METHODOLOGICAL APPROACHES TO ANALYSIS OF CORRELATION RELATIONSHIPS BASED ON ECONOMIC STATISTICS

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International Journal of Civil Engineering and Technology (IJCIET)
Volume 10, Issue 05, May 2019, pp. 281-295, Article ID: IJCIET_10_05_029
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJCIET&VType=10&IType=5
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication
METHODOLOGICAL APPROACHES TO
ANALYSIS OF CORRELATION
RELATIONSHIPS BASED ON ECONOMIC
STATISTICS
A.M. Petrov
Doctor of Economic Sciences (Advanced Doctor), Professor of Department of the
Accounting, Analysis and Audit,
Financial University under the Government of the Russian Federation
T.M. Vorozheykina
Doctor of Economic Sciences (Advanced Doctor), Professor of Department of the
Accounting, Analysis and Audit,
G.I. Lukyanenko
PhD, Associate Professor of Department of the Accounting, Analysis and Audit,
L.A. Melnikova
PhD, Associate Professor of Department of the Accounting, Analysis and Audit,
ABSTRACT
Clear economic activity management is one of the most essential aspects of any
company’s stable financial standing under contemporary conditions. Economic
activity management at a company is impossible without an in-depth and detailed
study of all the processes related to it. Analytics is of paramount importance for
managing a company’s settlement system.
This article is devoted to analyzing of correlations/correlation relationships
analysis methods based on economic statistics. The correlation analysis is used to
measure the strength of a relationship between variables and to evaluate the factors
that affect the result attribute the most, which distinguishes it from regression analysis
used to select the relationship form, model type, to determine rated values of the result
attribute. The regression and correlation analysis methods are used holistically. Pair
correlation aimed at studying correlations of a factor attribute and a result attribute
can be regarded as the most developed theoretically and used in practice. Such study
is called single-factor correlation and regression analysis used as the basis for
studying multi-factor stochastic relationships. The article also examines the approach

Methodological Approaches to Analysis of Correlation Relationships Based on Economic
Statistics
of chain substitutions as a method of deterministic factor analysis in an accounting
and financial management system.
Key words: correlation relationships, stochastic analysis, correlation analysis, factor
analysis methods, factor analysis models
Cite this Article: A.M. Petrov, T.M. Vorozheykina, G.I. Lukyanenko,
L.A. Melnikova, Methodological Approaches to Analysis of Correlation Relationships
Based on Economic Statistics, International Journal of Civil Engineering and
Technology 10(5), 2019, pp. 281-295.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=10&IType=5
1. INTRODUCTION
Economic analysis is an essential element of the corporate management system [1, 3, 5].
Economic analysis is understood as a set of methods to determine the material and financial
position of an economic entity within a passed period, as well as its potential possibilities.
The company’s earning power has become the main efficiency criterion in the competitive
business environment. From this perspective, we can formulate the economic analysis
purpose as determination of the most efficient ways to achieve profitability.
The main economic analysis tasks are as follows:
 Profitability analysis (profitability management in terms of financial stability assessment,
budgeting, liquidity analysis as the correlation of receipts and payments).
 Analysis of operational and financial risks to prevent losses or refinance them.
Economic analysis is based on various initial information. All information sources can be
divided into regulatory and planned, accounting, and extra-accounting. Individual streams are
specified in the diagram of Fig. 1.
Figure 1 Tentative diagram of information necessary to take management decisions
Official documents and
regulatory and planned sources
 State laws
 Presidential decrees
 Decrees of the
government and local
authorities
 Superior orders
 Economic and legal
documents (contracts,
arbitraments, court judgments
etc.)
 Resolutions of
shareholder meetings
 Business plans
 Budgets
Accounting information
sources
 Synthetic and analytic
accounting data
 Financial statements
 Management accounting
and accountancy data
 Statistical accounting
and accountancy data
 Routine accounting and
accountancy data
 Fiscal accounting and
accountancy data
Extra-accounting information
sources
 Materials, certificates, reports
of regulatory authorities (auditors,
inspectors, revenue authority, banks
etc.)
 Laboratory, medical, and
sanitary examination reports
 Findings of professional
consulting firms
 Information from mass media,
Internet, regional statistics
departments
 Results of personal contacts
with contractors
 Technical and process
documentation
 Special examinations (time
study)
 Reporting notices,
correspondence with contracting
parties
 Advertising
 Selection and
concentration of accounting,
reporting, and other
information
 Secondary estimation
information and analytics
 calculation and
estimation of factor and result
indicators
 Ratings
 Documents for
presentation of analysis
results
 Textless analysis based
on organized information
 Graphs, diagrams etc.
Business summary information
to choose a management
decision

A.M. Petrov, T.M. Vorozheykina, G.I. Lukyanenko, L.A. Melnikova
Various types of economic analysis are distinguished depending on goals and tasks,
subjects of research and information sources, analysis procedure (Fig. 2).
Figure 2 Economic analysis types
The operational analysis is used for tracking of the deviation rate from the normal course
of business; for prompt identification of the inner and outer reasons that caused deviations; for
assessment of the current situation from the perspective of performing external liabilities; for
development of management decision options depending on the deviation parameters and the
need for interference of managers of different levels.
The operational analysis is focused on assessment of performing current tasks to a great
extent and, as a rule, it is carried out for a limited and occasionally reviewed range of
indicators and parameters for prompt response from managers.
Primary and statistical accounting is used as information sources; business accounting for
responsibility and cost centers; accounting of norm alterations and deviations from them, if
the normative cost accounting method is actually implemented; materials of direct activity
observations; conversations with unit managers and contractors; expert and specialist
estimates, and other sources [6, 7, 8, 9].
Sampling express analysis is an independent type of operational analysis.
Operational analysis corresponds closely to short-term predictive analysis for the
remaining days of a month/quarter.
Predictive analysis gains particular significance in the modern context. Intensification of
pre-production studies and analytic and predictive support are widely used in strategic
management. Analytic and predictive activities are carried out in such directions as marketing
research, company situation analysis, and environment analysis/scanning.
Marketing research includes studying the trends of demand development, formation of
new buyer wants, consolidation of the company’s competitiveness, and other directions.
Economic analysis
types
Operational
analysis
Sampling express
analysis
Predictive/strategic
analysis
Marketing research
Internal activity
analysis
Environmental
analysis
Economic scanning
Technical scanning
Political scanning
Comparative
analysis
Benchmarking
Retrospective
analysis
Functional-cost
analysis
Margin analysis
Risk analysis

Statistics
Analysis of the company’s situation is associated with identification of problems and
applicability of internal resources by comparing the main company’s features with
corresponding parameters of the major competitors, as well as with studying of problem
domains for future management activities and development [22, 19, 12, 11].
Economic scanning (behavior analysis of macroeconomic performance, the economic
and competitive situation in the industry, the situation in the financial markets etc.) involves
environment scanning as a method of analysis; technical scanning (changes in the course of
research and engineering competition, occurrence of essential innovations, unconventional
use of known technologies etc.); political scanning (assessment of the overall political
situation, stability of government, the regulatory economics system, stability and rationality of
economic management; economy legislation efficiency; the extent of political risk of
investment in a particular region etc.).
As we can see, the goals and tasks of predictive/strategic analysis, as well as the diversity
of its study subjects are quite complicated. The qualitative and substantive aspects are
essential methods of economic analysis used for predicting, the quantitative methods of
analysis play a supporting role. Correlation and regression analysis are also of considerable
importance.
2. MATERIALS AND METHODS
The purposes and objectives of the research were achieved using the methods of observation,
sampling, grouping, systematization, comparison, generalization. Analysis of theoretic and
practical materials enabled drawing of conclusions and development of recommendations.
Contemporary comparative analysis has a special efficient direction – benchmarking
based on activity comparison of both competitors and leading companies of other industries.
The peculiarity if this analysis type consists in strategic planning based not on the tasks
determined by accomplishments, but on studying the most successful parameters both in the
own and other industries. It is aimed at strategic activity optimization and development of
measures to eliminate the gap in the indices of own business and that of the competitors in
order to get the most of economy innovations.
Method development and improvement of benchmarking as a special strategic analysis
direction enables incorporation of new philosophy for assessment of competitive performance
of business, when its highest level is attributed to continuous improvement of the best and to
the ability of staying ahead.
Despite the doubtless independent role of predictive analysis in the strategic management
mechanism, one should not neglect the fact that it is closely related to subsequent
retrospective analysis. Strategic business management is impossible without using results of
retrospective analysis.
Contemporary business is closely related to enhancement of the role of functional-cost
analysis; its core principle is studying the functionality of analysis subjects and the costs for
their implementation in order to minimize the latter at high quality of products, goods, work,
and services. This type of analysis is distinguished by the creative nature of analytical studies,
innovative thinking, and wide use of heuristic analysis methods.
Commercial activities of companies contribute to prevalence of margin analysis based on
studying the relationship and correlation of costs, volume, and profit, as well as on dividing
costs into constant and variable. It is the so-called CVP analysis (cost-volume-profit analysis).
It is sensitive analysis widely used abroad for business profit management, optimization of the
profit parameters depending on the level deviations of volume parameters, specific variable
costs, unit price etc. [2, 22, 13, 10].

From the point of view of developing special procedures, commercial risk analysis is in
a formative stage; it is of great importance as companies carry out their activities under
uncertainty and in the presence of risky business situations.
Economic analysis involves the dialectic approach and the methods of studying,
measurement, and generalization of the influence of numerous factors on variation of
company performance results to improve them, namely:
 Studying of events and processes in motion, in development, in progress.
 Identification of beneficial and negative impacts, internal contradictions.
 Determination of cause-effect relationships between events and processes.
 Research of quantitative characteristics of cause-effect relationships.
 Assessment of analysis subjects as complicated systems with specification of development
factors and causes.
 Generalization and development of metrics for integrated and comprehensive studying of
cause-effect relationships between events and processes in economic activities.
The method is implemented via particular procedures depending on purposes, tasks,
subjects, means, and hardware of research.
The research method is closely related to the procedure used to implement it. A procedure,
as a set of rules and means for reasonable implementation of any work, is always specific and
includes the following items:
 Identifications of purposes, tasks, and users of analytic information.
 Selection of metrics to study and simulate their relationship.
 Selection of research methods, techniques, and hardware.
 Preparation of information sources for performance of analysis.
 Interpretation of the research results.
 Presentation of analysis results.
The hub element of the procedure is selection of metrics to study the objects and subject-
matter of analysis, as well as development of their relationship models. Measurement of
cause-effect relationships in economic analysis, evaluation of the results of other factors
influence on the final indices, and initial processing of source information are performed
using special tools means and techniques. Means and techniques of economic analysis are the
most important components of its procedure (Fig. 3).

Statistics
Figure 3 Means and techniques of economic analysis
In practice, solution of any analytic question in various contemporary business areas is
impossible without corresponding calculations, for example in financial evaluation,
description of factor models, factor calculations, relationship study of quantitative
characteristics, integrated assessment of commercial activity results etc. Analysts will be
constantly assuring themselves of this both studying the economic analysis theory and in
practice [4, 17, 11].
3. RESULTS AND DISCUSSION
Let us review the methods of studying correlation relationships on the basis of stochastic and
correlation analysis.
Stochastic relations between numerous events and their attributes are distinguished from
strictly determined functional relations by the fact that a dependent variable (a result attribute)
is affected by both the independent factors under analysis and a number of
uncontrolled/random factors. Besides, it should be noted that the complete list of factors is
unknown initially, as well as the way they affect the dependent variable. In this context, the
result attribute values cannot be measured precisely, they can only be determined with some
probability as they are subject to random scatter with inadvertent errors in measurement of
variables.
Studying stochastic relations, analysts should identify them, quantify their relationships,
identify the form of relations between result and factor attributes, and suggest its analytic
expression [18, 20, 21]. Regression and correlation analysis solve all of these issues.
Measurement of the relationship strength between variables is a task of correlation
analysis which is also used to assess the factors that affect the dependent variable most of all.
As distinct from correlation analysis, regression analysis is used to select the model type,
relationship form, to determine the rated values of the result attribute (dependent variable).
The regression and correlation analysis methods are used holistically. Pair correlation is
one of the most theoretically developed and practically used methods of studying correlations
Analysis means and techniques
Means of mathematical statistics
Conventional
information
processing
techniques
Mathematical
description of
factor models
Methods of
deterministic
and stochastic
factor analysis
Optimization of
indices
Methods of
financial
evaluation and
assessment of
business risks
Heuristic means
Means of
creative search
Intuitive means
Expert
estimates

between a result attribute and a factor attribute (single-factor correlation and regression
analysis). Such type of analysis is the basis for studying multi-factor stochastic relationships.
We turn our attention to the method of single-factor correlation and regression analysis.
The linear correlation coefficient (r) is a rather objective index to analyze the correlation
degree of two variables. This coefficient measures the linear dependence degree between two
variables, one of which is the result index (y) and the other is the factor index (х). The
correlation coefficient can vary from –1 to +1. Besides, the values of r close to +1 or –1
indicate high dependency between two variables.
The calculation algorithm of this coefficient is given below:
,
2222




 



 




ynyxnx
yxnxy
r
n is the number of sampled data.
y is arithmetic average of the result index.
x is arithmetic average of the factor index.
Let us study the dependence between sales revenue and business expenses for advertising.
Then we evaluate the nature of correlation between the two variables using the correlation
coefficient where the factor index is expenses for advertising (х) and the result index is sales
revenue (у). Table 1 contain the source information for seven months.
Table 1 Initial data for analysis
Month
I II III IV V VI VII
Sales (revenue), mln. rubles 70 72 68 65 80 75 78
Advertisement expenses, thous. rubles 40 42 38 46 44 48 50
Table 2 determines the parameters of the derivative values necessary for further
calculations.
Table 2 Derivative values to determine the correlation coefficient
Result index n x y x2
y2
Xy
01 40 70 1600 4900 2800
02 42 72 1764 5184 3024
03 38 68 1444 4624 2584
04 46 65 2116 4225 2990
05 44 80 1936 6400 3520
06 48 75 2304 5625 3600
07 50 78 2500 6084 3900
Total: 7 308 508 13664 37042 22418
Let us calculate the average monthly values of the sales revenue and the advertisement
expenses, when analysis is being carried out, as well as their squared values x = 308 : 7 = 44;
y = 508 : 7 = 72.57;
2
x = 1936;
2
y = 5266.4.
Then we determine the correlation coefficient:

Statistics
   
.4716,0
88,140
44,66
4,19846
44,66
4,52667370421936713664
57,7244722418
2222









 



 




уnухnх
yхnху
r
Based on analysis of this correlation coefficient, we come to the conclusion that it is rather
difficult to comment it as the obtained correlation coefficient value is intermediate between 0
and 1, in other words, between no correlation and high correlation. It should be noted that the
correlation coefficient significance depends on the sampling volume to a large extent. Thus, at
the sampling of 100 value pairs, the correlation coefficient equal to 0.31 will be more
significant than that equal to 0.67 at the sampling of 20.
Additional studies and samplings within a longer period will make the correlation
coefficient more conclusive.
The determination coefficient is an alternative index of the dependence degree between
two variables. This coefficient is the squared correlation coefficient (
2
r ). The specified
determination coefficient can be expressed as percentage and reflects the variation value of
the result index (у) due to variation of other variable — the factor index (х). According to the
results of the example shown above, the determination coefficient was as follows: r = 0.47162
=
0.2224 = 22.24 %. It means that more than 22 % of variations in the sales revenue are
associated with variations in the advertisement expenses.
The twenty per cent level of dependence between the sales revenue and advertisement
expenses is supposed to signal that the advertising campaign should be continued.
Certainly, there may be situations where measurement of variables cannot be reliable and
accurate enough. In such case, it makes sense to measure the relationship between two
variables using the rank correlation coefficient:
 1
6
1 2
2



nn
d
r
,
wherein d is the difference between the rank pairs.
This algorithm is used to calculate the ranking correlation coefficient on the basis of the
source information about the correlation between variations of the sales revenue and the
advertisement expenses for the first seven months of the year shown in Table 1 above.
The ranking result are matched in Table 3.
Table 3 Derivative values to determine the ranking correlation coefficient
x 6 5 7 3 4 2 1
y 5 4 6 7 1 3 2
d -1 -1 -1 4 -3 1 1
d2
1 1 1 16 9 1 1
 2
d
= 30
   
4643,05357,01
336
180
1
1497
30.6
1
1
6
1 2
2






nn
d
r

56,211002156,04643,0 22
r %
In this example, the calculated values of the ranking correlation coefficient (0.4643) and
the correlation coefficient (0.4716) based on the same source data are very close. In some
cases, correlation between the ranks of two data sets is not accompanied by correlation
between the actual values of the sets. Then it is reasonable to get additional information,
increase the sampling, and, as a consequence, obtain more convincing calculation results.
The regression methods are used to determine dependence between two or more variables,
where dependence between a result variable (у) and a factor variable (х) can be expressed in
form of a mathematical model; for example, the following formula is used for linear
dependence:
вхау  .
It is a rectilinear equation of the regression line that reflects the relationship between у and
х and enables calculation of the expected value of у at given х. Such calculations can be used
for prediction, if necessary.
Coefficients ‘a’ and ‘в’ in the given straight-line equation are the regression parameters to
be defined. Parameter ‘а’ is the constant value of the result factor independent of factor
variations. Coefficient ‘в’ reflects the average variation of the result index subsequent to
variation of the factor value.
A system of equations obtained applying the least square method is used to determine the
regression parameters (‘a’ and ‘в’):
  хвnау
;
   2
хвхаху
,
Wherein n is the number of observations.
Using the information above (see Table 2), we calculate the regression parameters
depending on the sales revenue and advertisement expenses.
In the system of equations , we use the derivative values from Table 2.
508 = 7а + 308в;
22418 = 308а + 13664в.
Then, all members of the first equation should be multiplied by average value x which
equals 44 in our case:
44 * 508 = 44 * 7а + 44 * 308в.
In this case, the system of equations will be as follows:
22352 = 308а + 13552в;
22418 = 308а + 13664в.
By subtracting the first equation from the second equation, we obtain the following:

Statistics
66 = 112В; в = 66 : 112 + 0.5893.
Coefficient ‘a’ is calculated using the first equation and the following algorithm:
n
хву
а
 

;
64,46
7
308.5893,0508


а
.
We can compose a constraint equation using the obtained values of parameters ‘a’ and ‘в’
that describe dependence between the sales revenue and the advertisement expenses for our
case:
Y=а+вх=46.64+0.5893х.
The obtained constraint equation can be used to predict the sales value, if the
advertisement expenses, for example, change and amount to 65,000 rubles.
Y=46.64+0.5893х=46.64+0.5893*65000 rubles = 85,000 rubles
Correlation between studied phenomena can be not only rectilinear but curvilinear, as well
[14, 15, 16]. For example, if one index increases, the values of the other index can decrease
after a certain level. An example would be relationship between the production cost and the
production output, the labor efficiency and the age of employees. In those cases, rectilinear
correlation is observed between result and factor variables.
The following hyperbolic curve equation is used to reflect rectilinear correlation:
х
в
ау 
.
Parameters a and b are determined using the following system of equations:
 
х
вnfу
1
;
   











2
111
х
в
х
а
х
у
.
There is a large number of various equations to determine the nature and degree of
dependence between variables under analysis: parable, hyperbola, exponential functions etc. It
is necessary to be able to choose an equation that corresponds to the correlation nature
between variables and would be adequate to the economic analysis goals, the required level of
detail, and technical feasibility to carry out indicated analysis.
To increase the quality of correlation and regression analysis, it is required to fulfill a
number of conditions such as correlation coefficient significance, homogeneity of the
information under analysis, reliability of the constraint (regression) equation, and other
parameters.
Information homogeneity is evaluated depending on its relative distribution near the
average level; in this case, the mean-square deviation and the variation coefficient determined
for each factor and result index are used as criteria.
Absolute deviation if individual values from the arithmetic mean value is described by
mean-square deviation () calculated as follows:
n
xx 

2
)(

.

The relative measure of deviation from the arithmetic mean value (the variation
coefficient (V)) is determined using the following formula:
x
V


.
If variation is below 10 %, it is considered insignificant. It should be noted that in case the
variation coefficient exceeds 33 %, such unrepresentative observations should be excluded
from calculations.
Student t-test is an instrument to evaluate the correlation coefficient significance. The
following algorithm is used to calculate this criterion in case of single-factor linear
correlation:
2
1
2
r
n
rtэ



.
Besides, if the obtained empirical value of the criterion (tэ) exceeds the critical table value
(tэ > tт), such correlation coefficient should be considered as significant.
Significance of simple linear regression coefficients (‘a’ and ‘в’) can also be determined
using the Student t-test. Besides, validity of a single-factor regression model can be evaluated
using the F-test and the following formula:
12
2



m
mn
F
ост
y
э


,
Wherein
2
y
is variance along the regression line;
2
ост
is residual variance;
n is the sample volume, number of observations;
m is the number of parameters in the regression equation.
The regression equation should be considered eligible to be used in practice, if the rated
value of the F-test exceeds the table value (Fэ > Fт). As the higher the F-test value is, the more
accurate correlation between the factor and result indices will be in the constraint equation.
Then we consider the chain substitution method. The chain substitution method has been
used widely to measure influence of factors in deterministic models since it can be used in all
the types of deterministic models. According to this method, to measure influence of a factor,
its basic value is replaced with the actual value while the values of all other factors remain
unchanged. Subsequent comparison of the result indices before and after replacement of the
factor under analysis enables calculation of its influence on the result index variation. The
mathematical formulation of the chain substitution method used, for example, in three-factor
multiplicative models is as follows.
A three-factor multiplicative system:
оооо сваy 
.
Subsequent substitutions:
.
;
;
1111
3
11
2
1
1
усваy
сваy
сваy
о
оо




Statistics
Then the following actions should be taken to calculate influence of each factor:
.
;
;
23
12
1
ууу
ууу
ууу
с
в
о
а



Balance of deviations:
сва
о ууууу 1 .
We use a particular numerical illustration, where dependence of the result index on the
factor indices can be represented by a four-factor multiplicative model, to review the
calculation algorithm using the chain substitution method.
The cost of sold products is used as the result index. The goal is studying variation of this
parameter under the influence of the comparison base of a number of labor factors: the
number of workers, day-long and shift-long loss of working hours, and the hourly average
output. The source information is given in Table 1.
Table 1 Information for factor analysis of cost variation of sold products
Indicator
Designat
ion
Compari
son base
Report Absolute
deviation
Rate of
increas
e, %
Relative
deviation,
percentage
points
1. Sold products,
thous. rubles
РП=N 417000 432012 +15012 103.6 +3.6
2. Average annual
labor force, persons
СЧ 1700 1660 -40 97.65 -2.35
3. Total number of
the work man-days,
thous.
ОД 420 414 -6 98.57 -1.43
4. Total number of
work the man-hours
, thous.
ЧЧ 3360 3226 -134 96.01 -3.99
5. Work days of a
single worker per
year (p. 3 : p. 2)
Д 247 249 2 100.95 0.95
6. Average work
day duration, hours
(p. 4 : p. 3)
Ч 8 7.79 -0.21 97.40 -2.60
7. Hourly average
output, rubles
(p. 1 : p. 4)
СВ 124.11 133.92 +9.81 107.90 +7.90
8. Annual average
output of one
worker, thous.
rubles
(p. 1 : p. 2)
ПТ 245.29 260.25 +14.95 106.10 +6.10
Initial four-factor multiplicative model:
оооооо СВЧДСЧРПN 
417000 = 1700 х 247 х 8 х 124.11.
Chain substitutions:

ооо СВЧДСЧРПN  111
407188.2 = 1660 х 247 х 8 х 124.11.
оо СВЧДСЧРПN  1122
411042.9 = 1660 х 249 х 8 х 124.11.
оСВЧДСЧРПN  11133
400369.6 = 1660 х 249 х 7.79 х 124.11.
111144 СВЧДСЧРПN 
432012 = 1660 х 249 х 7.79 х 133.92.
The calculations of the influence of factor indices variation are given below.
1. Average annual labor force variation:
..8,98112,4071884170001 ртысРПРП о 
2. Variation of the number of work days of a worker:
..7,38542,4071889,41104212 ртысРПРП 
3. Variation of the average work day duration:
..3,106736,4003699,41104223 ртысРПРП 
4. Hourly average output variation:
..4,316426,40036943201234 ртысРПРП 
Balance of deviations:
..150124170004320121 ртысРПРП о 
..150124,31642)3,10673(7,3854)8,9811(1 ртысРПРП о 
The calculation results of the chain substitution method depend on the properly
determined hierarchy of factors and on sorting the factors as quantitative and qualitative.
Variation of quantitative multipliers should take place before that of the qualitative
multipliers.
4. CONCLUSION
To ensure efficient development of an economic entity, it is necessary to be able to take
management decisions that are often related to the need to clearly identify both the bottleneck
area and the most potentially efficient area of the business economics to focus efforts on.
Thus, it is necessary to realize the influence power of particular factors as compared to other
factors, for example, when using multi-factor regression models to understand the influence
of a factor index on the result index. It is reasonable to use beta coefficients and coefficients
of elasticity in such cases.
Partial coefficients of elasticity (Эi) indicate increase of the result attribute and expected
increase of the result attribute expressed as percentage in case the factor attribute increases by
1 %. The calculation algorithm to determine a partial coefficient of elasticity:
i
i
ii
y
x
bЭ 
.
Regression coefficients do not reflect which factor affects the result attribute more. This is
due to the fact that the coefficients are measured in different units and variation of the factor
attributes is not considered.

Statistics
In case the specified coefficients are expressed in fractions of the mean-square deviation
(), i.e. the standard  coefficients are calculated (i), the variables in the regression equation
will be comparable:
i
xi
ii b


 
Wherein i is the mean-square deviation of the result index.
xi is the mean-square deviation of i factor.
 coefficient reflects the part of its mean-square deviation by which the result index
changes, if the factor attribute changes by the value of its single standard deviation. Thus, the
higher the  coefficient is, the stronger influence of the factor under analysis on the result
attribute will be.
REFERENCES
[1] D. Bell. Future Post-Industrial Society. Experience of Social Forecasting. M., 1999, 578 p.
[2] S. Belyakov. Modernization of Education in Russia: Management Development. Maks
Press, Moscow, 2009, p. 437 (359 — 361).
[3] A framework for PEST analysis based on fuzzy decision maps. Maikel Leyva Vázquez;
Jesús Hechavarría Hernández; Noel Batista Hernández; José Abel Alarcón Salvatierra;
Oiner Gómez Baryolo
[4] A study of the Internet and connectivity in South American countries to 2017: An
analytical perspective. Jorge Vinueza-Martínez; Mirella Correa-Peralta; Denis Mendoza-
Cabrera
[5] Actual problems of land monitoring in the Russian Federation. Kustysheva Irina
NIKOLAEVNA; Skipin Leonid Nikolaevitch; Petukhova Vera Sergeevna; Dubrovsky
Alexey Viktorovich; Martynov Olesya Igorevna
[6] Akhmadeev, R.G. , Bykanova, O.A. , Philippova, N.V. , Vashchekina, I.V., Turishcheva,
T.B. (2018) Macroeconomic indicators and their impact on the foreign debt burden: The
case of BRICS countries. International Journal of Economics and Business
Administration, 6 (2), pp. 68-82.
[7] Akhmadeev, R.G., Bykanova, O.A., Morozova T.V., Safonova E.G., Turishcheva, T.B.,
Lehoux, L. (2018) Evaluation of Financial and Analytical Activities of the Biggest Car
Makers of the Russian Federation. Jurnal Pengurusan, 54, pp. 18 -36
[8] Akhmadeev, R.G., Bykanova, O.A., Turishcheva, T.B. (2018) Brics' foreign debt burden
and its impact on core institutional basis. Journal of Reviews on Global
Economics, 7, pp. 345-359.
[9] Akhmadeev, R.G., Kosov, M.E., Bykanova, O.A., Korotkova, E.M., Mamrukova,
O.I.(2016) Assessment of the tax base of the consolidated group of taxpayers in Russia
using the method of polynomial interpolation. Indian Journal of Science and
Technology, 9 (12), 89533
[10] Braian A. Vtoraia ekonomika [Elektronnyi resurs]. – Rezhim dostupa:
http://www.obs.ru/article/1887/ (data obrashcheniia: 14.12.2016).
[11] Crisis y economía sumergida en Norte de Santander (Colombia). Jorge Ramírez
Zambrano; Johanna Milena Mogrovejo; Liliana Marcela Bastos Osorio
[12] Evolutionary institutional analysis and prospects of developing tax systems. Оlga N.
Grabova; Alexander Evgenievich Suglobov; Oleg Gennadievich Karpovich

[13] Gartner: Programmiruemaia ekonomika izmenit vsë [Elektronnyi resurs] – rezhim
dostupa: https://bitnovosti.com/2015/12/11/gartner-says-programmable-economy-will-
disrupt-global-economy/
[14] Information technologies for monitoring the territory of subsoil use. Valentina Alekseevna
Budarova; Natalia Viktorovna Cherezova; Alexey Viktorovich Dubrovskiy; Natalia
Grigorievna Martynova; Julia Dmitrievna Medvedeva
[15] Kevorkova, Z.A., Petrov, A.M., Savina N.V. Towards liabilities of corporate systems.
International Journal of Civil Engineering and Technology. Volume 10, Issue 2, February
2019, Pages 1582-1593
[16] Liquidity risk evaluation. Galiya jaxybekova; aliya nurgaliyeva; azhar nurmagambetova;
nazira gumar , altynai asanova
[17] Lymar, M.P., Kevorkova, Z.A., Petrov, A.M. The convergence of national and
international accounting standards: Chinese experience. International Journal of Civil
Engineering and Technology. Volume 9, Issue 13, December 2018, Pages 82-94
[18] New «connectography»: networks of cities in the global world. Daria E. Dobrinskaya;
inna a. Vershinina
[19] Philippova, N.V., Akhmadeev, R.G., Bykanova, O.A., Chaykovskaya, L.A. (2018) Social
equity: A route to progressive taxation of individuals. European Research Studies
Journal, 21 (4), pp. 317-330.
[20] Selection decisions based on the scenario of cash flows. Vasiliev Vladimir Dmitrievich;
Vasiliev Evgeny Vladimirovich
[21] Specially protected natural areas as an object of investment activity. Bogdanova Olga
Viktorovna; Chernykh Elena Germanovna; Kryakhtunov Alexander Viktorovich
[22] T.P. Karpova, A.M. Petrov, O.V. Antonova Directions of Accounting Development in the
Conditions of Digitalization. Jour of Adv Research in Dynamical & Control Systems, Vol.
10, 07-Special Issue, 2018, pp. (117-125)

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