CC BY
57
УДК 330.341.13
macroeconomic indicators of the factors influencing gdp (on the example of Russian economy)
Usoltsev M. K., Dvoichenkov V. O.,
students, Financial University, Moscow, Russia
Abstract. The article examines macroeconomic indicators of the effect of innovation on GDP in terms of economy of Russia. Innovation and R&D indicators were chosen from all possible macroeconomic indicators to be used in this research. The authors conducted correlation analysis, basing on which they have constructed a regression model. This model was tested by means of a number of tools, such as F-test, t-test, Goldfeld-Ouandt test and others. The model was initially used to "predict" the value of Russian GDP for the year of 2016, and that"test-drive" was fairly successful. The authors also used the model to predict future values of Russian GDP basing on pessimistic and optimistic forecasts. Further development of the model consists of inclusion of other countries' data so that the model would be applicable for any economy.
Keywords: GDP; regression; model; prognosis; innovation
макроэкономические индикаторы факторов, влияющих на ввп ( на примере экономики россии)
Усольцев М.К., Двойченков В. О.,
студенты, Финансовый университет, Москва, Россия
Аннотация. В статье рассматривается влияние факторов инноваций на ВВП страны на примере экономики России. Проведен анализ различных макроэкономических показателей, определяющих ВВП государства, из которых были выбраны индикаторы инновационного развития. Проведенный авторами корреляционный анализ позволил построить регрессионную модель, адекватность которой в дальнейшем была протестирована с применением F-тестов, t-тестов, тестов Голдфелда-Квандта и некоторых других. С помощью модели в качестве показательного «тест-драйва» было проведено прогнозирование ВВП за 2016 г., а также построен прогноз ВВП России на ближайшее будущее на основе оптимистических и пессимистических прогнозов экономистов. В дальнейшем авторы планируют расширить и улучшить модель путем включения в анализ данных других стран.
Ключевые слова: ВВП; регрессия; модель; прогнозирование; инновации
Supervisor: Pyrkina O.E., Cand. Sci. (Physico-math.), associate professor, Department of data analysis, decision-making and financial technology, Financial University.
Научный руководитель: Пыркина О.Е., кандидат физико-математических наук, доцент Департамента анализа данных, принятия решений и финансовых технологий, Финансовый университет.
Introduction
All economists know the macroeconomical equation of GDP1 of a country. This is GDP = C + I + G + (X - M), where C is consumption, I - investments, G - governmental expenditures and X - M states for net exports. However, a lot more macroeconomical indicators also show viable status of an economy. To be precise, Federal State Statistics Service of Russia (Rosstat) gives more than a dozen of most commonly used. That is why we decided to check, whether there is a connection between such indicators and the GDP of a country, just like the equation stated above.
First, the chosen indicators need to be specified, in other words, future variables of the regression equation. Out of all possible ones, those were chosen which show the implementation or use of innovations and modern technologies. Truly, it is nowadays commonly known that Russia is not a top-ten country when it comes for innovations. Moreover, some people think that extensive growth could still be better than intensive one. That is why the topic of the investigation becomes more urgent - by showing possible relation between innovations and GDP it is good to state that government should pay more attention to what is important.
The indicators under investigation would be:
1. State financing of scientific development
2. The number of patented innovative technologies used during obscured period
Those two are declared as "innovations and R&D indicators" in Rosstat2, because of that we chose them for our research.
We need to determine precisely the indicators to understand fully their meaning.
First, the state financing of scientific development - all figures are given in million rubles. That is, from our point of view, simple to comprehend - this is the amount of money that is spent by government on various scientific researches and the implementations of scientific breakthroughs.
1 Wikipedia page concerning GDP of Russia. URL: https:// ru.wikipedia.org/wiki/BBn_Poccuu (accessed: 18.04.2017). (In Russ.).
2 Official web-page of Rosstat. Innovations and R&D section. URL: http://www.gks.ru/wps/wcm/connect /ross-tat_main/rosstat/ru/statistics/science_and_innovations/ science/# (accessed: 18.04.2017). (In Russ.).
The number of patented innovative technologies also gives us a simple amount of new patents that were given to the population of the Russian Federation at a given period.
Overall, above-mentioned indices show various aspects of innovative policies in Russia. It was suggested that there is a connection between those and the GDP of our Motherland, which later would be checked later in this work.
Economic Review
As it was already mentioned, many factors could influence the GDP of a country.
First, let us mention factors that are mainly considered as GDP-forming. Those are Consumption, Investments, Government expenditures and Net Exports.
Consumptions states personal consumption expenditures of the citizens of a country. They are typically broken down into Durable goods, Non-durable goods and Services. Investments are gross private investments, broken into changes in business inventory. Government expenditures include spending on items that were consumed in the given period. Net Exports explain the amount of exports subtracted the amount of imports in the given period. However, not only those microeconomical coefficients could be used in estimating the GDP3.
In 2010, professor Grishel of Grodno University in Belarus declared in her article "Brand of a country as an economical factor" [1, p. 3-4] that deterioration of capital assets could influence GDP. However, she stressed that there is practically no statistical data available concerning the data on deterioration since its calculation is very time-consuming.
"Analysis of primary income", written by Lozovski and Raizberg [2, 2012, p. 231], states that primary income could be a crucial indicator that could be used in estimating the value of GDP in a country. They claimed that primary income could solely give good values of GDP.
In addition, in 2006 a group of American scientists invented so-called "International Happiness Index"4. Using this index and the values of GDP of 178 coun-
3 Official web-page of the Financial University, research on initial macroeconomic index. URL: http://www.fa.ru/institutes/ efo/science/Pages/index.aspx (accessed: 19.04.2017). (In Russ.).
4 Official web-page of the World Happiness index Group with index data. URL: http://worldhappiness.report/down-load (accessed: 13.05.2017).
25 000,00 20 000,00 15 000,00 10 000,00 5 000,00 0,00
GDP and Scientific Financing
• ...... • •
/ j • 9- *
х**
100000
200000
300000
400000
500000
Diagram 1. Correlation Field of GDP and scientific Financing
Source: Rosstat [Appendix 1, Appendix 2].
Diagram 2. Gorrelation Field Between GDP and Number of Innovative Technologies
Source: Rosstat [Appendix 1, Appendix 3].
tries, they toLd that countries with high Levels of happiness among citizens had higher values of GDP.
Analytical Part
Statistical Data
First, the endogenous and exogenous variables in the model need to be determined. The only endogenous variable would be the GDP of Russian Federation5, later denoted by Y [Appendix 1].
5 Official web-page of Rosstat. GDP section URL: http:// www.gks.ru/wps/wcm/connect/rosstat_main/rosstat/ru/ statistics/accounts/# (accessed: 18.04.2017). (In Russ.).
Exogenous variables, hence, would be the macro-economical indicators discussed in the introductive part. State scientific financing is X1 [Appendix 2], and Number of Innovative technologies is X2 [Appendix 3].
All the statistical data is presented from the first quartile of 2005 to the last quartile of 2014 with the quartile steps, namely there are 40 measurements. All data is given in respective Appendices for this work.
For better understanding of the relations between variables and the GDP, the scatter diagrams were plotted for each one of them.
Diagram 1 represents the relation between GDP and State Scientific Financing. Here we can clearly see that the relationship exists and it is quite nice. The trend line shows small deviations from it - this means high correlation between GDP and State Scientific Financing.
Diagram 2 shows existence of correlation between GDP and number of Innovative Technologies. Despite the fact that the image is not that good as the first one, it is still fine. To prove the existence of possible correlation, examined in Diagram 1 and Diagram 2, one need to construct the correlation matrix, which is shown below.
Y X2 X3
Y 1
X2 0,971 1
X3 0,738 0,7197 1
Diagram 3. Correlation Matrix of GDP (Y), Scientific Financing (X1) and Number of Innovative Technologies (X2)
Source: Rosstat [Appendix 1, Appendix 2, Appendix 3].
From the Diagram 3, it can be seen that all coefficients have strong correlation with each other and Y. That is why we can state that the variables are good for exploitation and prognosis.
Econometrical Model
First, one need to ensure the regression equation in its initial form exists.
Assuming Gauss-Markov conditions hold, it should look as following:
Coefficients
Y-intercept 1508,9437
Variable X 1 0,0305
Variable X 2 0,0163
Diagram 4. Estimated coefficients of the equation
Source: RosStat [Appendix 1, Appendix 2, Appendix 3].
After finding the estimated coefficients one could use them to construct the estimated regression equation, which would be:
Y =1508,94 + 0,031 xXj +0,016 xX2 +s E (s) = 0 Var (s) = 963970,91.
This model needs to be specified and tested before accepting.
The coefficients of the model state that for every unit increase in X2 Y would increase by 3% and for every increase in X2 Y would roughly increase by 1,6%.
Then R2 test was performed. The results are:
R-squared 0,9456
Adjusted R-squared 0,9427
Y = ß1 +ß2 xX! +ß3 xX2 + s E (s) = 0 Var (s) = const.
As Y array, Y [Appendix 1] data would be used, as X array - Xx [Appendix 2] and X2 [Appendix 3]. Using the initial form of the regression equation, we can proceed to estimating coefficients using the "regression" service in MS Excel.
Diagram 5. R2 Data for the Regression Equation
Source: Rosstat [Appendix 1, Appendix 2, Appendix 3].
For the initial equation, determination coefficient (R2) is 0.946, which means that almost 95% of data under consideration is covered by the regression equation. Since the estimated coefficients were used in second equation, we need adjusted R2 value, which is 0.943. That means that 94.3% of the data could be explained by the estimated equation, which is a nice result. The determination test gives good results and we could proceed to other tests.
After assessment of the determination coefficient, one need to value the significance of the model. For this, Fischer's F-test would be applicable.
F crit. F emp.
4,0982 321,81
Diagram 6. F-values for F-test
Source: RosStat [Appendix 1, Appendix 2, Appendix 3], F-distri-bution table.
It can be obviously seen that the F value that was empirically got from the data is much greater than the critical F value from the table of F-distribution (321.81 > 4.098). That means that the regression equation is statistically significant. Significance of the model leads us to other tests.
Since the model is statistically significant, one should also assess the significance of the estimated coefficients of the equation. For this, Student's t-test is applied.
Coefficients t-statistics
Variable X 1 0,031 16,517
Variable X 2 0,016 1,482
Diagram 7. T-statistics Values for Coefficients
Source: Rosstat [Appendix 1, Appendix 2, Appendix 3], t-distri-bution table.
Both t-values of coefficients gave good results (16.517 for b and 1.482 for b2) which leads to the statistical significance of the coefficients of the regression equation. While the coefficients are significant, we can be sure that we do not need to get rid of any variable. However, the heteroscedasticity should also be checked.
The Goldfeld-Ouandt test was performed to find or reject the heteroscedasticity of data. The sum of squared errors in the first third was 2894689.921 [Appendix 4], and the same sum for the last third was 15802589.68 [Appenndix 5].
F 5,4592
Fcrit 2,2
Diagram 8. F-values for GO Test
Source: Rosstat [Appendix 4, Appendix 5], F-distribution table.
From the table of F-distribution it was seen that the critical value of F for our data would be 2.2 while GO test gave us 5.459, which means that we reject the hypothesis of heteroscedasticity, hence, our data appears to be homoscedastic. This means that data is uniformly dispersed around the trend line. However, autocorrelation needs to be tested before approval of the model.
Durbin-Watson test should prove the absence of autocorrelation in the data. Using the tables of Durbin-Watson coefficient and the knowledge of DW-test, such data showed out:
Dl 1,39
Du 1,6
DW 1,636
Diagram 9. Data for the DW Test
Source: Rosstat [Appendix 2, Appendix 3], DW-distribution table.
This means that our DW-value is greater than the upper critical value for the DW-statistics (1.636 > 1.6). Following assumption would be the absence of autocorrelation in the data. This is a very good result,
Diagram 10. Time Series Graph of True and Estimated Values of GDP
Source: Rosstat [Appendix 1], Estimated GDP values.
Diagram 11. Residuals Histogram
Source: Rosstat [Appendix 1], Estimated GDP values.
Diagram 12. Time series Graph of GDP and Predicted GDP
Source: Rosstat [Appendix 1], Estimated GDP values.
meaning that our model is not needed to be reconstructed. All necessary tests were done by this point, so the rule-of-thumb analysis is coming.
Overall, from the tests performed it turned out that the model is statistically significant - it covers almost 95% of the data. The coefficients of the regression equation are statistically significant too. The data is homoscedastic and there exists no autocorrelation. All those tests have proven the adequacy and applicability of the model.
After that it was interesting to see, how well the approximated values correspond to the true
values of GDP. For that a time series graph was plotted.
As it turns out from the Diagram 10, estimated values of GDP lie very close to true ones without significant dispersion. However, despite the fact that overall quality of the model is good, there is a possibility to make the approximation even better. For that one should analyze the residuals and see, what can be done.
From the "regression" tool in Excel the residuals were found and used to plot the above graph. From the Diagram 11 possible trend could be seen. It seems that every year the first two quartiles give
smaller residuals than last two. Moreover, the first quartile value is the highest negative value and the fourth quartile possesses highest positive values.
Using this knowledge, one could decide to introduce another lag variable with "-1" in the first quartiles, "0" in the second and third and "1" in every fourth quartiles for better approximation. Here the new time series graph is presented.
After carrying out a regression analysis one more time with the values for quartiles it was found out that the model became much better. Here it is:
Y = р1 +p2 x!1 +p3 xl2 +p4 x!3 +s E (e) = 0 Var (e) = const.
Now one needs to perform the estimation of coefficients again.
Diagram 13. R2 Values for the New Model
Source: Rosstat [Appendix 7].
Diagram 13 means that introduction of new fiction variable let us cover almost 3% more of data!
Coefficients
Y-intercept 1901,1927
Variable X 1 946,2325
Variable X 2 0,0303
Variable X 3 0,0145
Diagram 14. Coefficients of New Regression Equation
Source: Rosstat [Appendix 7].
Other coefficients of the model did not change significantly and they still possess all qualities of the previous model. Overall, the best possible regression equation was capable to find, is:
Y =1901,193 + 946,233 xX1 +0,03xX2 +0,015 xX3 +s E (s) = 0 Var (s) = 509102,3.
where X is a fictional introduced variable.
Economic Analysis of Model Results
First, the definition of what a nominal GDP is. "Gross domestic product (GDP) is a monetary measure of the market value of all final goods and services produced in a period (quarterly or yearly). Nominal GDP estimates are commonly used to determine the economic performance of a whole country or region, and to make international comparisons." This is why it was decided to choose nominal GDP instead of real GDP - to make it possible to draw connections to other countries in the future.
All X variables are taken from the official state statistics, which may serve as a proof of their significance. Our country nowadays suffers from a severe lack of Innovations in economics. However, government decided to avoid spending too much on innovations, research, and development because we have many natural resources to export. However, there is a historical cause not to think so.
In the 1980th USSR also followed the road of extensive growth and exported a lot of oil and gas for a sustainable economy. However, this policy led to an economic crisis of late 1980th and, hence, derived the decay of the Soviet Union itself.
Our investigation showed a clear dependence of GDP and innovation policy of the country. Since GDP is a most common way to assess country's economics, We would like to say that it is unwise to ignore innovations that could affect our main competitive index.
Using our model one could easily find the possible value of GDP at a given point in time knowing, of course, the indices and the quartile of the year.
Model Forecasting
Since all the indices are calculated every month and GDP values - only in quartiles, there is a possibility to assess the GDP values in shorter periods. That gives wider abilities for economists to compare and contrast intra and intercountry performance.
Let us perform a forecasting for 1 year, namely, for the end of 2016.
The value of GDP at the 31.12.2016 was 24076.8751 billion rubles. Corresponding values of coefficients are 527161.3 and 254733.29. Using the regression equation it is possible to find
Diagram 15. Forecasted GDP for 2016
Source: [Appendix 1].
Diagram 16. Positive Forecast for GDP up to 2018
Source: [Appendix 1], [Appendix 6].
the estimated value of GDP for the end of 2016. This gave us 22461,3291, while the true value was 24076,8752. The graph shows that the deviation is relatively small:
According to this investigation, we can see that the model could be used for forecasting future values of GDP.
Using this knowledge, it turned out to be necessary to forecast positive and negative future values for GDP using the model.
First, official documents were checked to find the information concerning any data that would be used in the forecasting.
On 3.03.2017 the government of the Russian Federation published6 its strategy for the economic development in the sphere of innovations.
From this document, it comes to mind that innovations come to focus of our economic strategy. Real figures are not stated but there are words "we expect doubled outcome from the implementation of the strategies discussed" lead us to understand-
6 Official web-page of the Government of Russian Federation concerning its plans on innovative development. URL: http://government.ru/govworks/28/events, Accessed 13.05.2017. (In Russ.).
Diagram 17. Negative Forecast of GDP up to 2018
ing that officials plan to heavily invest into it. Assuming the fact that the documents' aims are up to the year of 2025, it turned out that for the year of 2018, we would see at least 1.2 times increase in the observed values.
So, using the regression equation, one could forecast the GDP of Russian Federation to be 26384.1097 billion rubles, which is a good sign for our economy after the recession of 2014-2015.
However, not only positive view is there, but also a negative one. Professor of economics of Tyumen University, Ms. Ivanova, suggests [6, p. 15] that due to many political conflicts and sanction our country would be forced to cut down on innovations in the observed period up to 2020 at least. She wrote that the worst case would include almost a half cutting down on innovations and development budget.
Conclusion
The problem of transition to innovative development is the cornerstone of today's domestic and foreign policy of Russia. Numerous attempts undertaken at the state level over the past 10 years7 have not brought the expected results - the country has never been able to restore its former power and
7 The Federal law "On innovative activity and state innovation policy" (Project N99029071-2) URL: http://www. consultant.ru/cons/cgi/online.cgi?req=doc; base=PRJ; n=1149#0 (accessed: 07.05.2017). (In Russ.).
become one of the world's technological leaders, the scientific and technological potential continues to decline, the quality of life of the population is much lower than in countries G8, etc. In this regard, the need to develop a draft strategy of the innovative development of the Russian Federation for the period until 2020th, covering all aspects of the life of the state, and determining main vectors and mechanisms of development, there is no doubt.
Obviously, when developing the Project, it is necessary to analyze and take into account the reasons why for 20 years that have passed since the beginning of economic reforms, Russia has not been able to take advantage of the market economy and its competitive advantages [5, p. 17-18]: a strong fundamental science, a strong education system, a developed industry of nuclear energy, aircraft and shipbuilding industry, defense equipment, and others.
At the same time, Russia not only did not become an innovative power, but also significantly reduced its authority in the world scientific and technological community. Moreover, as noted by Nobel laureate of 2001 in economics D. Stiglitz: "Globalization and the transition to a market economy did not yield the promised results in Russia... The new economic system... brought unprecedented poverty: in many respects for the majority public market economy was even worse than that predicted by the communist leaders."
In other words, the development of the country's innovative strategy [3, p. 5-7] requires a critical analysis of economic theories that served as the methodological basis of Russia's economic policy in 1991-20108, creating new approaches that ensure the country's withdrawal to world leaders.
It is necessary to make full use of modern science of innovation [4, p. 8], take into account the prevailing socio-economic realities.
My model gives a primitive in most aspects, but a working tool that can help to produce such strategy in order to regain lost prosperity.
8 The Federal law "On science and state scientific and technical policy" of 23.08.1996 No. 127-03 (latest revision). URL: http://www.consultant.ru/document/cons_doc_ LAW_11507 (accessed: 07.05.2017). (In Russ.).
Recommendations
There are some recommendations on use and improvement of existing model.
First, one should try to use the model not only in Russian Federation, but also in other states of former Soviet Union to gain more statistical data in the field of innovation usage in those countries. After that, same research should be conducted in prospering countries like Germany or US in order to understand, whether the model is fully applicable for every country or not. If not, one should try to improve the model.
Second, one could also try to use more variables (innovative indices), so that more data would be included in the model and it would be more precise.
The most viable recommendation is to clearly specify the quartile of the year under consideration, since the model works much better in this way.
Список источников
1. Гришель В.М. Бренд страны как фактор повышения конкурентоспособности. Гродно: РИО БарГУ, 2012.
2. Райзберг Б.А,Лозовский Л.Ш., Стародубцева Е.Б. Современный экономический словарь. 6-е изд., перераб. и доп. М.: ИНФРА-М, 2011.
3. Данилина М.В., Щербакова К.С. Анализ инновационной политики Российской Федерации на современном этапе // Гуманитарные научные исследования. 2014. № 10. URL: http://human.snauka.ru/2014/10/7918, (дата обращения: 29.04.2017).
4. ЩитоваА.Н. «Инновационная политика экономики России» / Инновационная экономика: материалы Междунар. науч. конф. Казань: Бук-Казань, 2014.
5. Молчанова В.А. Инновационная политика России: проблемы развития // Креативная экономика. 2014. Т. 8. № 11 (95). С. 144-154. URL: http://bgscience.ru/Lib/5206 (дата обращения: 30.04.2017).
6. Иванова С.А. Основные проблемы инновационного развития России (компаративный анализ) // Современные научные исследования и инновации. № 4. Ч. 1. М., 2014. URL: http://web.snauka.ru/ issues/2014/04/33127 (дата обращения: 03.05.2017).
References
1. GrisheLL V. M. Brand of country as a factor of competitiveness. Grodno: RIO BarGU, 2012. (In Russ.).
2. Raizberg B. A., Lozovskiy L. Sh., Starodubtseva E. B. Modern economic dictionary. 6th ed., Rev. and ext. Moscow: INFRA-M, 2011. (In Russ.).
3. DaniLina M. V., Shcherbakova K. S. Analysis of innovative policy of the Russian Federation at the present stage. Gumanitarnye nauchnye issledovaniya = Humanitarian Scientific Researches, 2014, no. 10. Available at: http://human.snauka.ru/2014/10/7918 ^cessed: 29.04.2017). (In Russ.).
4. Shchitova A. N. Innovation policy of the Russian economy. In The Innovation economy: Proceedings of the international scientific conference. Kazan: Buk-Kazan, 2014. (In Russ.).
5. MoLchanova V. A. Innovation policy of Russia: problems of development. Journal of Creative Economy, 2011, vol. 8, no. 11 (95), pp. 144-154. AvaiLabLe at: http://bgscience.EN/Lib/5206 ^cessed: 30.04.2017. (In Russ.).
6. Ivanov S. A. The main probLems of innovative deveLopment of Russia (comparative anaLysis). Sovremennye nauchnye issledovaniya i innovatsii = Modern scientific researches and innovations, 2014, no. 4, Part 1. AvaiLabLe at: http://web.snauka.EN/issues/2014/04/33127 ^cessed: 03.05.2017). (In Russ.).
Appendices
Appendix 1. GDP of Russian Federation, in billions rubles
31.03.2005 31.07.2005 30.09.2005 31.12.2005 31.03.2006 31.07.2006 30.09.2006 31.12.2006
4458.60 5077.90 5845.20 6228.10 5792.90 6368.10 7275.80 7480.30
31.03.2007 31.07.2007 30.09.2007 31.12.2007 31.03.2008 31.07.2008 30.09.2008 31.12.2008
6780.20 7767.50 8902.70 9797.00 8877.70 10,238.30 11,542.00 10,618.90
31.03.2009 31.07.2009 30.09.2009 31.12.2009 31.03.2010 31.07.2010 30.09.2010 31.12.2010
8334.60 9244.80 10,411.30 10,816.40 9995.80 10,977.00 12,086.50 13,249.30
31.03.2011 31.07.2011 30.09.2011 31.12.2011 31.03.2012 31.07.2012 30.09.2012 31.12.2012
11,954.20 13,376.40 14,732.90 15,903.70 12,844.26 14,313.68 15,663.57 16,876.61
31.03.2013 31.07.2013 30.09.2013 31.12.2013 31.03.2014 31.07.2014 30.09.2014 31.12.2014
14,925.02 16,148.96 17,442.14 18,410.74 15,891.72 17,015.07 18,543.47 19,566.47
Appendix 2. State Scientific Financing, thousands rubles
31.03.2005 31.07.2005 30.09.2005 31.12.2005 31.03.2006 31.07.2006 30.09.2006 31.12.2006
47,478.1 49,652.7 58,307.5 76,909.3 79,003.6 84,267.9 92,552.4 97,363.2
31.03.2007 31.07.2007 30.09.2007 31.12.2007 31.03.2008 31.07.2008 30.09.2008 31.12.2008
103,556.9 124,007 130,260.1 132,703.4 142,873.5 159,672.4 167,620.2 162,115.9
31.03.2009 31.07.2009 30.09.2009 31.12.2009 31.03.2010 31.07.2010 30.09.2010 31.12.2010
175,678.6 189,452.2 198,382.8 219,057.6 220,785.5 226,002.4 230,971.3 237,644
31.03.2011 31.07.2011 30.09.2011 31.12.2011 31.03.2012 31.07.2012 30.09.2012 31.12.2012
246,045 267,451.5 293,468 313,899.3 327,842.8 331,873.1 345,987.9 355,920.1
31.03.2013 31.07.2013 30.09.2013 31.12.2013 31.03.2014 31.07.2014 30.09.2014 31.12.2014
378,123.5 399,678.3 405,056.2 425,301.7 426,562.1 429,977 432,890 437,273.3
Appendix 3. Quantity of Innovative Technologies Used
31.03.2005 31.07.2005 30.09.2005 31.12.2005 31.03.2006 31.07.2006 30.09.2006 31.12.2006
130,452 131,327 133,668 140,983 147,532 154,099 163,683 168,311
31.03.2007 31.07.2007 30.09.2007 31.12.2007 31.03.2008 31.07.2008 30.09.2008 31.12.2008
175,334 179,935 180,030 180,324 180,983 182,405 184,300 184,374
31.03.2009 31.07.2009 30.09.2009 31.12.2009 31.03.2010 31.07.2010 30.09.2010 31.12.2010
187,893 195,003 199,617 201,586 201,836 202,420 202,819 203,330
31.03.2011 31.07.2011 30.09.2011 31.12.2011 31.03.2012 31.07.2012 30.09.2012 31.12.2012
203,056 197,562 193,437 191,650 192,672 191,420 191,388 191,372
31.03.2013 31.07.2013 30.09.2013 31.12.2013 31.03.2014 31.07.2014 30.09.2014 31.12.2014
191,429 192,335 193,078 193,830 195,643 197,097 200,562 204,546
Appendix 4. First Third of data for GO test
X1 Х2 Y YA Остатки еЛ2
47478.1 130452 4458.6 4806.319 -347.719 120908.7755
49652.7 131327 5077.9 4914.532 163.3679 26689.06972
58307.5 133668 5845.2 5360.942 484.2577 234505.4853
76909.3 140983 6228.1 6288.948 -60.848 3702.479882
79003.6 147532 5792.9 6314.533 -521.633 272101.1274
84267.9 154099 6368.1 6515.193 -147.093 21636.22194
92552.4 163683 7275.8 6841.316 434.4842 188776.5278
97363.2 168311 7480.3 7043.613 436.6874 190695.8824
103556.9 175334 6780.2 7289.391 -509.191 259274.9938
124007 179935 7767.5 8357.018 -589.518 347531.4039
130260.1 180030 8902.7 8701.547 201.1526 40462.3771
132703.4 180324 9797 8832.627 964.3729 930015.1703
142873.5 180983 8877.7 9386.021 -508.321 258390.4056
Appendix 5. Third Part of data for GO test
293468 193437 14732.9 14521.47 211.4265 44701.15155
313899.3 191650 15903.7 14629.88 1273.824 1622628.265
327842.8 192672 12844.2616 15061.24 -2216.98 4914978.39
331873.1 191420 14313.68 14939.21 -625.53 391287.3364
345987.9 191388 15663.5694 15205.82 457.7454 209530.8059
355920.1 191372 16876.6061 15394.47 1482.134 2196720.017
378123.5 191429 14925.0181 15830.99 -905.968 820777.7197
399678.3 192335 16148.9631 16390.37 -241.41 58278.95098
405056.2 193078 17442.1423 16612.36 829.7819 688537.9324
425301.7 193830 18410.7399 17121.99 1288.749 1660875.15
426562.1 195643 15891.7213 17435.31 -1543.59 2382662.038
429977 197097 17015.0722 17732.86 -717.793 515226.5076
432890 200562 18543.4683 18341.38 202.0857 40838.63748
437273.3 204546 19566.467 19060.95 505.5163 255546.779
Appendix 6. Regression data from Excel
ВЫВОД ИТОГОВ
_Регрессионная статистика_
Множественный R 0,972438786 R-квадрат 0,945637193 Нормированный R-квадрат 0,942698663 Стандартная ошибка 1008,00667 Наблюдения_40
Дисперсионный анализ
df SS MS F Значимость F
Регрессия 2 653960031,9 326980016 321,8061942 4,00945E-24
Остаток 37 37594865,51 1016077,446
Итого 39 691554897,4
Коэффициенты Стандартная ошибка ¿-статистика Р-Значение Нижние 95% Верхние 95% Нижние 95,0% Верхние 95,0%
У-пересечение 1508,943709 1747,272822 0,86359937 0,393371925 -2031,367314 5049,254732 -2031,367314 5049,254732
Переменная X 2 0,030527078 0,001848202 16,51717556 1,16763Е-18 0,026782265 0,034271892 0,026782265 0,034271892
Переменная X 3_0,01634272_0,011025623_1,482249189 0,146741737 -0,005997313 0,038682754 -0,005997313 0,038682754
ВЫВОД ОСТАТКА
Предсказанное Y Остатки
1 5090,251962 -631,6519616
2 5170,936027 -93,03602683
3 5473,400094 371,7999061
4 6160,805702 67,29429813
5 6331,767039 -538,8670385
6 6599,793383 -231,6933829
7 7009,323597 266,4764029
8 7231,817376 248,4826236
9 7535,667868 -755,4678679
10 8235,142532 -467,6425316
11 8427,583964 475,1160357
12 8506,975535 1290,024465
13 8828,208828 49,49117193
14 9364,269515 874,0304854
15 9637,862084 1904,137916
16 9471,041247 1147,858753
17 9942,580887 -1607,980887
18 10479,2454 -1234,445398
19 10827,27584 -415,9758365
20 11490,59589 -674,1958945
21 11547,42931 -1551,629313
22 11716,23018 -739,2301777
23 11874,43692 212,0630768
24 12086,48609 1162,81391
25 12338,46617 -384,2661703
26 12902,15717 474,2428313
27 13628,95118 1103,948817
28 14223,45464 1680,245361
29 14665,81122 -1821,549596
30 14768,38342 -454,7034162
31 15198,74406 464,8253912
32 15501,68362 1374,92252
33 16180,42009 -1255,402001
34 16853,23166 -704,2685426
35 17029,54588 412,5963995
36 17659,87157 750,8682799
37 17727,97726 -1836,255994
38 17855,98649 -840,9143075
39 18001,5394 541,9288668
40 18200,45814 1366,008834
Appendix 7. Regression data from Excel, new model
Регрессионная статистика
Множественный R_0,985540131
R-квадрат 0,971289351
Нормированный R-квадрат 0,968896797
Стандартная ошибка 742,6489771 Наблюдения_40
Дисперсионный анализ
df SS MS F Значимость F
Регрессия 3 671699907,3 223899969,1 405,9633796 8,46761E-28
Остаток 36 19854990,11 551527,5031
Итого 39 691554897,4
Коэффициенты Стандартная ошибка ^статистика Р-Значение Нижние 95% Верхние 95% Нижние 95,0% Верхние 95,0%
Y-пересечение 1901,192655 1289,159952 1,474753115 0,148971418 -713,3449101 4515,73022 -713,3449101 4515,73022 166,8423031 5,671418498 1,91073E-06 607,86065 1284,604398 607,86065 1284,604398 0,001362414 22,21830922 1,30865E-22 0,027507434 0,033033642 0,027507434 0,033033642 0,008129443 1,786819485 0,082390068 -0,001961427 0,031013121 -0,001961427 0,031013121
Переменная X1 946,2325241
Переменная X 2 0,030270538
Переменная X 3 0,014525847
ВЫВОД ОСТАТКА
Наблюдение_Предсказанное Y_Остатки
1 171,5264418
2 -233,942511
3 237,3670263
4 -995,3085679
5 303,4311204
6 -322,3458353
7 195,362173
8 -759,2214763
9 143,6419156
10 -501,159566
11 443,3757753
12 313,212646
13 968,9507591
14 854,1507343
15 1889,74007
16 185,9507573
17 -667,5508801
18 -1223,796462
19 -394,6527898
20 -1590,224032
21 -574,2949091
22 -705,7288992
23 247,56401
24 254,722557
25 601,7648947
26 509,5510948
27 1138,436753
28 770,4954674
29 -833,4005294
30 -414,0276656
31 509,0640142
32 475,4475569
33 -256,6122922
34 -644,5355992
35 475,058927
36 -126,341645
37 -817,3835361
38 -764,7565804
39 625,1293621
40 511,3397216
