Acta Universitatis Danubius. Œconomica, Vol 14, No 3 (2018)
ISSN: 20650175 Œconomica
Operations Research; Statistical Decision Theory
An Analysis of Two Types of Regressions for the same Dataset
Cătălin Angelo Ioan^{1}, Gina Ioan^{2}
Abstract: The paper analyzes two regression methods for a set of data relative to the absolute values, respectively their variation indices. A number of conclusions are drawn regarding the closest forecast to reality.
Keywords: regression; forecast; index
JEL Code: E17; E27
1. Introduction
In the forecasting activity, the used methods are of particular importance. Thus, for the same set of data, the absolute data and the growth indexes can be used.
The problem studied here is which prognosis is closer to the real situation.
In the article, we will consider a set of data relative to a certain period, performing both types of regressions after which we compare the results with the real ones obtained in the next period.
Also, the predicted value is often based on a final value of the estimated data set due to insufficient reporting. The question is to what extent interim data influence the forecast in both cases.
2. The Analysis
Considering a set of indicators , the regression equation corresponding to this set obtained by the least squares method is x=at+b, where:
a= , b=
Considering a set of temporal indicators: , from the above formulas, t_{k}=k, n=T (where T is the time period of the analysis), we obtain:
a_{1}= , b_{1}=
Let us now consider the growth indices corresponding to the values : , , k2.
From above, we obtain:
a_{2}= = ,
b_{2}= =
Let us consider the forecast at the time T+1 through the first relationship:
=a_{1}(T+1)+b_{1}=
By the second relationship, we obtain:
=a_{2}(T+1)+b_{2}=
The predicted value will therefore be:
= x_{T}=
The difference between the two forecasts is therefore:
 =
Let us consider that x_{T} is provisionally calculated. Let therefore the function:
Noting:
= , =
we have:
The second grade polynomial has = . If 0 then:
0
Therefore, if x_{T} belongs to the above range, then the indexbased forecast will provide a higher value than the one based on absolute data.
3. Case Study
Consider the absolute values of Romania's GDP (adjusted quarterly) between Q12015  Q12017.
Table 1
Quarter 
Absolute GDP 
GDP Index 
QIV 2014 
34009.2 
 
QI 2015 
34459.7 
1.013 
QII 2015 
34439.8 
0.999 
QIII 2015 
35093 
1.019 
QIV 2015 
35443.6 
1.010 
QI 2016 
35853.2 
1.012 
QII 2016 
36399.3 
1.015 
QIII 2016 
36650.7 
1.007 
QIV 2016 
37233.1 
1.016 
QI 2017 
37897.2 
1.018 
QII 2017 
38540.1 
1.017 
Source: INSSE
where the data in the last line is provisional but useful (in our case) to see the quality of the forecast for the data in the analyzed period. We also mention that QIV 2014 data was only considered for the calculation of the growth index.
Figure 1.
Regression analysis for absolute data reveals:
SUMMARY OUTPUT 






Regression Statistics 






Multiple R 
0.991778 





R Square 
0.983624 





Adjusted R Square 
0.981285 





Standard Error 
164.9608 





Observations 
9 





ANOVA 







df 
SS 
MS 
F 
Significance F 

Regression 
1 
11441540 
11441540 
420.4582 
1.65E07 

Residual 
7 
190484.5 
27212.07 



Total 
8 
11632025 





Coefficients 
Standard Error 
t Stat 
Pvalue 
Lower 95% 
Upper 95% 
Intercept 
33320.97 
139.1072 
239.5345 
5.83E15 
32992.03 
33649.9 
X Variable 1 
436.6833 
21.29635 
20.50508 
1.65E07 
386.3255 
487.0412 
therefore the regression is: GDP=436,6833Quarter+33320,97.
The forecast for QII 217 is therefore: 38124.5 with a relative error: 1.08%.
Regression analysis for index data reveals:
therefore the regression is: GDP%=0.0008667Quarter+1.0069111.
The forecast for QII 217 is therefore: 1.016 or for absolute data: 38503.5 with a relative error: 0.09%.
The interval for a higher forecast in the case of indices is: [51219.3, 37480,3].
4. Conclusions
As a result of the above analysis, we find that for the case of Romania, the regression based on growth indices provides conclusions closer to reality than relative absolute values.
5. References
Ioan, C.A. (2011). Elements of econometrics. Galați: Zigotto Publishers.
Ioan, C.A. & Ioan G. (2011). n Microeconomics. Galați: Zigotto Publishers.
Ioan, C.A. & Ioan, G. (2013). The LSM adjustment method of time series. Euroeconomica, nr. 3(32), pp. 150155.
1 Associate Professor, PhD, Danubius University of Galati, Department of Economics, Romania, Address: 3 Galati Blvd., Galati 800654, Romania, Tel.: +40372361102, Corresponding author: catalin_angelo_ioan@univdanubius.ro.
2 Senior Lecturer, PhD, Danubius University of Galati, Department of Economics, Romania, Address: 3 Galati Blvd., Galati 800654, Romania, Tel.: +40372361102, Email: ginaioan@univdanubius.ro.
AUDŒ, Vol. 14, no. 3, pp. 312318
Refbacks
 There are currently no refbacks.
This work is licensed under a Creative Commons Attribution 4.0 International License.