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OTHER WAYS TO BUILD CORRELATION
MODELS
Sh. B. Ochilov, A. N. Tagaev, O.K.Khudayberdieva
Bukhara, Uzbekistan
Bukhara engineering technological institute
--------------------------------------------------------------***-------------------------------------------------------------
Abstract:
This article has developed a new
method for building production functions. On the
basis of accurate data, the methodology for
calculating the coefficients of any mathematical
models is shown.
Key
words:
production
function,
correlation
auxiliary information. This thing has the same drawbacks as in
medicine, physics and biology.
For instance, let
y
be the cotton yield and
x
be the amount of local fertilizer applied to the soil.
As a result of statistical analysis, it is known
analysis,
product
function,
approximation,
forecasting.
that the
y
18,0
1,6
x
link is established. In that
Introduction
Reflecting the main connections in nature and society in
mathematical language has always been one of the main problems of
science. Everyone
case, when 10 tons of local fertilizer is applied to 1
hectare of land, the employee who works in practice will never accept the
assertion that the yield will be
y
34
s
/
ha
as 100% correct.
So are there any ways to further increase the
knows that this problem has been solved in general cases in science. The
most complex methods of this
accuracy
level
of
the
y
f
x
1
;
x
2
; ...
x
n
process are the collection of statistical figures about an existing object, the
preliminary hypothesis that the function available on the basis of these
figures is reflective of this process, proving it in mathematical ways. By
this time, all specialists will effectively use this path.
Of course, there are shortcomings in this method, as well as in
certain shortcomings of any method. Predictions derived from the
construction of mathematical models in economics do not always provide
clarity. Everyone knows that seismology has a very low accuracy level of
forecasts based on models under construction.
Therefore, the results obtained from mathematical models in
many areas are used not as the main tool for compiling conclusions,
but as
correlation relationships that are being built, or their
role in their production, or are the methods used to date the last resort?
This article has tried to prove that there are such ways.
First of all, let's think about the fact that the most mistakes can come out
within the hypotheses that are made in tradition methods:
- The first shortcoming is that in our opinion is
y
i
- the results of
the experiment directly - correspond directly to a certain class
of functions.
- We think that the second shortcoming is that we do not take into
consideration the change nature in the experiments results obtained from
point to point.
INTERNATIONAL JOURNAL ON HUMAN COMPUTING STUDIES
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9
0
If it were possible to avoid the above drawbacks, then we would
increase the level of correlation that will be detected to real realities.
Research conducted in this way shows that in order to realistically
express the processes, we need to
look for the product of this function, not the
conclusions by comparing the numbers found using the new path with
the numbers found based on the connection found in the inaccessible
way.
relationship
y
f
x
1
;
x
2
;....
x
n
,
based
on
the
given statistical numbers.
With a fully constructed derivative function, it will not be
difficult to find a single integrated primary connection. Based on the
results of the given experiment, the structure of the derivative function
makes it possible to take into account the characteristics of the decrease in
the growth of the function, flexure– bending, which characterizes this
process.
Here
y
- is the cotton yield and
x
- is the amount of local
fertilizer applied to 1 ha of land.
y
Suppose
x
-
grows
linearly,
i.e
let
So on the basis of
y
i
-
we deal with the
problem of finding the product of the function, not
dy
a
dx
0
bx
. Let’s find this connection. In
y
i
x
the function itself.
the small squares method,
x
i
is used
It is known from the course of mathematical
y
y
x
y
f
x
x
f
x
instead of
i
i
instead of
i
0
analysis that
x
0
f
x
or
x
and we have the following system of equations.
y
i
1
y
i
f
x
0
for statistical
numbers.
9
y
9
a
b
x
x
Hence, if
y
- are statistical numbers and their
i
1
x
y
0
i
i
1
9
9
i
x
a
0
x
i
x
corresponding
x
i
are given
by
i
1,
n
, then at
у
x
i
1
i
1
n
1
points we can also find the values of the product
function
corresponding
to
the
point
corresponding to the points
x
i
. This allows us to
Based on the numbers above, we get the following and solve
this system to find the unknowns of the necessary coefficient.
34,83
9
a
40,8
b
f
x
0
find
. Let's take a brief example.
Provide information on cotton yields and
164,6
40,8
a
0
186,17
b
a
0
23,645
organic fertilizers used (figures are conditional). Based on them, we will
find a productive function and then integrate the main function.
We draw
b
6,07
i
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dx
2
1
2
That
is,
by
integrating
The first of the functions sought,
y
1
f
1
x
1
dy
23,645
6,07
x
,
c
is determined
based
dx
on
the
initial
condition
had already been calculated. So now we only calculate
y
2
f
2
x
2
. Taking the relevant data
y
23,645
6,07
x
dx
y
23,645
x
3,035
x
2
c
and
from the table №2 above, we construct an equations system for
y
2
f
2
x
2
y
3,035
x
2
23,645
x
69,5795 2y-3 is determined.
0,469
9
a
0
995
b
But using traditional methods it is possible to solve this
problem and find the linear function
y
18,212
1,6
x
. Now
the question arises as to
what if the process is in the form of a multivariable function. It should be
noted that in this case a lot of mathematical problems arise. In this
case, the
54,98
995
a
0
112011
b
Solve
the
equation
and
find
y
0,11989
0,001556
x
2
. But we found
dy
2
0,11989
0,001556
x
. Integrating it
2
problem cannot be solved in one attempt.
We propose to define this problem for each
on the basis of the condition
y
2
80
24
, we get
variable separately as
y
i
f
x
i
for each
variable,
y
2
28,62
0,11989
x
2
0,000776
x
.
2
and then to define the resulting function as the average of the
sum of the functions. That is
So
we
also
created
f
x
3,035
x
2
23,645
x
69,5795
1 1
and
y
f
x
;
x
;....
x
f
1
x
1
f
2
x
2
....
f
n
x
n
f
x
28,62
0,11989
x
0,000776
x
2
1
2
n
n
2
2
2
2
Let’s look at this solution in a concrete example.For convenience,
we consider the above example as a function of two variables rather
than
.
Now
the
resulting
relationship
y
f
x
1
;
x
2
49
11,8225
x
1
1,5175
x
0,0599
x
0,000388
x
2
one variable. Hence
y
- is the cotton yield; let
x
1
-
2
f
x
;
x
f
1
x
1
2
f
2
x
2
be the amount of local fertilizer (T) per hectare and
since
1
2
2
.
x
2
- be the amount of mineral fertilizer per hectare (kg). Below are
the results of several years of
This function can be used to estimate how close the
calculated relationship is to the actual
observations. Let
y
f
x
1
;
x
2
be required to
values by calculating the values at the corresponding
determine the relationship by constructing the product function.
points.
Now, based on the above numbers, let us
Table 2
construct a model of
2
INTERNATIONAL JOURNAL ON HUMAN COMPUTING STUDIES
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f
x
1
;
x
2
in the form
y
a
0
a
1
x
1
a
2
x
2
using traditional methods
INTERNATIONAL JOURNAL ON HUMAN COMPUTING STUDIES
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and compare the results with the results of the connection constructed
on the basis of the method we propose.
Table № 3
252,7
10
a
0
44,3
a
1
1075
a
2
1126,95
44,3
a
0
198,455
a
1
4838,5
a
2
27302
1075
a
4838,5
a
118407
a
0
1
2
Solving the equations system, we obtain
y
21,8344
1,12383
x
1
0,07827
x
2
.
Now
we
have
the
function
f
x
;
x
49
11,8225
x
1,5175
x
2
0,0599
x
0,000388
x
2
1
2
1
1
2
2
generated
by
the
new
method
and
y
21,8344
1,12383
x
1
0,07827
x
2
found
in the traditional method. Comparing the results obtained on the basis of
these two functions, it is possible to be sure that the proposed method
does not lag behind the traditional methods.
The following table shows
y
x
is an actual
experimental results,
y
T
are results calculated by
the traditional method,
y
is a sequence of
INTERNATIONAL JOURNAL ON HUMAN COMPUTING STUDIES
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Volume: III Issue: 3 May-June 2021
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numbers calculated by the proposed method.
But there are many questions that require mathematical validation.
1)
is the proposed method always effective?
2)
is it possible to compare these two methods mathematically.
3)
how the reliability of predictions can be assessed mathematically.
These are questions that need to be addressed in the future.
Reference
1.
Kremer N. Sh. Econometrics: textbook . – M.: Publishing House, 2018 Yurayt. – p 354.
2.
State statistics committee of the Republic of Uzbekistan [electronic resource] - access procedure:http://www.stat.uz
