Predicting the Number of Beijing Science and Technology Personnel Based on GM ( 1 , N ) Model

In this paper, based on the Science and Technology Statistics in Beijing Statistical Yearbook, grey theory is used to study the relationship among S&T (Science and Technology) activities personnel, R&D (research and development) personnel FTE (Full Time Equivalent), intramural expenditure for R&D and Patent Application Amount. According to the grey correlation coefficient, screening of grey GM(1,N) prediction variables, the grey prediction model is established. Meanwhile, time series model and GM(1,1) model are established for patent applications and R&D personnel equivalent FTE. By comparing the simulating results with the real data, the absolute relative error of prediction models is less than 10%. The results of the prediction model are tested. In order to improve the prediction accuracy, the mean values of the predicted values of the two models are brought into the GM(1,N) model to predict the number of scientific and technical personnel in Beijing during 2015-2025. Forecast results show that the number of science and technology personnel in Beijing will grow with exponential growth trend in the next ten years, which has a certain reference value for predicting the science and technology activities and formulating the policy in Beijing.


Introduction
The functions of Beijing in the Beijing-Tianjin-Hebei integrations region are the national political center and cultural center, international exchange center, science and technology innovation center.While science and technology innovation is the core of a country, a regional competitiveness, national strategy advocates strengthening science and technology innovation ability.Beijing, as the capital of China and international metropolis, its science and technology innovation plays a role of "leader".Scientific and technological innovation capability is an important guarantee to optimize the allocation of scientific and technological resources, improve the efficiency of investment in science and technology, and promote the economic development of technology.Many scholars have made a lot of research on the impact of science and technology investment on economic output.Wei and Li (2005) using the econometric methods to study the impact of R&D input intensity, scientific and technical personnel, the per capita possession of a number of factors on the export of high-tech products [1].
Guo and Wang (2011) use science and technology statistics by SPSS statistical software to study the relationship between the number of scientific and technological activities and high-tech products exports [2].Scientific and technical personnel is the fundamental factor to promote scientific and technological progress and technological innovation; science and technology personnel's strength reflects the local science and technology strength and innovation ability [3].The patent application, scientific and technological activities and R&D expenses and other variables are used to estimate the specific knowledge production function of Henan Province by Luo (2015) [4].Fu (2012) involved in scientific and technological activities of personnel in the comparison of the transformation of R&D institutions and foreign R&D institutions in Beijing, and pointed out that the study of scientific and technical personnel assessment should be strengthened [5].
The number of patent application is the barometer of economic and social development.In this paper, based on the Science and Technology Statistics in Beijing Statistical Yearbook, grey theory is used to study the relationship among S&T activities personnel, R&D personnel FTE, intramural expenditure for R&D and Patent Application Amount.And time series and GM(1,1) model are used to predict the number of patent applications and research and development (R&D) staff equivalent to full-time equivalents for years of 2015-2025, and then GM(1,N) model is used to predict the number of municipal scientific and technological activities for the next decade.

Grey Correlation Analysis
Grey correlation analysis is a systematic and effective analysis method in the grey system theory.The quantitative description of the development trend of the system is based on the correlation between factors [6].
The specific process of grey correlation analysis is: 1) Determine the analysis sequence A reference sequence to determine the behavior characteristics of the system is: A comparative sequence to influence the behavior characteristics of the system is: 2) Dimensionless variables The sequence of the factors in the system of data may be due to the different dimension, not easy to be compared, or cannot get the correct conclusion, so in advanced dimensionless analysis of the grey correlation.
Resulting from the reference sequence of dimensionless sequence is as follows: After the comparative sequence of dimensionless get sequence is as follows: 3) Grey correlation coefficient Calculate grey correlation coefficient between reference sequence X 0 and compare sequence 1 2 , , , n X X X  .The calculation formula is as follows: where, [ ] 0,1 ξ ∈ is distinguishing coefficient, the smaller the coefficient, the greater the resolution.The general value is 0.5 ξ = .4) Gray correlation degree The grey correlation degree between the reference sequence 0 Y and the comparison sequence i Y is calculated.Because the reference sequence and comparative sequence in the curve of the various points of the degree of correlation is not a value, but too scattered, so calculating the average of the various points in the curve, as the correlation degree of reference sequence and compare sequence.The formula is as follows: ( ) In the formula, i r represents the grey correlation degree between the reference sequence 0 Y and the comparison sequence i Y .5) Correlation degree ranking When 1 2 r r > , it means the comparison sequence 1 X is much more similar than sequence 2 X for reference sequence Y.
In the Beijing statistical yearbook, according to the statistical data from 1996 to 2014, the grey theory is used to make the gray correlation analysis of S&T activities personnel, R&D personnel FTE, intramural expenditure for R&D and Patent Application Amount.Specific data are shown in Table 1.
According to the data calculation results of 1996-2014 in Beijing, it is shown that the correlation of S&T activities personnel, R&D personnel FTE, intramural expenditure for R&D with Patent Application Amount in the order: 1 .The order of correlation degree is R&D personnel FTE, S&T activities personnel and intramural expenditure for R&D.
According to the selection of affecting the main factor greater than 65% [7], then select R&D personnel FTE and S&T activities personnel which have close grey co-relationship with Patent Application Amount as indicators.First of all, time series method and GM(1,1) model are used to predict Patent Application Amount and R&D personnel FTE for years of 2015-2025.Followed by GM(1,N) model predicts the number of National S&T personnel in Beijing in 2015-2025.

GM(1,1) Model
GM(1,1) model, which is basing on the past and now known or uncertain information to establish one order grey model of a variable from the past extended to future.The GM(1,1) model is used to determine the trend of the development and changes in the future.Grey prediction does not pursue the effect of individual factors, which trying to find the inherent law of the influence of the random factors on the processing of the original data [8].
Specific algorithm is: 1) In this paper, the original data sequence is assumed to be where 2) The GM(1,1) parameters a, b of ( ) x , according to the following formula recognition ( ) where 3) GM(1,1) model: The grey differential equation is: The whitening differential equation is: Time response of the whitening equation is: 4) GM(1,1) model accuracy (error) for the residual test.
Record ( ) ( ) x k as model value, ( ) ( ) x k as actual value, ( ) k ε as the relative residual values, then

Time Series Analysis
According to historical data, time series forecasting method was used, the prediction model of Beijing patent application amount is obtained: t = 1 for the year of 1997.The simulation value of patent application (Table 2) can be calculated through equation (17).
The average absolute relative error of model is 6.20%, which is less than 10.00%.Thus the model can be used.And the number of patent application for 2015-2025 in Beijing (Table 3) can be predicted by the model.

GM(1,1) Prediction Model
Matrix â can be obtained by calculating historical data of patent application in Beijing.
Then the amount of patent application in Beijing Grey differential equation is: Whitening equation is: Thus model value of patent application for 2002-2008 in Beijing (Table 4) can be predicted.The average absolute relative error of model is 7.18%, which is less than 10.00%.Thus the model can be used.And the number of patent application for 2015-2025 in Beijing (Table 5) can be predicted by the model.

The Average of the Two Prediction Results
The results of two groups are averaged.Thus the predict value of the patent application in Beijing in 2015-2025  (Table 6) is obtained by taking average of the two prediction results.

Time Series Analysis
According to historical data, time series forecasting method was used, the prediction model of Beijing R&D personnel FTE is obtained:  7) can be calculated through Equation (21).
The average absolute relative error of model is 8.23%, which is less than 10.00%.Thus the model can be used.And the number of R&D personnel FTE for 2015-2025 in Beijing (Table 8) can be predicted by the model.

GM(1,1) Prediction Model
Matrix â can be obtained by calculating historical data of R&D personnel FTE in Beijing.
thus, grey differential equation is: whitening equation is: Thus model value of R&D personnel FTE in Beijing for 1998-2014 in Beijing (Table 9) can be predicted.The average absolute relative error of model is 9.68%, which is less than 10.00%.Thus the model can be used.And the number of R&D personnel FTE for 2015-2025 in Beijing (Table 10) can be predicted by the model.

The Average of Two Prediction Results
The results of two groups are averaged.Thus the forecast value of the R&D personnel FTE in Beijing in   2015-2025 (Table 11) is obtained by taking average of the two prediction results.

GM(1,N) Model
GM(1,N) model, which is based on past and present known or uncertain information to establish a one order N variables from the past to the future, to determine the development trend of the system in the future [9].This model is based on the assumption that there is a causal relationship between the amount of patent application and the amount of scientific and technical personnel, R&D personnel FTE.According to the prediction results of the patent application and R&D personnel FTE, the number of scientific and technical personnel in the future can be predicted by Table 12.
1) GM(1,N) modeling, we first need to pre-test with a cover formula, which uses step ratio ( ) k σ of modeling sequence and the size of subordinate interval to determine [10].
First, i x is defined as the Covering formula is: then, the selected sequence can be modeled.
2) For ( ) x according to Equation (27) to generate ( ) x , that can be seen in Table 13.
x ,according to Equation (29) for the mean of processing as ( ) b) Based on ( ) x and ( ) z has GM(1,N) data matrix B and data vector y N ,   Then the model is: Comparing the actual value with the model value, fitted values and errors of the GM(1,n) prediction model (Table 14) can be obtained.
The average absolute relative error of model is 2.03%, which is less than 10.00%.Based on the forecast value of the amount of patent application and R&D personnel full time equivalent, the model is used to predict the number of scientific and technological personnel in Beijing (Table 15).15).The prediction results were analyzed, the number of Beijing Science and technology activities is exponential growth trends such as Figure 1.The results of a number of scientific and technological activities for the next ten years of Beijing prediction has certain reference national science and technology talent investment policies provide certain basis.

Conclusions
The prediction of the S&T activities personnel is an important issue for controlling and monitoring education reforming.The training of scientific and technical personnel is a basic project of "the strategy of developing the country through science and education", "the strategy of talent powerful nation" and "national innovation system construction".The study on this issue is meaningful and valuable for controlling, monitoring and improving National Science and technology innovation ability.This paper aims to use prey theory to predict the condition of S&T activities personnel, R&D personnel FTE, intramural expenditure for R&D and Patent Application Amount in recently for the last ten years.
• GM(1,1) and GM(1,N) are introduced in this paper.In comparison, the GM(1,N) model has better predictability under the condition of scanty data than GM(1,1) [11].We need to collect relevant data of variables that involved, then according to the GM(1,N) model to predict the target variables [12].• Data analysis showed that the number of science and technology activities in Beijing showed an exponential growth trend.According to the characteristics of the index function, the total number of people engaged in  scientific research in China is growing at a faster pace.The number of scientific and technical personnel directly represents the status of scientific research in a country.Higher education is the main bearer of innovation oriented national talent cultivation and scientific research.The number and quality of scientific and technical personnel as the main body of scientific and technological innovation are the focus of all the countries in the world.Therefore, the national policy should ensure that the number of scientific and technical personnel.At the same time, China should strengthen the evaluation of the quality of scientific and technical personnel, improve the scientific and technological personnel of scientific research products, and thus enhance the country's ability to innovate.
the year of 1996.The simulation value of Beijing R&D personnel FTE (Table ) c) According to the method of least squares identification algorithm

Table 1 .
Statistical data of innovation and development indicators in Beijing during 1996-2014.

Table 2 .
Comparison of the simulation value and the actual value of the patent application in Beijing (unit: piece).

Table 4 .
Comparison of the simulation value and the actual value of the patent application in Beijing (unit: piece).

Table 6 .
Prediction of patent application for 2015-2025 in Beijing.

Table 7 .
Comparison of the simulation value and the actual value of the R&D personnel FTE in Beijing (unit: one year).

Table 8 .
Prediction of R&D personnel FTE for 2015-2025 in Beijing city (unit: one year).

Table 9 .
Comparison of the simulation value and the actual value of the R&D personnel FTE in Beijing (unit: one year).

Table 12 .
Historical data of innovation evaluation in Beijing (Patent Application Amount, S&T activities personnel, R&D personnel FTE).

Table 13 .
The results of AGO for( )

Table 14 .
Fitted values and errors of the GM(1,n) prediction model.According to the time sequence and GM(1,1) prediction model, taking average value of each results of patent applications and R&D personnel FTE are took into GM(1,n) model to predict Beijing 2015-2025 S&T activities personnel (Table

Table 15 .
Prediction of S&T activities personnel for 2015-2025 in Beijing.