METHOD OF ANALYZING SOCIO-ECONOMIC MATTERS QUANTITATIVELY:
USING NON-LINEAR HYPERBOLIC REGRESSION MODEL
• NGUYEN NAM THANG - HOANG DINH DUNG
ABSTRACT:
When analyzing socio-economic matters quandtatively, most researchers often implement univariate or multivariate linear regression models. However, as datasets of socio-economic matters are linear, results of researches are inconsistent with economic principles. Therefore, this study IS to present some Hyperbolic linear regression models to help researchers regression methods in econometrics.
Keywords: Non-linear regression. Hyperbolic regression. Parabolic regression, exponential regression.
1. Introduction
In the study, to draw conclusions from the findings on the fluctuations of socio-economic phenomena that require the establishment of scientific arguments, this is also a challenge and demonstrates the scientific value of researchers. In reahty, in Vietnam, some research works, despite great efforts, still feel confused and have difficulties in applying scientific research methods, especially applying regression methods in econometric. Regression method in econometrics is represented by linear regression model or non- linear regression model The linear regression model is used by researchers so it is very popular.
Therefore, in the scope of this study, we only present some non-linear models of Hyperbolic, Parabolic and application exponential functions for specific cases, non-hnear Hyperbolic regression models with matching with linear regression model in a straight line.
2. Theory basis
Regression methods in econometrics allow us to define the theoretical regression line on the basis of the least .squares technique, i.e the total distance from the points representing the actual fluctuations in the past to the regression line, taking on the vertical axis is the smallest. Then based on the theoretical regression line assesses the level of volatihty of future socio economic phenomena to determine the theoretical regression line requires summarizing past data, specifically:
Carl Friedrich Gau p (1777-1855), in the field of mathematics, the regression method is the study of the influence of one or more variables called cause or explain or independent variables to a variable called the result variable or dependent variable to predict the outcome variable based on the known data of the independent variables.
Arthur S. Goldberger, John Wiley and Sons (1964), regression understands the simple approach 86 So 19-Thang 10/2019
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that means going back in time to stadstical study the data that happened in the past or time series data or at the same tune or cross section to find the rules of the relationship between them. That reladonship is represented by a regression model that can explain, quandfy in nature, support, reinforce theories and predict the future.
Paul Newbold (1991), econometrics is integrated from economic theories of economics, from mathematical equations of econometrics based on collected statistics of socio economic phenomena measurement in the form of value.
Amir D. Aczel and Jayavel Sounderpandian (2002), in econometrics, the regression method is to use theoretical algorithms to express the development trend of research phenomena based on the characteristics and properties of them over time.
Peter Kennedy (2006), in business as well as in many other fields, regression is an irreplaceable powerful analytical tool that is the statistical method used to analyze, test, estimate and forecast.
Events that will occur in the future based on the laws of the past. The estimation results using the regression method presented on the graph will be straight hues or curves showing a trend of development rather than kinked lines.
Damodar N. Gujarad and Dawn C. Porter (2009), choosing a linear regression mode! or a non-linear regression model shows the development tfend of research phenomena based on analyhcal nature, characteristics and characteristics of the phenomenon of research and its development law.
Alan Stuart and Keith Ord (2010), if the research phenomenon has a relatively constant increase or decrease in the number of variables, evenly in a certain direction, a univariate or muluvariate hnear regression model can be used.
The variables to calculate and show the development trend of the research phenomenon are shown in the graph as lines.
Richar I. Levin et al. (2014), if the research phenomenon has a variable level of development variable according to special rules, according to a certain cycle such as increase or decrease in a repeated cycle or fluctuate according to the rule of increasing or slowing down. It is possible to use non-linear regression models such as Hyperbolic regression. Parabolic regression. Exponential
regression, etc to analyze the development ti'end of the research phenomenon which is shown on graphs IS the curve.
Thus, the data collected in the past may be linear or non-linear if shown on the graph. The following IS a presentation of some non-hnear regression models applied to a specific case.
Hyperbolic non-linear regression.
3. Non linear regression model
Correlation relationships between criteria are not always represented in a straight line. In many cases, these relationships are represented by different .shaped curves called non-hnear regressions. Mathematically, these curves are represented by several models below.
3.1. Hyperbolic non-linear regression model The Hyperbolic nonhnear regression model Y, = Pi -I- P2"x'^'^^ ^1 '^ ^^^ outcome variable, X, is the cause variable and n is the observed number.
The model used to study the non-linear relationship between an increasing volatility factor causes the other element to flucmate in the opposite direction, which can be used to determine the development trend of the research phenomenon.
Using the OLS method, the coefficients |3|, P2 are calculated from the standard equation system as follows:
y.Y. ^ M
•^x^ ' M X /
'^-U
3.2. Parabolic non-linear regression model If, after analyzing past data on the graph, it is found that the trend is not in a straight line but in the form of a parabola, apply the model Y, = p, + '^2^1 + p3X^, with Yj as the dependent variable, Xj as the explanatory variable and n numbers if the observations of the aggregated data using OLS method, the coefficients p,, P2, P3 are calculated from the standard equaUon system as follows:
ZY.=nP, + |J,j;x,+[J,Xxf Xx,Y,=fi',ix,+p,x;xf+p,xx:
xx'Y,=p,jx:+p,xx:+p,i:x:
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3.3. Exponential no- linear regression model If after analyzing the past data on the graph, it found that the expression of the development trend of the research phenomenon has an approximate continuous growth rate, then apply the model Yj ^ p| -i- p^'^' with P, the coefficient as the original point and P2 is speed increases in time units. Ln, on both sides, has a non-linear model LnY, - LnPi -I- X.Lnp,. Using the OLS method, the coefficients p ,, p , - are calculated from the standard system of equations as follows:
^ L n Y , = n L n p | + L n p , ^ X ,
^X^LnY, - L n p i J ^ X ^ + L n p j J ^ X ^ . Z L n Y ,
L n p , - ^ J]X,LnY,
4. Application of hyperbolic non linear regression model
Studying the relationship between the movement of goods and the ratio of non-production costs of 10 Service Trading Enterprises m Ba Ria - Vung Tau province, obtained the statistical data in Table 1.
An item of non-production costs that increases in proportion to the rate of increase in goods consumption is selling expenses such as transportation costs, packaging costs, trade discount costs, cost of natural attrition, etc., so the ratio of non-production costs of this item is almost constant, also known as constant cost, denoted byP,-
An item of non-production costs that grows more slowly than the growth rate of goods consumption is management costs such as administrative management costs, preservation costs, depreciation expenses of fixed assets, etc..
due to then the ratio of non-production costs of this item is reduced to be determined by P i ^ . where Xj IS the level of goods consumption.
(2) See Figure 1, we can see the equation showing the relationship between the cost of non- production Yj and the flow of goods in X| type Hyperbol Yj = p, + Pj-^- (Figure 1).
(3) Based on the data in Table 1, calculate some values to determine the coefficients of the Hyperbolic non-linear regression model see Table 2.
(4) Result: Building a non-linear Hyperbolic regression model Y, = 5 -f- 4 0 0 ^ that reflects in normal production and sales conditions, the size of the Enterprise does not change, namely the level of goods flow does not increase or not. If reduced, the ratio of non-production costs is 5%. If the rate of goods flow increases by 1%, the ratio of non- production costs will decrease by 400 times or 4%
and vice versa.
Table 1.
Goods flow (1000 000 VND) Cost of non-production {%)
75 10
Soods flow a n d cost of non-producfion 90
9,2 120 8,1
150 7,8
180 7,9
220 7,0
300 6.1
450 5,8
600 5,3
800 5,0
(1) According to N. Gregory Mankiw (2013), the size of business and sales ratio of the service trade enterprises are inversely related. Indeed, the higher the consumption of goods, the lower the cost of sales ratio and vice versa, but for large-scale enterprises, this speed is somewhat slower than small and medium sized enterprises.
This is due to the impact of non-production costs including two items:
Source- http://thongkebariavungtau.gov.vn (2019) (5) Discussion: In case of using a straight line regression with Y, the ratio of non-production cost is the outcome criterion and X, the level of goods consumption is the cause criterion. According to Table 1, using Intercept and Slope functions in MS Excel is calculated p | = 9 and p2=-0,006 are the coefficients of the linear regression model Y| = 9 - 0,006 X|, namely the rate of goods flow does not increase or not decrease, the rate of cost of So 19-Thang 10/2019
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Figure 1. A gtaph showing the relationship between Yj and Xj. Source: Author (2019)
. Calculate some values to determine the regression coefficient of the Hyperbol model
n 1 2
3 4 5 6 7 8 9 10
I
yi 10 9,2 8,1 7,8 7,9 7,0 6,1 5,8 5,3 5,0 72,2
Xj 75 90 120 150 180 220 300 450 600 800 2.985
U\i
0,013333 0,011111 0,008333 0.006667 0,005556 0,004545 0,003333 0,002222 0,001667 0,001250 o.osaois
IvXj^
0,000178 0,000123 0,000069 0,000044 0,000031 0,000021 0,000011 0,000005 0,000003 0,000002 0,000487
J F " !
0.133333 0.102222 0,067500 0,052000 0,043889 0.031818 0,020333 0,012889 0,008833 0,006250 0,479068
yi' 100,00 84,64 65,61 60,84 62,41 49,00 37,21 33,64 28,09 25,00 546,44
yi"!
10,33 9,44 8,33 7,67 7,22 6,82 6,33 5,89 5,67 5,50 73.20
yi- yixi -0,33 -0,24 -0,23 tO,13 tO,68 tO,18 -0,23 -0,09 -0,37 -0,50 -1,01
( y i - J i x i ) ' 0,11 0,06 0,05 0,02 0,46 0,03 0,05 0.01 0.13 0.25 1,18
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[MX,
' -^x^^ r;xf
72,2 = IOp, + 0,058Pj
=^
0,48 = 0,058p,-fO,0005Pj P,=5
^ Y , = 5 + 4 0 0 — P, = 400
Source: Author (2019).
non-production is 9% higher than the Hyperbol regression of 4% (9% -5%) and if freight flow decreases by 1%, non-production costs will be reduced by 0,006 times or 0,6%. It is not consistent with the economic principle of N. Gregory Mankiw (2013) that the flow of goods decreases, the ratio of selling expenses increases. Thus, the linear regression method m this case is not feasible.
5. Conclusion
This research has great scientific and practical
significance, helping economists to identify optimal options, production, business, services and trade that are reasonable and bring high economic efficiency at the same time, show that more care must be taken before using quantitative methods based on whether the variance of the data presented on the graph is linear or non-linear and analyzing the relative nature of the phenomena or research phenomena that apply economic model appropriately or the results will be worth zero •
REFERENCES:
/- Alan Sluarl and Keith Ord Advanced Theoiy of Slatimcs and Kendall's Library of Statistics 6lh Edition by ixmdon School of Economics. 2010.
2. AmirD. Aczel and Jayavel Sounderpandian Complete Business Statistics, Published by Mcgraw Hdi, 2002.
3. Arthurs. Goldberger, John Wiley and Sons. Econometric theory. New York, 1964.
4. Carl Friedrich Gauji Deutscher Mathematiker, gilt allgemein als einer der grofiten Mathematiker alter Zeitenfiir seine Beitrage zur Zahlentheorie, Geonietrie. Wahrscheinllchkeitstheorie. Geoddsie. Planelena.slronomie.
Funklionentheorie und Polenlialtheorie Goltingen, Hannover in Deutschland, 1777-1855.
5. Damodar N. Gujarati and Dawn C. Porter. Basic Econometrics 5th Edition, Published by Douglas Reiner, 2009.
6 Mankiw N Gregory Principles of Economics 8th Edition by Havard University, 2013 7. Paul Newbold. Statitsics for Business and Economics. Published by Prentice Hall, 1991.
8 Peler Kennedy A Guide to Econometric, Blackwell Publishing, USA. 2006.
9. Richar I. l^vm, David S.Rubin, Sanjay Rastogi and Masood H. Siddiqui. Slatislics for Management. 7lh Edition bv Publisher Pear.ion Education in South Asia, 2014
10. The rale of goods movement and the ratio of non-production costs of 10 Service Commercial Enterprises Ba Ria - Vung Tau province littp//ihongkebariavungtau.gov.vn, 2019.
Receiving date: 20/9/2019 Reviewing date: 01/10/2019 Accepting date: 10/10/2019
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Author's information:
PhD. NGUYEN NAM THANG Master. HOANG DINH DUNG Faculty of Finance and Accounting Ho Chi Minh City University of Food Industry
PHlJdNG PHAP DINH LUdNG CAC HIEN TlfdNG KINH TE - XA HOI tfNG DUNG MO HINH HOI QUY
PHI TUYEN TINH DANG HYPERBOL
• TS. NGUYIN NAM THANG
• ThS. HOANG DINH D O N G Khoa Tdi chinh Ke'toan,
TrUdng Dgi hoc Cong nghiep ThUc phdm TP, Ho Chi Minh
TOM TAT:
Phan Idn cac nha nghien cti^ khi dung phifdng phap dinh lifcfng cac hien ttfdng kinh ti - xa hoi thuTcfng ap dung ngay mo hinh hoi quy tuye'n tinh dOn bie'n hoac da bie'n. Trong khi do, chu'a chac diJ" lieu thu thap du'dc da phai la tuyen tinh, dan de'n ket qua nghien cu'u khong phii hdp vdi nguyen ly kinh te hoc. Vi vay, muc tieu chinh ctia nghien cu'u nay la tap trung trinh bay mot so'mo hinh hoi quy phi my&'n tinh dug dung dang Hyperbol, giiip cho cac nha nghien cu'u can than hdn khi sicdung phifdng phap hoi quy trong kinh te Itfdng.
Tiif khoa: Hoi quy phi tuye'n tinh, hoi quy dang Hyperbol, hoi quy dang Parabol, hoi quy danghamso'mu.
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