European International Journal of Pedagogics
44
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TYPE
Original Research
PAGE NO.
50-53
DOI
OPEN ACCESS
SUBMITED
30 October 2024
ACCEPTED
19 December 2024
PUBLISHED
20 January 2025
VOLUME
Vol.05 Issue01 2025
COPYRIGHT
© 2025 Original content from this work may be used under the terms
of the creative commons attributes 4.0 License.
Skills required to perform
two-factor econometric
analysis
Ravshanova Mukhayyo Makhmanazarovna
University of Economics and Pedagogy, Uzbekistan
Abstract:
In this article, the author provides information
on the selection of factors, the implementation of
correlation and regression analysis. The construction of
an econometric model is shown step by step.
Information is also provided on the stage of generating
a regression equation using correlation coefficients and
a system of normal equations.
Keywords:
factor, endogenous, exogenous, correlation,
linear and nonlinear relationships, regression, least
squares method, econometric model.
Introduction:
Students can be taught to perform two-
factor econometric analysis using several steps.
Specifically:
Stage 1. Selection of factors. They learn to classify
statistical data and work with economic factors.
Statistical classification is understood as the processing
of collected data from the point of view of the goals and
objectives of scientific research. One of the most
common methods of processing and analyzing statistical
observation data is grouping. In statistics, grouping
refers to the division of units of a set into the same
groups and subgroups according to their most
important characteristics.
Stage 2. Working with factors. Data obtained as a result
of statistical observations for the purpose of studying
economic processes are signs that represent a certain
aspect (edge) of the process, which are divided into
resulting and influencing factors in the process of
change. If a change in one sign also changes the second
sign, then the first sign is called a factor sign, and the
second sign is called a resulting sign, and these show the
interrelation of factors and are expressed as follows:
𝑦 = 𝑓(𝑥
1
, 𝑥
2
, … 𝑥
𝑛
).
Here, y is the outcome variable, and xi are the factor
European International Journal of Pedagogics
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European International Journal of Pedagogics
variables.
Variables are divided into dependent and independent
variables.
Whether
they
are
dependent or
independent is determined based on the results of
correlation analysis.
Factors have their own qualitative and quantitative
aspects. Signs that are expressed in numbers are called
quantitative signs, signs that are not expressed in
numbers, that is, expressed in words, expressing the
qualitative side of factor and resultant signs are called
attributive signs. Factors must be quantitatively
measurable. If factors consist of qualitative indicators
that cannot be measured quantitatively, they must be
quantified (for example, a resultant sign - the quality of
soil that affects productivity - a factor sign should be
converted into a value, not a score).
In the study of economic processes, the factors studied
are divided into endogenous and exogenous factors. In
economic processes expressed by a system of
equations, the resulting characteristics ui, that is,
dependent variables, are called endogenous factors.
Exogenous variables are previously defined variables
that affect endogenous variables but are not
dependent on them, usually denoted as x.
Stage 3. Correlational connection.
The concepts of types, shape, and density of
correlations are presented with the participation of 3
students.
The relationship between factors is divided into 2
types: functional relationship and correlation
relationship.
Depending on the direction of the change, bonds are
divided into two types: direct bonds and inverse bonds.
Depending on the form of analytical expressions,
connections are divided into two types: linear and
nonlinear connections.
In functional relationships, each value of one variable
corresponds to exactly one value of another variable.
Correlation analysis is based on determining correlation
coefficients and assessing their significance and
reliability..
The correlation coefficient (r) ranges from
–
1 to +1. If
there is no relationship between the factors, then there
is a direct relationship - if there is an inverse
relationship, then there is a functional relationship.
The level of bond density is usually interpreted as
follows. If
up to
–
weak connection;
–
Weaker than average density
binding;
–
average connection;
–
higher than average bonding;
–
Students provide information about
close contact.
Steps to establish teacher-student relationships.
Stage 4. Correlation task.
Students, divided into two groups, are given tasks on
direct and inverse correlation. Based on the distributed
tasks, they are divided according to the density of the
connection and analyzed. Through this presented task,
the groups complete the tasks.
Table 1.
Ye
ar
1-
y.
2-
y.
3-
yil
4-
y.
5-
y.
6-
y.
7-
y.
Y
1,
6
3,
2
5,5
8,6
11,
4
14,
9
22,
0
X
5,
4
7,
9
17,
4
23,
9
38,
8
60,
3
91,
5
Task 1
:
−
−
−
−
=
2
2
)
(
)
(
)
)(
(
y
y
x
x
y
y
x
x
r
i
i
i
i
xy
2
,
0
4
,
0
2
,
0
6
,
0
4
,
0
8
,
0
6
,
0
99
,
0
8
,
0
European International Journal of Pedagogics
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European International Journal of Pedagogics
The first group determines the correlation coefficient using the formula for calculating the linear correlation
coefficient..
Task 2:
The second group also determines the nonlinear correlation coefficient based on Table 1.
Stage 5. Regression task.
Students will construct a regression equation using the normal equation using the “Least Squares”
method based
on Table 1.
=
→
−
n
i
x
i
i
y
y
1
2
min
)
ˆ
(
"Least squares" method
system of normal equations:
=
+
=
+
=
=
=
=
=
n
i
n
i
i
i
i
n
i
i
n
i
n
i
i
i
y
x
x
b
x
a
y
x
b
a
n
1
1
2
1
1
1
.
,
(3.8)
From this system of equations, a and b can be found..
−
−
=
2
2
)
(
)
(
)
(
)
(
)
(
i
i
i
i
i
i
x
x
n
y
x
y
x
n
b
.
A regression equation is constructed based on the calculated values.
e
bx
a
y
+
+
=
Econometric analysis. Analysis of a two-factor
regression equation shows that an increase in the x-
exogenous (influencing) factor by one unit leads to an
increase in the y-endogenous (resultant factor) by b
units. If there is no factor x affecting the y-resultant
factor, the resulting factor will be equal to a (free
margin). Therefore, the obtained correlation and
regression coefficients are analyzed economically.
After the economic analysis, the students' knowledge is
assessed. The values calculated by the students are
checked in the Excel program with the active
participation of the students. The skills of the students
who calculate the correlation coefficient and construct
linear two-factor regression equations are assessed.
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