Volume 05 Issue 04-2023
21
The American Journal of Social Science and Education Innovations
(ISSN
–
2689-100x)
VOLUME
05
I
SSUE
04
Pages:
21-27
SJIF
I
MPACT
FACTOR
(2020:
5.
525
)
(2021:
5.
857
)
(2022:
6.
397
)
(2023:
7.
223
)
OCLC
–
1121105668
Publisher:
The USA Journals
ABSTRACT
The article proposes an universal method for developing a correlation model that can be applied in solving economic
problems in planning and forecasting. Based on the equation of the developed correlation model, the number of labor
resources of the Bukhara region for the period 2021-2030 is predicted and their prospective trends are determined
KEYWORDS
Modelling, correlation model, labor resources, correlation and regression analysis, forecasting, accuracy, suitability,
labor market.
INTRODUCTION
Scientific management in economics is to ensure the
efficient use of factors. For this, you need to know how
many units this or that indicator will change if the other
changes by one. To study the intensity and form of
dependencies, correlation-regression analysis is used,
which is a methodological tool for solving problems of
forecasting, planning and analyzing the economic
activity of an enterprise.
A correlation model is a mathematical expression of
the equation type, in which the average value of the
effective indicator is formed under the influence of one
or more factors. It allows you to determine the
Research Article
DIFFERENTIAL METHOD FOR FORECASTING LABOR RESOURCES
BASED ON CORRELATION MODELS
Submission Date:
April 10, 2023,
Accepted Date:
April 15, 2023,
Published Date:
April 20, 2023 |
Crossref doi:
https://doi.org/10.37547/tajssei/Volume05Issue04-03
Sherali Baratovich Ochilov
Professor, Department Of "Economy", Candidate Of Economic Sciences, Uzbekistan
Oisha Kurbanovna Khudayberdieva
Assistant, Department Of "Management", Uzbekistan
Khusenova Mehriniso
Student Bukhara Engineering Technological Institute, Republic Of Uzbekistan
Journal
Website:
https://theamericanjou
rnals.com/index.php/ta
jssei
Copyright:
Original
content from this work
may be used under the
terms of the creative
commons
attributes
4.0 licence.
Volume 05 Issue 04-2023
22
The American Journal of Social Science and Education Innovations
(ISSN
–
2689-100x)
VOLUME
05
I
SSUE
04
Pages:
21-27
SJIF
I
MPACT
FACTOR
(2020:
5.
525
)
(2021:
5.
857
)
(2022:
6.
397
)
(2023:
7.
223
)
OCLC
–
1121105668
Publisher:
The USA Journals
expected value of the performance indicator. The
correlation model is used to check whether resources
are used correctly and to justify the value of economic
indicators for the future.
The main part. The existing method of constructing
correlation models of the type y=f(x) in the presence
of data on the state of the object under study y
𝑖
and x
𝑖
is widely used in the practice of planning and
forecasting. We described the shortcomings of this
method in published works. [1,2,3]
In this article, we propose a universal method for
determining the dependence of the type y=f(x) that
differs from the existing ones.
Let the real process proceed on some law y=f(x). And
let the function f(x) be continuous and smooth i.e. has
an n-th derivative. As you know, all the functions used
in predicting socio-economic phenomena are such.
And the data x
𝑖
at our disposal is the value of the
function y=f(x) at the points x
𝑖
.
Since in our condition the function (x) has an n-th
order derivative, then
(1)
Consequently
(2)
Accordingly
(3)
Based on (1), (2), (3), we can write the following equality:
(4)
Now let's look at a specific example.
The following table 1 shows real data on the population of the Bukhara region of the Republic of Uzbekistan in
the period 2016-2020. It is required to make a forecast for these indicators in the period, for example, 2020-2025.
Let
Based on this equality, we fill in other graphs of the table. Here
=
х
+1 and
accordingly
for all
𝑖
=1,
х
n
and
х
=1,
х
n
Volume 05 Issue 04-2023
23
The American Journal of Social Science and Education Innovations
(ISSN
–
2689-100x)
VOLUME
05
I
SSUE
04
Pages:
21-27
SJIF
I
MPACT
FACTOR
(2020:
5.
525
)
(2021:
5.
857
)
(2022:
6.
397
)
(2023:
7.
223
)
OCLC
–
1121105668
Publisher:
The USA Journals
Table 1
𝚝
i
𝚢
i
1
𝚈
2
𝚈
3
𝚈
4
𝚈
1
1815
-
-
-
-
2
1843
28
-
-
-
3
1870
27
-1
-
-
4
1894
24
-3
-2
-
5
1923
29
5
8
10
And so according to our data y
IV
, subject to y
III
. That’s why y
III
, from here
and
Thus
, at y
II
(1)=
and y
II
(1) = 5*1-12+
e
=-1
→
𝑒
=6.
That’s why
y
II
=∫(5
dx)
y
I
=5
→
y
I
(1) =28.
Further
=28
→
𝑒
=28-1,67
𝑒
=26,33;
y
I
=
, provided y (1)=1815;
y = ∫(
) dx=
x+
𝑒
y(1) =
→
e=1787
The desired function has the following form:
У
=
By checking this function, you can verify the suitability of the constructed model. But the proposed method has
the following disadvantages:
if the amount of data increases, then the degree of the polynomial y=
𝑓
(x) also increases in proportion to the
amount of data. For example, if the amount of data is n=20, then we get a polynomial of the 20th degree, after n=20
a short integrated;
Volume 05 Issue 04-2023
24
The American Journal of Social Science and Education Innovations
(ISSN
–
2689-100x)
VOLUME
05
I
SSUE
04
Pages:
21-27
SJIF
I
MPACT
FACTOR
(2020:
5.
525
)
(2021:
5.
857
)
(2022:
6.
397
)
(2023:
7.
223
)
OCLC
–
1121105668
Publisher:
The USA Journals
As an accuracy of the constructed models depends on
when solving economic problems
⃒
= 1. Especially if time series are considered, but when solving the problem of physics, chemistry and biology
∆
x=
can be reduced indefinitely, as this will depend on the desire of the scientific researcher conducting
the experiment.
When solving economic problems, it is possible to successfully apply the proposed method, limiting the
calculation
Table 2 shows data on labor resources for the Bukhara region of the Republic of Uzbekistan in the period 2010-
2020. It is necessary to make a forecast based on these indicators for the period 2021-2030. We use the above method.
At the same time, we limit ourselves only
or
.
Table 2
T
∆
1
971,9
-
-
-
2
1008,3
36,4
-
-
3
1025,7
17,4
-19
-
4
1035,1
9,4
-8
11
5
1045
9,9
0,5
8,5
6
1055,8
10,8
0,9
0,4
7
1065,4
9,6
-1,2
-2,1
8
1073,1
7,7
-1,9
-0,7
9
1081,6
4,7
-3
-1,1
10
1083,8
3,2
-1,5
1,5
11
1070,4
-10,6
-13,8
-12,3
Subsequently, to determine the function y=
𝑓
(x), we calculate the average value
Volume 05 Issue 04-2023
25
The American Journal of Social Science and Education Innovations
(ISSN
–
2689-100x)
VOLUME
05
I
SSUE
04
Pages:
21-27
SJIF
I
MPACT
FACTOR
(2020:
5.
525
)
(2021:
5.
857
)
(2022:
6.
397
)
(2023:
7.
223
)
OCLC
–
1121105668
Publisher:
The USA Journals
y
II
=-5,2 or
,2 provided y
I
(1) = 36,4
and 36,4=5,2*1+
𝑒
→
𝑒
=41,6
y
I
=
under the initial condition y (1) = 971,9
у
=-1,73
x
2
+
41,6
x
+
e
971,9 = -1,73
x
2
+
41,6
x
+
e
→
𝑒
= 932,03
As a result, this function looks like:
у
=-1,73
x
2
+
41,6
x
+932,03
To check the reliability of the found function, we compare the actual
and calculated values of the process
under study using the Excel program.
Table 3
971,9
1008,3
1028
1035
1048
1056
1065
1073
1077
1081
1070
971,9
1005,3
1034
1057
1076
1084
1098
1095
1099
1093
1082
0
+3
-6
-22
-28
-28
-32
-22
-22
-12
-12
If y
I
= (-1.73 +41.6x+932.03)
ˈ
= 0 then we get x =
= 12.02.
This means that the maximum value of labor resources reached in the period 12
. And in the future
there is a decrease in the number of labor resources in this area. For example, in 7 years the volume of labor resources
in the region will decrease by 20% (Table 4).
Table 4
Years
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
Number of
labor
resources
1182,28
1180,43
1174,6
1166,75
1154,72
1097,6 1120,08
1098,4 1072
1042,67
Volume 05 Issue 04-2023
26
The American Journal of Social Science and Education Innovations
(ISSN
–
2689-100x)
VOLUME
05
I
SSUE
04
Pages:
21-27
SJIF
I
MPACT
FACTOR
(2020:
5.
525
)
(2021:
5.
857
)
(2022:
6.
397
)
(2023:
7.
223
)
OCLC
–
1121105668
Publisher:
The USA Journals
Thus, the predicted value of the number of labor resources by 2030 will decrease by 28 thousand people
compared to 2020, this is 3%, which is primarily due to a decrease in population growth in the Bukhara region.
It should also be emphasized that finding and integrating the mean value
is not the only way to
establish the relationship y=
𝑓
(x).
Consider the data in table №1.
has the value
;
We
find
the
function
y
II
in
the
form
y
II
=
or
.
We will substitute x=1
y
II
(1)=
and find
and for
x
=2 y
II
2)=
and find
, then for x=3
y
II
(3)=5 find
.
And so our function looks like y
II
=
or
y
II
=
Now integrating twice the last function based on the initial conditions y
I
(1) = 28
и
y
I
(1) = 1815 we will define the
function. It looks like y=0,467
The suitability of this model can be tested by supplying x to the appropriate values.
Based on the above theory, the following conclusions can be drawn:
If in the available static data
or in other words ∆x =
then as in table 1.
We will find
, , where A = cong t or after replacing
with
we get. Integrating n times, we get
the required function.
If
does not go to zero, then
it violates. Therefore, it
is necessary to proceed as follows, it is enough to calculate ∆y,
or
.
In the next step, we will calculate these values. The average value and is replaced by ∆y,
,
by
у
I
, y
II
and
y
III
we get an equation like y
I
(x)= , y
II
, = or y
II
(x) = .. By solving these differential equations, we get this model.
At this stage, we will finish the calculations of ∆y,
,
, , and replace the point value of these variables with
a continuous function. For example, if the column
has only 3 data, then the function looks like this:
y
II
= (x) =
.
After integrating this function twice, we get this function.
Volume 05 Issue 04-2023
27
The American Journal of Social Science and Education Innovations
(ISSN
–
2689-100x)
VOLUME
05
I
SSUE
04
Pages:
21-27
SJIF
I
MPACT
FACTOR
(2020:
5.
525
)
(2021:
5.
857
)
(2022:
6.
397
)
(2023:
7.
223
)
OCLC
–
1121105668
Publisher:
The USA Journals
CONCLUSION
The most important advantage of the proposed
technique is the construction of correlation models
based on the definition of the derivative of the
function. Based on this, the desired function is not
taken from a certain function, but is obtained as a
result of successive integration. Mathematical
justification is the theorem of high approximation of
any continuous function using polynomials and degree
in the course of mathematical and functional analysis.
The model described in this article is the first step
towards building a truly functioning system for making
managerial decisions by regional authorities based on
a labor market forecast. The forecast of the situation
on the labor market is of great economic, social and
political importance. In conclusion it is important to
note that the proposed methodology lends itself to
computer programming and can be used in assessing
the prospects for the development of the labor market
in the development of employment promotion
programs, making a forecast of the main indicators of
the socio-economic development of the region.
REFERENCES
1.
Герасимов Б.И., Н.П.Пучков, Протасов Д.Н.
Дифференциальные динамические модели.
Учебное пособие. Тамбов: Изд
-
во ГОУ ВПО
ТГТУ. 2010. 80с.
2.
Очилов Ш.Б., Хасанова Г.Д. Aльтернативный
метод
построения
корреляционных
моделей.
Научно
-
методический
журнал
«Academy» № 6
3.
Ochilov S. B., Khasanova G. D., Khudayberdieva
O. K. Method for constructing correlation
dependences for functions of many variables
used finite differences //The American Journal
of Management and Economics Innovations.
–
2021.
–
Т. 3. –
№. 05. –
С. 46
-52.
4.
Ochilov S. B., Tagaev A. N., Khudayberdieva O.
K. Other ways to build correlation models
//International Journal of Human Computing
Studies.
–
1935.
–Т.
3.
–
№. 4. –
С. 1
-5.
5.
Sh. B. Ochilov, A. N. Tagaev, O.K.
Khudayberdieva
Other
ways
to
build
correlation
models.
(https://journals.researchparks.
org/index.
php/IJHCS/article/view/1935) 51-54.
6.
Бараз В. Р. Корреляционно
-
регрессионный
анализ связи показателей коммерческой
деятельности
с
использованием
программы Excel: учеб. пособие.
Екатеринбург: УГТУ
-
УПИ, 2005.
7.
Глинский В. В., Ионин В. Г. Статистический
анализ: учеб.пособие. М.: ИНФРА
-
М, 2002.
8.
Годовой
статистический
сборник
Республики Узбекистан 2010
-2020.. -
Т.: 2020.
-
396 с.
9.
Статистический
информационный
бюллетень Бухарской области. январь
-
декабрь 2020. Б.: 2020г.
10.
Худайбердиева
О.
К.
ТЕНДЕНЦИИ
СТРЕМИТЕЛЬНОГО РАЗВИТИЯ СФЕРЫ УСЛУГ
В
УЗБЕКИСТАНЕ
//ИННОВАЦИОННОЕ
РАЗВИТИЕ: ПОТЕНЦИАЛ НАУКИ, БИЗНЕСА,
ОБРАЗОВАНИЯ. –
2021.
–
С. 102
-113.
11.
Худайбердиева О. К. ЭКОНОМИЧЕСКИЕ
РЕФОРМЫ СФЕРЫ УСЛУГ В УЗБЕКИСТАНЕ
//АКТУАЛЬНЫЕ
ПРОБЛЕМЫ
РАЗВИТИЯ
НАЦИОНАЛЬНОЙ
И
РЕГИОНАЛЬНОЙ
ЭКОНОМИКИ. –
2021.
–
С. 216
-220.
