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.
Grey Relational Analysis GM(1N) Model Time Series Science and Technology1. 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.
2. 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 X0 and compare sequence.
The calculation formula is as follows:
where, is distinguishing coefficient, the smaller the coefficient, the greater the resolution. The general value is.
4) Gray correlation degree
The grey correlation degree between the reference sequence and the comparison sequence 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, represents the grey correlation degree between the reference sequence and the comparison sequence.
5) Correlation degree ranking
When, it means the comparison sequence is much more similar than sequence 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:.The order of correlation degree is R&D personnel FTE, S&T
Statistical data of innovation and development indicators in Beijing during 1996-2014
Year
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
Patent application
6595
6313
6321
7723
10,344
12,174
13,842
17,003
18,402
22,572
S&T activities personnel
265,552
273,161
237,127
229,584
261,113
240,609
257,326
270,921
301,202
383,153
Intramural expenditure for R&D
418,614
532,257
861,138
938,437
1,557,011
1,711,696
2,195,402
2,562,518
3,169,064
3,795,450
R&D personnel FTE
84,793
84,913
86,602
85,740
98,723
95,255
114,919
110,358
152,132
177,765
Year
2006
2007
2008
2009
2010
2011
2012
2013
2014
Patent application
26,555
31,680
43,508
50,236
57,296
77,955
92,305
123,336
138,111
S&T activities personnel
382,756
450,331
450,147
529,985
529,811
605,980
651,003
681,346
726,792
Intramural expenditure for R&D
4,329,878
5,270,591
6,200,983
6,686,351
8,218,234
9,366,440
10,633,640
11,850,469
12,687,953
R&D personnel FTE
168,875
204,668
200,080
191,779
193,718
217,255
235,493
242,175
245,384
Intramural expenditure for R&D, Unit: million.
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.
3. 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
The one-time accumulated generating sequence of is
where
2) The GM(1,1) parameters a, b of, 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 as model value, as actual value, as the relative residual values, then
4. Beijing Patent Application Forecast4.1. 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.
4.2. GM(1,1) Prediction Model
Matrix 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.
4.3. 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
Comparison of the simulation value and the actual value of the patent application in Beijing (unit: piece)
Year
1997
1998
1999
2000
2001
2002
2003
2004
2005
Patent applications
6313
6321
7723
10,344
12174
13,842
17,003
18,402
22,572
Simulation value
5469.0
6591.6
7944.6
9575.4
11,540.9
13,909.9
16,765.1
20,206.4
24,354.1
Relative error
0.1337
−0.0428
−0.0287
0.0743
0.0520
−0.0049
0.0140
−0.0981
−0.0789
Year
2006
2007
2008
2009
2010
2011
2012
2013
2014
Patent applications
26,555
31,680
43,508
50,236
57,296
77,955
92,305
123,336
138,111
Simulation value
29,353.1
35,378.3
42,640.2
51,392.8
61,942.0
74,656.5
89,981.0
108,451.0
130,712.2
Relative error
−0.1054
−0.1167
0.0199
−0.0230
−0.0811
0.0423
0.0252
0.1207
0.0536
Prediction of patent application for 2015-2025 in Beijing (unit: piece)
Year
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
Predicted value
157,543
189,881
228,857
275,834
332,453
400,694
482,943
582,074
701,554
845,559
1,019,124
Comparison of the simulation value and the actual value of the patent application in Beijing (unit: piece)
Year
2002
2003
2004
2005
2006
2007
2008
Actual value
13,842
17,003
18,402
22,572
26,555
31,680
43,508
Model value
11,534.8
14,138.2
17,329.4
21,240.8
26,035.0
31,911.3
39,114.0
Error value
0.1667
0.1685
0.0583
0.0590
0.0196
−0.0073
0.1010
Year
2009
2010
2011
2012
2013
2014
2010
Actual value
50,236
57,296
77,955
92,305
123,336
138,111
57,296
Model value
47,942.4
58,763.4
72,026.8
88,283.9
108,210.4
132,634.4
58,763.4
Error value
0.0457
−0.0256
0.0760
0.0436
0.1226
0.0397
−0.0256
Prediction of patent application for 2015-2025 in Beijing (unit: piece)
Year
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
predicted value
162,571
199,265
244,241
299,368
366,938
449,760
551,274
675,702
828,214
1,015,149
1,244,277
(Table 6) is obtained by taking average of the two prediction results.
5. Beijing R&D Personnel FTE Forecast5.1. Time Series Analysis
According to historical data, time series forecasting method was used, the prediction model of Beijing R&D personnel FTE is obtained:
t = 1 for the year of 1996. The simulation value of Beijing R&D personnel FTE (Table 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.
5.2. GM(1,1) Prediction Model
Matrix 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.
5.3. 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
Prediction of patent application for 2015-2025 in Beijing
Year
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
Predicted value
160,057
194,573
236,549
287,601
349,695
425,226
517,108
628,888
764,884
930,354
1,131,700
Comparison of the simulation value and the actual value of the R&D personnel FTE in Beijing (unit: one year)
Year
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
FTE
84,793
84,913
86,602
85,740
98,723
95,255
114,919
110,358
152,132
177,765
Simulation value
68,572
77,632
86,836
96,181
105,670
115,302
125,077
134,994
145,055
155,258
Relative error
0.1913
0.0857
−0.0027
−0.1218
−0.0704
−0.2105
−0.0884
−0.2232
0.0465
0.1266
Year
2006
2007
2008
2009
2010
2011
2012
2013
2014
FTE
168,875
204,668
200,080
191,779
193,718
217,255
235,493
242,175
245,384
Simulation value
165,604
176,094
186,726
197,501
208,419
219,479
230,683
242,030
253,519
Relative error
0.0194
0.1396
0.0667
−0.0298
−0.0759
−0.0102
0.0204
0.0006
−0.0332
FTE: full-time equivalent.
Prediction of R&D personnel FTE for 2015-2025 in Beijing city (unit: one year)
Year
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
Predicted value
265,151
276,927
288,845
300,906
313,110
325,457
337,947
350,580
363,355
376,273
389,335
Comparison of the simulation value and the actual value of the R&D personnel FTE in Beijing (unit: one year)
Year
1998
1999
2000
2001
2002
2003
2004
2005
2006
Actual value
86,602
85,740
98,723
95,255
114,919
110,358
152,132
177,765
168,875
Model value
95,941
102,247
108,967
116,129
123,762
131,896
140,566
149,804
159,651
Error value
−0.1078
−0.1925
−0.1038
−0.2191
−0.0769
−0.1952
0.0760
0.1573
0.0546
Year
2007
2008
2009
2010
2011
2012
2013
2014
Actual value
204,668
200,080
191,779
193,718
217,255
235,493
242,175
245,384
Model value
170,144
181,327
193,245
205,946
219,482
233,908
249,282
265,667
Error value
0.1687
0.0937
−0.0076
−0.0631
−0.0103
0.0067
−0.0293
−0.0827
Prediction of R&D personnel FTE for 2015-2025 in Beijing (unit: one year)
Year
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
Predicted value
283,128
301,737
321,569
342,705
365,230
389,235
414,818
442,083
471,140
502,106
535,108
2015-2025 (Table 11) is obtained by taking average of the two prediction results.
6. 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 of modeling sequence and the size of subordinate interval to determine [10] .
First, is defined as Equation (25)
the Covering formula is:
then, the selected sequence can be modeled.
2) For according to Equation (27) to generate, that can be seen in Table 13.
a) For,according to Equation (29) for the mean of processing as.
b) Based on and has GM(1,N) data matrix B and data vector yN,
Prediction of R&D personnel FTE for 2015-2025 in Beijing
Year
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
FTE
274,140
289,333
305,207
321,806
339,170
357,346
376,383
396,331
417,247
439,190
462,221
Historical data of innovation evaluation in Beijing (Patent Application Amount, S&T activities personnel, R&D personnel FTE)
Year
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
Patent application (x1)
6595
6313
6321
7723
10,344
12,174
13,842
17,003
18,402
22,572
FTE (x2)
84,793
84,913
86,602
85,740
98,723
95,255
114,919
110,358
152,132
177,765
S&T personnel (x3)
265,552
273,161
237,127
229,584
261,113
240,609
257,326
270,921
301,202
383,153
Year
2006
2007
2008
2009
2010
2011
2012
2013
2014
Patent application (x1)
26,555
31,680
43,508
50,236
57,296
77,955
92,305
123,336
138,111
FTE (x2)
168,875
204,668
200,080
191,779
193,718
217,255
235,493
242,175
245,384
S&T personnel (x3)
382,756
450,331
450,147
529,985
529,811
605,980
651,003
681,346
726,792
c) According to the method of least squares identification algorithm
Thus,
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).
The results of AGO for<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/1-2310577x69.png" xlink:type="simple"/></inline-formula>
k
1
2
3
4
5
6
7
8
9
10
6595
12,908
19,229
26,952
37,296
49,470
63,312
80,315
98,717
121,289
84,793
169,706
256,308
342,048
440,771
536,026
650,945
761,303
913,435
1,091,200
265,552
538,713
775,840
1,005,424
1,266,537
1,507,146
1,764,472
2,035,393
2,336,595
2,719,748
k
11
12
13
14
15
16
17
18
19
147,844
179,524
223,032
273,268
330,564
408,519
500,824
624,160
762,271
1,260,075
1,464,743
1,664,823
1,856,602
2,050,320
2,267,575
2,503,068
2,745,243
2,990,627
3102,504
3,552,835
4,002,982
4,532,967
5,062,778
5,668,758
6,319,761
7,001,107
7,727,899
Fitted values and errors of the GM(1,n) prediction model
Year
1997
1998
1999
2000
2001
2002
2003
2004
2005
Actual value
6313
6321
7723
10,344
12,174
13,842
17,003
18,402
22,572
Fitted values
3957
5673
7440
9609
120,185
14,326
17,454
20,017
23,437
Residual error
0.3731
0.1026
0.0366
0.0711
0.0129
−0.0350
−0.0265
−0.0878
−0.0383
Year
2006
2007
2008
2009
2010
2011
2012
2013
2014
Actual value
26,555
31,680
43,508
50,236
57,296
77,955
92,305
123,336
138,111
Fitted values
27,935
33,062
39,961
50,098
61,478
75,812
93,517
115,763
142,936
Residual error
−0.0520
−0.0436
0.0815
0.0028
−0.0730
0.0275
−0.0131
0.0614
−0.0349
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 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 value, also for the national science and technology talent investment policies provide certain basis.
7. 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
Prediction of S&T activities personnel for 2015-2025 in Beijing
Year
2015
2016
2017
2018
2019
2020
Predicted value
680,208
725,040
773,663
826,683
884,834
949,005
Year
2021
2022
2023
2024
2025
Predicted value
1,020,271
1,099,941
1,189,606
1,291,208
1,407,114
Prediction of S&T activities personnel for 2015-2025 in Beijing
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.
Acknowledgements
This work was supported by the National Natural Science Foundation of China (71540028, F012408), and Major Research Project of Beijing Wuzi University. Funding Project for Technology Key Project of Municipal Education Commission of Beijing (ID: TSJHG201310037036); Funding Project for Beijing key laboratory of intelligent logistics system (No: BZ0211); Funding Project of Construction of Innovative Teams and Teacher Career Development for Universities and Colleges Under Beijing Municipality (ID: IDHT20130517); Funding Project for Beijing philosophy and social science research base specially commissioned project planning (ID: 13JDJGD013) ; Beijing Intelligent Logistics System Collaborative Innovation Center.
Cite this paper
Xiaocun Mao,Zhenping Li, (2016) Predicting the Number of Beijing Science and Technology Personnel Based on GM(1,N) Model. Open Journal of Applied Sciences,06,299-309. doi: 10.4236/ojapps.2016.65029
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