Acta Universitatis Danubius. Œconomica, Vol 14, No 3 (2018)

Operations Research; Statistical Decision Theory

An Analysis of Two Types of Regressions for the same Dataset

Cătălin Angelo Ioan¹, Gina Ioan²

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:

a₁= , b₁=

Let us now consider the growth indices corresponding to the values : , , k2.

From above, we obtain:

a₂= = ,

b₂= =

Let us consider the forecast at the time T+1 through the first relationship:

=a₁(T+1)+b₁=

By the second relationship, we obtain:

=a₂(T+1)+b₂=

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 index-based 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 Q1-2015 - Q1-2017.

Table 1

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:

therefore the regression is: GDP=436,6833Quarter+33320,97.

The forecast for QII 2-17 is therefore: 38124.5 with a relative error: -1.08%.

Regression analysis for index data reveals:

therefore the regression is: GDP%=0.0008667Quarter+1.0069111.

The forecast for QII 2-17 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. 150-155.

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