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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.

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 [

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 [

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 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 [

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

The calculation formula is as follows:

where,

4) Gray correlation degree

The grey correlation degree between the reference sequence

In the formula,

5) Correlation degree ranking

When

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

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:

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% [

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 [

Specific algorithm is:

1) In this paper, the original data sequence is assumed to be

The one-time accumulated generating sequence of

where

2) The GM(1,1) parameters a, b of

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

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 (

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 (

Matrix

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 (

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 (

The results of two groups are averaged. Thus the predict value of the patent application in Beijing in 2015-2025

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 |

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 |

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 |

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 |

(

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 (

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 (

Matrix

thus, grey differential equation is:

whitening equation is:

Thus model value of R&D personnel FTE in Beijing for 1998-2014 in Beijing (

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 (

The results of two groups are averaged. Thus the forecast value of the R&D personnel FTE in Beijing in

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 |

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.

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 |

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 |

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 (

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 [

1) GM(1,N) modeling, we first need to pre-test with a cover formula, which uses step ratio

First,

the Covering formula is:

then, the selected sequence can be modeled.

2) For

a) For

b) Based on _{N},

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 |

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 (

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 (

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 |

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 (

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) [

・ 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

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 |

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.

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.

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