
a x b x c x d x x y
i i i i i i
а b с d
а b с
+ + + =
+ + + =
+ + + =
+ + + =
+
+ + =
+ + + ;5 1446391
514314716545 3095098343 19527793 133487 199771115;
88073231543207 514314716545 3095098343 19527793 30604113883.
d
а b с d
а b с d
=
+ + + =
++
+=
Solving the system of linear equations by Kramer's method:
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The cubic one-factor regression equation, which
describes the impact of the amount of agricultural
products sold on the gross regional product
(GRP) of the Chernivtsi region, will be:
GRP= 0.0015AP3 – 0.5699AP2 + 73.0908AP –
1693.1478
GRP – gross regional product of the Chernivtsi
region;
AP – the volume of agricultural products sold in
Chernivtsi region.
Fig. 4 shows the dependence between two
indicators, namely the influence of the volume of
agricultural products sold on the gross regional
product of the Chernivtsi region.
19527793 133487 1045 10
3095098343 19527793 133487 1045 3,814277662511121 23;
514314716545 3095098343 19527793 133487
88073231543207 514314716545 3095098343 19527793
е = = +
12321 133487 1045 10
1446391 19527793 133487 1045 565339319481689240000
199771115 3095098343 19527793 133487
30604113883 514314716545 3095098343 19527793
565339319481689240000 0,0015
3,814277662511121 23
а
а
а
е
= =
= =
+;
19527793 12321 1045 10
3095098343 1446391 133487 1045 2,1736585449016174 23
514314716545 199771115 19527793 133487
88073231543207 30604113883 3095098343 19527793
2,1736585449016174 23
3,814277662511121
b
b
b
е
е
= =
= =
+
−+
;0,5699
23е−
+
19527793 133487 12321 10
3095098343 19527793 1446391 1045 2,78788459895433 25
514314716545 3095098343 199771115 133487
88073231543207 514314716545 30604113883 19527793
2,78788459895433 25
3,814277662511
c
c
c
е
е
= =
= =
+
+;73,0908
121 23е
+
19527793 133487 1045 12321
3095098343 19527793 133487 1446391 6,458135938364854 26
514314716545 3095098343 19527793 199771115
88073231543207 514314716545 3095098343 30604113883
6,458135938364854 26
3,81
d
d
d
е
е
= =
= =
−+
−+
.1693,1478
4277662511121 23е−
+
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Figure 4. Graphic representation of the influence of the amount of agricultural products sold on the gross
regional product of the Chernivtsi region.
Source: developed by the authors.
Table 5.
The value of auxiliary values for evaluating the significance of correlation parameters (Chernivtsi region)
i
i
i
x
i
y
ŷ
і
хx−
2
()
і
хx−
і
2
і
і
А
і
1
169
1634
1537,1459
401,9
161523,61
96,8541
9380,7184
0,0593
—
—
2
142
1686
1438,6649
453,9
206025,21
247,3351
61174,6556
0,1467
150,481
22644,5311
3
191
1754
1805,1483
521,9
272379,61
-51,1483
2616,1534
0,0292
-298,4835
89092,3731
4
136
1108
1435,1257
-124,1
15400,81
-327,1257
107011,2395
0,2952
-275,9774
76163,5126
5
45
558
577,0035
-674,1
454410,81
-19,0035
361,134
0,0341
308,1222
94939,2894
6
62
820
1001,1246
-412,1
169826,41
-181,1246
32806,1039
0,2209
-162,121
26283,2277
7
59
850
939,8807
-382,1
146000,41
-89,8807
8078,5441
0,1057
91,2438
8325,4369
8
59
1136
939,8807
-96,1
9235,21
196,1193
38462,7714
0,1726
286
81796
9
105
1369
1414,3114
136,9
18741,61
-45,3114
2053,1184
0,0331
-241,4306
58288,7484
10
77
1406
1232,7143
173,9
30241,21
173,2857
30027,9431
0,1232
218,5971
47784,682
∑
—
—
—
—
1483784,9
—
291972,382
1,22
—
505317,8012
Source: calculated by the authors
The correlation coefficient:
The determination coefficient:
Fisher's F-test:
‒ critical (tabular)
‒ factual
where k1 = m = 3, k2 = n – m – 1 = 12– 3 – 1 = 8,
(a=0.05)
m – the number of parameters in the variables of
the regression equation.
The analysis of the impact of the volume of
agricultural products sold on the gross regional
product for the Transcarpathian region is carried
out as follows. The value of the auxiliary values
necessary for calculations is presented in Table
6.
2
2.
291972,382
1483 4
()
1 1 0,89
862
() 7 ,9
ii
i
yy
Ryy
−
= − = −
−
22
0,8962 0,8032.R=
12
( , , ) (0,05,3,6) 4,7571.
tabl
F F a k k F= =
22
faсt 21
0,8032 6 8,1639.
1 1 0,8032 3
k
R
FRk
= =
−−
258
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Table 6.
Results of calculations of auxiliary values (Transcarpathian region)
Source: calculated by the authors
Solving the system of linear equations by Kramer's method:
32 ;
4 3 2 ;
5 4 3 2 2 ;
6 5 4 3 3 .
105922566 341004 1326 10 18729,
34192164852 105922566 341004
a x b x c x nd y
i i i i
a x b x c x d x x y
i i i i i i
a x b x c x d x x y
i i i i i i
a x b x c x d x x y
i i i i i i
а b с d
а b с
+ + + =
+ + + =
+ + + =
+ + + =
+ + +
=
++ 1326 3207806,
11131499494926 34192164852 105922566 341004 898567190,
13632039679526764 11131499494926 34192164852 105922566 284214771776
d
а b с d
а b с d
+=
+ + + =
++
+=
105922566 341004 1 326 1 0
34192164852 1 05922566 341004 1 326
11131499494926
= 1,6997378314774298 26;
34192164852 1 05922566 341004
3632039679526764 1 1131499494926 34192164852 1 05922566
е+=
18729 341004 1326 10
3207806 105922566 341004 1326 1,465169819909349 23
898567190 34192164852 105922566 341004
284214771776 11131499494926 34192164852 105922566
1,465169819909349 23
1,6997378314774298
еа
а е
е
а
= = +
= =
+
+0,0009;
26
105922566 1 8729 1 326 1 0
34192164852 3207806 341004 1326
11131499494926
b= 7,081523586277719 25
898567190 1 05922566 341004
3632039679526764 284214771776 34192164852 1 05922566
7,081523586277719 25
1,69973783147
b
b
е
е
= −
=
+
=
−+
0,4166;
74298 26е−
+
105922566 341004 1 8729 1 0
34192164852 1 05922566 3207806 1 326
11131499494926
c= 8,90039704793933 27
34192164852 898567190 341004
3632039679526764 1 1131499494926 284214771776 1 05922566
8,90039704793933 27
1,699
еc
c
е=
=
+
+
=
;52,3634
7378314774298 26е
+
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259
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So, the cubic one-factor regression equation,
which describes the impact of the amount of
agricultural products sold on the gross regional
product (GRP) of the Transcarpathian region,
will be:
GRP= 0.0009AP3– 0.4166AP 2 + 52.3634AP +
6.0812.
GRP – gross regional product of yhe
Transcarpathian region;
AP – the volume of agricultural products sold in
Transcarpathian region.
Fig. 5 shows the dependence between two
indicators, namely the impact of the volume of
agricultural products sold on the gross regional
product of the Transcarpathian region.
Figure 5. Graphic representation of the influence of the amount of agricultural products sold on the gross
regional product of the Transcarpathian region.
Source: developed by the authors
Table 7 provides supporting data for evaluating the significance of the correlation parameters.
Table 7.
The value of auxiliary values for evaluating the significance of correlation parameters (Transcarpathian
region)
Source: calculated by the authors
105922566 341004 1 326 1 8729
34192164852 1 05922566 341004 3207806
111314994
d= 1,0336494102946565 27
94926 34192164852 1 05922566 898567190
3632039679526764 1 1131499494926 34192164852 284214771776
1,033649410d
d
е=
= =
+
.
2946565 27 6,0812
1,6997378314774298 26
е
е
+
+
260
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The correlation coefficient:
The determination coefficient:
Fisher's F-test:
‒ critical (tabl)
‒ factual
where k1 = m = 3, k2 = n – m – 1 = 12– 3 – 1 =
8, (a=0.05)
m – the number of parameters in the variables of
the regression equation.
The fourth region of the Carpathian Economic
Region is Ivano-Frankivsk. Let’s analyze the
impact of the volume of agricultural products
sold on the gross regional product of the Ivano-
Frankivsk region. The value of the auxiliary
values necessary for calculations is presented in
Table 8.
Table 8.
Results of calculations of auxiliary values (Ivano-Frankivsk region)
Source: calculated by the authors
Solving the system of linear equations by Kramer's method:
2
2.
249461,8354
36
()
19
1 0,9674
(8
)84 48,
ii
i
yy
Ryy
−
= − = −
−
22
0,9674 .0,9358R=
12
( , , ) (0,05,3,6) 4,7571.
tabl
F F a k k F= =
22
fakt 21
0,9358 6 29,1442.
1 1 0,9358 3
k
R
FRk
= =
−−
32 ;
4 3 2 ;
5 4 3 2 2 ;
6 5 4 3 3 .
147670237 533657 2167 10 28548,
45152219861 147670237 533657
a x b x c x nd y
i i i i
a x b x c x d x x y
i i i i i i
a x b x c x d x x y
i i i i i i
a x b x c x d x x y
i i i i i i
а b с d
а b с
+ + + =
+ + + =
+ + + =
+ + + =
+ + +
=
++ 2167 6867186,
14953511877876,998 45152219861 147670237 533657 1846115008,
15258131039007717 14953511877876,998 45152219861 147670237 547838235486.
d
а b с d
а b с d
+=
+ + + =
++
+=
147670237 533657 2167 10
45152219861 1 47670237 533657 2167
14953511877876,998 451522
= 1,3347003245641903 27;
19861 1 47670237 533657
5258131039007717 1 4953511877876,998 45152219861 147670237
е+=
28548 533657 2167 10
6867186 1 47670237 533657 2167
1846115008 45152219861 1
а= 8,117299831574964 22
47670237 533657
547838235486 1 4953511877876,998 45152219861 147670237
8,117299831574964 22 0,0001;
1,3347003245641903 27
е
е
е
а
а
=
−
−+
+−
+
= =
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261
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The cubic one-factor regression equation, which
describes the influence of the volume of
agricultural products sold on the gross regional
product (GRP) of the Ivano-Frankivsk region
will be:
GRP= -0.0001AP3+ 0.019AP 2 + 13.6147AP –
211.2456
GRP – gross regional product of the Ivano-
Frankivsk region;
AP – the volume of agricultural products sold in
Ivano-Frankivsk region.
Fig. 6 shows the dependence between two
indicators, namely the influence of the volume of
agricultural products sold on the gross regional
product of the Ivano-Frankivsk region.
Figure 6. Graphic representation of the impact of the volume of agricultural products sold on the gross
regional product of the Ivano-Frankivsk region
Source: developed by the authors
147670237 28548 2167 10
45152219861 6867186 533657 2167
14953511877876,998 1 846115008
b= 2,535663738503598 25
1 47670237 533657
5258131039007717 547838235486 45152219861 147670237
2,535663738503598 25 0,019;
1,3347003245641903 27
с
b
bс
е
=
= =
+
+
+
147670237 533657 2167 10
45152219861 1 47670237 6867186 2167
14953511877876,998 4515221
c= 1,817148554
;
0403015 28
9861 1 846115008 533657
5258131039007717 1 4953511877876,998 547838235486 147670237
1,8171485540403015 28 13,6147
1,3347003245641903 27
ec
c
e
е
=
= =
+
+
+
147670237 533657 2167 28548
45152219861 1 47670237 533657 6867186
14953511877876,998
d= 2,8194954381027008 29
45152219861 1 47670237 1846115008
5258131039007717 1 4953511877876,998 45152219861 547838235486
2,8194954381027008 29
1,3347003245641903
d e
d
e+=
= =
−
−+
.211,2456
27е−
+
262
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Table 9 provides supporting data for evaluating the significance of the correlation parameters.
Table 9.
The value of auxiliary values for evaluating the significance of correlation parameters (Ivano-Frankivsk
region)
Source: calculated by the authors
The correlation coefficient:
The determination coefficient:
Fisher's F-test:
‒ critical (tabular)
‒ factual
22
fact 21
0,8073 6 8,3765.
1 1 0,8073 3
k
R
FRk
= =
−−
Where k1 = m = 3, k2 = n – m – 1 = 12– 3 – 1 =
8, (a=0.05)
m – the number of parameters in the variables of
the regression equation.
The correlation coefficient should be in the range
from -1 to 1, and when it approaches 1, the
closeness of the interaction is stronger. With a
value of 1, the equation is generally functional
rather than correlational. So, it can be stated that
the dependence between the two parameters in
the Lviv (0.8801), Chernivtsi (0.8962),
Transcarpathian (0.9674) and Ivano-Frankivsk
(0.8985) regions is significant, according to the
model, the change in the volume of agricultural
products sold in the region leads to the change in
gross regional product. Taking into account the
rapid development of the agricultural sector
before the start of hostilities on the territory of
Ukraine, the above is quite real and justified.
Also, the results of calculations demonstrate a
situation when Ffact > Ftabl, which suggests that the
determined regression model is significant and
corresponds as closely as possible to the real
functioning model for all four regions.
Conclusions
The conducted analysis proved the significant
role of agriculture in the development of the
economy of Ukraine’s regions. Ukraine is an
agrarian country with a rich agricultural history,
but in today's extremely difficult conditions of
war, it faces extreme challenges, including:
worker safety, limited access to resources,
significant economic losses, destruction of
agricultural facilities, insufficient funding and
support, environmental risks and natural
resources, etc.
The following should be noted among the
promising directions that should be aimed at the
restoration of the agricultural sector and the
formation of branding of agricultural regions.
Implementation of the latest technologies, digital
solutions, modern methods of soil cultivation and
plant cultivation, will contribute to increasing the
productivity and quality of agricultural products.
Stimulating young farmers and agro-
entrepreneurs, providing financial and consulting
support, training and providing access to modern
technologies helps young specialists develop
their agricultural businesses. Attracting
investments in the agricultural sector, which
optimizes the processes of introducing
innovative technologies, will contribute to the
development of infrastructure and the creation of
jobs. The development of organic production in
the agricultural sector aimed at protecting the
health of the population and the environment. It
is also extremely important to establish
cooperation with international partners, which
will facilitate the exchange of experience and
technologies, and financial support. Support is
effective through the creation of state programs
2
2.
1843078,1639
95623
()
1 1 0,8985
(,81
)6
ii
i
yy
Ryy
−
= − = −
−
22
0,8985 .0,8073R=
12
( , , ) (0,05,3,6) 4,7571.
tabl
F F a k k F= =
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aimed at financial assistance, consultations,
ensuring access to markets and exports,
encouraging start-ups in the field of agricultural
entrepreneurship development.
However, in the conditions of war, for the
recovery and further development of the
agricultural sector, it is necessary to create a
favorable investment climate, ensure
transparency and stability in legislation, which is
currently a significant problem for Ukraine.
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