Candidate of economic Sciences,
Kabashova E.V.
MULTIPLE REGRESSION MODELS IN PREDICTING INCOMES
Currently building multiple regression models – one of the most common
methods in Economics.
The purpose of the study is to build a model based on per capita
monetary income of the population from the most significant factors to predict
them in the future.
Forecasting based on regression models allows to take into account the
expected levels of factor variables play different versions of the forecast at
different combinations of factor values.
To build the multiple regression equation is needed to solve the issue
of model specifications, please select the most significant factors affecting
income of the population and to select the regression equation.
Special attention when building a multiple regression should be paid to
selection factors, which is preceded by a qualitative analysis of the essence
of the category «income of the population».
The selection of factors in multiple regression we observed the
following requirements:
1) Compliance with qualitative and quantitative analysis, that is, the
regression equation should include only the essential factors that truly affect
incomes.
2) All factors included in the model, quantitatively measurable.
3) The accuracy of the indices depends on the use of official statistics
from Rosstat.
4) No redundant factors, i.e. each factor in the multiple regression
equation represented by only one sign.
5) No collinear factors, that is, which are interconnected in a linear
relationship. If between the factors there is a high correlation, it is
impossible to determine the isolated effect on the effective indicator, and the
parameters of the regression equation prove to be uninterpreted.
For econometric modeling and forecasting of per
capita monetary income of population is selected the following indicators:
X1 ‒ gross regional product per capita,
rubles;
X2 ‒ level of employment, %;
X3 ‒ unemployment rate, %;
X4 ‒ retail trade turnover per capita,
rubles;
X5 ‒ investment in fixed capital per
capita, rubles;
X6 ‒ share of population of working age, %;
X7 ‒ average monthly nominal accrued wages
of employees of organizations, rubles;
X8 ‒ share of social benefits in monetary
incomes, %;
X9 ‒ share of wages in monetary income of
population, %;
X10 ‒ gross harvest of grain per capita,
kg;
X11 ‒ gross agricultural production per
capita, thousand rubles;
X12 ‒ volume of paid services per capita,
rubles.
In general, the
selection of factors is made on the basis of qualitative theoretical and
economic analysis. However, theoretical analysis does not always give
unambiguous answers to the question of the quantitative relationship of the
considered characteristics and the usefulness of including the factor in the
model. Therefore, the selection of factors in our study was conducted in two
stages: 1) selection of factors based on the nature of the problem; 2)
selection of factors based on the matrix of pair coefficients of correlation
and determination of the student's t-test for the regression parameters.
Multiple correlation
and regression analysis is performed on the data of the Volga Federal district
(for 2015), which is composed of 14 regions.
The most important
and significant the multiple regression equation are presented in table 1.
Table 1 Econometric modeling of per capita monetary
income of population
in the Volga Federal district
|
¹ |
The
regression equation |
Multiple ratio of |
F-Fisher criterion |
|
|
correlation |
determination |
|||
|
1 |
|
0,955 |
0,913 |
57,62 |
|
2 |
|
0,973 |
0,947 |
97,83 |
|
3 |
|
0,951 |
0,905 |
52,50 |
To analyze the results of correlation and regression analysis.
Model 1. With the increase of retail trade turnover per capita of 1 rubles
per capita monetary income on the average on regions of the Volga Federal
district will increase by 0,13 rubles with the same level of investment in
fixed capital. With the growth of investment in fixed capital per capita of 1 rubles
per capita income at an average increase of 0,009 to rubles with the same level
of retail trade turnover.
Multiple correlation coefficient of 0,955 describes a strong link
between incomes and the factors X4
and X5. 91,3% of the variation of per
capita incomes is explained by the variation of the retail trade turnover and
investment in fixed capital.
As the actual F (57,62) more
than F tabular (3,98), then with
probability 0,95 we conclude about the statistical significance of the
regression equation as a whole and of the indicator of the closeness of the
connection which was formed under the influence of nonrandom factors X4, X5.
Model 2. By increasing the proportion of the population of working age
by 1% per capita income on the average on regions of the Volga Federal district
will be reduced by 880,40 rubles for the same level of average monthly nominal
accrued wages. With the growth of average monthly nominal accrued wages by 1 rubles
per capita, average income will increase by 1,92 rubles for a constant
proportion of the working population.
Multiple correlation coefficient of 0,973 describes a strong link
between incomes and the factors X6
and X7. 94,7% variation of per capita
monetary income of the population due to the variation in the proportion of the
working population and wage workers.
As the actual F (97,83) more
than F tabular (3,98), then with
probability 0.95 we conclude about the statistical significance of the
regression equation as a whole and of the indicator of the closeness of the
connection which was formed under the influence of nonrandom factors X6, X7.
Model 3. By increasing the share of social
benefits in monetary income of population by 1% per capita income on the
average on regions of the Volga Federal district will be reduced by 1305,60 rubles
at a constant share of wages. With the
increase in the share of wages in monetary income of population by 1% per
capita, average income will increase by 143,72 rubles at a constant share of social benefits.
Multiple correlation coefficient of 0,951 when
describes the strong relationship between income and factors of X8 and X9. In 90,5% of variation of per capita monetary income of the
population due to the variation in the share of social benefits and the share
of wages in the structure of monetary incomes of the population.
As the actual F (52,50) more
than F tabular (3,98), then with probability 0,95 we conclude about
the statistical significance of the regression equation as a whole and of the
indicator of the closeness of the connection which was formed under the
influence of nonrandom factors X8, X9.
To determine forecast values of per capita
monetary income of the population according to the obtained regression
equations, calculated the predicted values of the factor variables. For the
period from 2005 to 2015 built equations trends and based on these identified
predictive values of factor signs. The choice of a mathematical function, most
adequately reflecting the dynamics of development of factor signs made on the
basis of maximum value of reliability of approximation.
Projected values of per capita monetary income
of population in the Volga Federal district will receive by substituting a
two-factor regression equation predicted values of factor variables.
Based on the results of the econometric
modeling provided the following forecasts of average per capita monetary income
of the population, depending on the selected factor signs on the above models
(table 2).
Table 2 Forecasting options of average per capita
money incomes of population
|
Number of model |
Factor signs |
The
predicted values of incomes |
||||
|
2017 |
2018 |
2019 |
2020 |
2021 |
||
|
1 |
Õ4 è Õ5 |
31294,66 |
33941,61 |
36588,56 |
39235,50 |
41882,45 |
|
2 |
Õ6 è Õ7 |
25564,37 |
25130,51 |
24737,03 |
24376,62 |
23655,50 |
|
3 |
Õ8 è Õ9 |
30107,61 |
33076,64 |
35819,39 |
38377,56 |
40695,30 |
Therefore, all the constructed multiple regression equations (except the
second) is observed to increase per capita income by 2021. The largest increase
is observed in the first regression model with the signs of the factors: the
retail trade turnover and investments in fixed capital per capita, which also
tend to increase.
The forecast for the third model, in principle, is unrealistic according
to the laws of economic science: the reduction of per capita incomes in nominal
terms is impossible. However, the practical significance of this model is the
need for perfection and optimization of the current structure of monetary
incomes of the population. The reduction in the share of wages in the structure
of monetary incomes of the population has occurred against growth of the share
of income from entrepreneurial activity and property, social benefits.
Thus, the main economic policy measures should be aimed at increasing
the real incomes of the population and optimizing the structure of monetary
incomes of the population, increasing the share and role of wages in the
formation of incomes.
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