Open Access Regression Analysis-based Chinese Olympic Games Competitive Sports Strength Evaluation Model Research

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1 Send Orders for Reprints to The Open Cybernetics & Systemics Journl, 05, 9, Open Access Regression Anlysis-bsed Chinese Olympic Gmes Competitive Sports Strength Evlution Model Reserch Guojin Tng * nd Jun Li Shndong Sport University, Jinn 500, Shndong, Chin Abstrct: The pper minly pplies weighted ccumultive method to predict Chinese previous Olympic Gmes medls totl mount nd nlyze golden medls totl mount floting chnge rule. According to nlysis, the pper thinks tht Olympic Gmes medls chnge rule cn be predicted from three spects tht re Chinese economic strength, number of Chinese prticipnts nd Chinese medls mount chnges followed by time. And then it estblishes plnning model tht trgets t minimum error mount between predicted vlue nd ctul vlue, by virtue of previous Olympic Gmes medls dt, pplying regression eqution method, it gets every influence fctor correltions with mount of medls; through pplying lgebric clculus, it solves every influence fctors weights nd then gets medls predicted formul. Use the prediction formul, it solves the mount of medls in 0, nd contrsts with ctul mount of medls in 0, tests formul ccurcy. Input Olympic Gmes relevnt prediction dt in 06 into formul, nd solve Brzil Rio de Jneiro Olympic Gmes predicted medls mount. Keywords: Economic strength, evlution model, lest squre method, sports helth. INTRODUCTION Since Chin s lwful set in interntionl Olympic Committee ws restored in 979, Chin ttended the 3rd Summer Olympic Gmes tht held in Los Angeles, Americ in 94, nd gined 5 golden medls t one stroke tht relized zero brekthrough in Olympic Gmes golden medl. After tht, Chin hs set foot on the rod to push Olympic Gmes development together with people round the world. In Beijing Olympic Gmes just ended, Chin sports delegtion chieved good results of 5 golden medls, silver medls nd copper medls tht rnked the top of golden medl tble nd the top two of medl tble []. Then, how to remin nd strengthen such development trends, let Chin to continue to mintin good momentum of more golden medls chieving in strong events nd gret brekthrough in wek events so tht relly become members of world thletics sports structure first group, which is gret problem bout Olympic Gmed development strtegy tht needs to serious reserch. Therefore, predict future Olympic Gmes performnce is one of hot issues tht re reserched by physicl eductors ll round the world t present, it reltes to ll countries sports strtegies development trget estblishment nd decision-mking mngement []. Olympic Gmes performnce is overll reflection of ll countries competitive sports strength, is sum totl of individul events strength, nd menwhile suffers other countries performnces influence nd mutul restricts. With time chnges, ll countries competitive sports strength will lso chnge, Chin s strong opponent in Olympic Gmes- Americ nd Russi s competitive sports strength is lso constntly chnging, therefore nlyze nd reserch on them is very necessry [3]. By compring Americ, Russi, nd Chin s Olympic Gmes strength, the cler understnding on Chin s competitive sports development sttus cn be obtined, nd then provide theoreticl references for London Olympic Gmes in 0, Sochi Winter Olympic Gmes in 04 nd Chin s competitive sports helthy development to provide theoreticl references for Chin s Olympic Gmes decision nd let Chin s Olympic strength to continue to improve [4]. Olympic Gmes strtegy is long-term stble plnning nd generl plns with trgets of striving for good results nd winning honor for the country in Olympic Gmes. Though Olympic Gmes golden medl is not the whole Olympic Gmes strtegy, it exctly is quite objective, specific nd its importnt prt in Olympic Gmes strtegy. A country sports development is up to mny fctors, including economic development level, sports investment, sports system, sports science nd technology nd else. Therefore, estblish models to predict Olympic Gmes performnces is beneficil to confirm correct Olympic Gmes strtegies nd guide the implementtion of the strtegies ll mesures; estblish models to mesure stte sports strength is beneficil to guide Chin s sports development nd let Chin to continue to keep sports power sitution. Xiong Qin took the th nd 9th summer Olympic Gmes obtined medls countries or regions s smples, reserched on countries economic strength, popultion mount, sports strength, politicl stble fctor, socil development extent, country system nd host effect s well s others seven fctors influences on the mount of obtined Olympic Gmes medls [5]. 74-0X/5 05 Benthm Open

2 730 The Open Cybernetics & Systemics Journl, 05, Volume 9 Tng nd Li Tble. All sessions Olympic Gmes obtined medls mount nd influence fctors sttisticl tble. Yer GDP one hundred million Yun Per cpit GDP Amount of golden medls Amount of medls The number of Chin s prticipnts The number of world prticipnts Rtio of the number of prticipnts % % % % % % % % Medl Number gold quntity medl numbers Per Cpit GDP Fig. (). Broken line figure bout the number of medls chnges with per cpit GDP. The pper minly pplies weighted ccumultive pproch to predict Chin s previous totl mount of Olympic Gmes medls nd nlyze totl mount of golden medls floting chnge rules, nd predicts mount of Chin s medls in 06 Olympic Gmes nd mesure Chin s comprehensive sports strength. RESEARCH ANALYSES Competitive sports hs stronger regulrities, individul event occsionlly doesn t deny necessity of overll development, which lso lets our sports events performnces prediction to be possible. Due to competitive sports is n symptotic development process, country my hve brekthrough in one event in one or two sessions Olympic Gmers cycles, but the country competitive sports overll strength substntilly rising cnnot fulfill in the shortest time, there re very strong correltion between djcent two sessions Olympic Gmes performnces. Therefore, we think chnge of Olympic Gmes medls is Mrkov process. We think Olympic Gmes medls chnge rule cn minly consider from three spects those re Chin s economic strength (tht is per cpit GDP), the number of Chin s prticipnts, s well s the number of Chin s medls entire stte with time chnges. Below re ll sessions Olympic Gmes obtined medls mount from yer 94 to 0 nd influence fctors sttisticl Tble. Economic Fctors Impcts on the Number of Medls We drw chnges tht number of medls follow by per cpit GDP into broken line Fig. (). From Fig. (), we cn see tht generlly, the number of medls is positive relted to per cpit GDP. Then, we dopt lest squre method to clculte one stright line of the highest fitting extent to predict, specific process is s following (due to host effect, it elimintes yer 00 dt): 6 xi * yi 6xy = 6 xi^ 6x^ ; b = y x Dt clcultion sttisticl result is s following Tble : Input tble s dt into solution formul, it solves: = b = Therefore, it gets the formul tht uses per cpit GDP to predict the number of medls s: Y = In the following, we use the formul nd get previous Olympic Gmes medls predicted vlues, list sttisticl tble s following Tble 3:

3 Regression Anlysis-bsed Chinese Olympic Gmes Competitive Sports The Open Cybernetics & Systemics Journl, 05, Volume 9 73 Tble. Ech fctor dt sttisticl tble. Yer code number i Per cpit GDP x i Amount of medls y i x i * y i x i Summtion Men vlue Tble 3. Tble of number of medls prediction through per cpit GDP. Yer Yer code Predicted vlue of totl mount of medls Medl Numbers Number of entries Fig. (). Broken line figure of medls mount chnges by Chinese prticipnts mount. Influence of Proportion of Number of Prticipnts on Number of Medls We crete medls mount chnges by Chinese prticipnts into figure s following Fig. (): From Fig. (), it is cler tht medls mount is incresing with Chinese prticipnts mount increses, similrly we dopt lest squre method to clculte regression eqution, clcultion process is s following: 6 = 6 xi * yi 6xy xi^ 6x^ ; b = y x Dt clcultion sttisticl result is s following Tble 4: Input bove Tble 4 dt into formul, it gets: = b = Therefore, use Chinese prticipnts mount to predict, it gets medls mount predicted formul is: y = x According to solved formul, we cn get Chin previous Olympic Gmes obtined medls mount predicted vlues from yer 94 to 00; crete these predicted vlues into sttisticl tble s following Tble 5: Anlysis of Chin Previous Medls Chnge Rule Followed by Time We drw medls mount chnges with time into following Fig. (3):

4 73 The Open Cybernetics & Systemics Journl, 05, Volume 9 Tng nd Li Tble 4. Ech fctor dt sttisticl tble. Yer code i Per cpit GDP x i Medls mount yi x i * y i x i Summtion Men vlue Tble 5. Tble of previous Olympic Gmes medls mount through prticipnts mount predicting. Yer Yer code x Medl predicted vlue gold quntity medl numbers Yers Fig. (3). Chnge curve figure of medls mount followed by yer. According to bove Tble time sequence informtion, it drws Chin previous Olympic Gmes totl mount of medls time sequence broken line Fig. (3). By observing time sequence figure, it is cler tht time sequence hs obvious chnging trend, from which dt in 00 hs obvious fluctution, we consider tht it hs host effects; therefore we eliminte group of dt in 00 in following nlysis. According to intuitionl judgment, which is crete fitting trend models for previous Olympic Gmes time sequence ttched figure the Olympic Gmes medls broken line figure. Estblish models: We select qudric curviliner trend model: Y (t) = + bt + ct In bove eqution, three unknown prmeters, b, c, ccording to lest squre method, it solves time sequence fitting one pieces of trend curve, nd lets it to meet following conditions: Y = n + b t+ ct ty = t+ bt + ct 3 t Y = t + bt 3 + ct 4 According to bove Tble 6 clcultion, it gets, b, c results s following: 6 = 6 + b + 9c =.6 3 = + 9b + 44c b = = b + 75c c = 0.5

5 Regression Anlysis-bsed Chinese Olympic Gmes Competitive Sports The Open Cybernetics & Systemics Journl, 05, Volume Tble 6. Olympic Gmes medls qudrtic curve clcultion tble. Yer Time mrk number t Observed vluey t t *Y t t t *Y t Y 3 t Tble 7. Rurl sports ground nd equipment mintennce. Yer Yer code Medls totl mount predicted vlue x Therefore, it gets Chin Olympic Gmes medls totl mount qudrtic curve eqution s: Y( t) = t 0.5t According to model, it cn get previous Olympic Gmes medl predicted vlue tble s following Tble 7To get round numbers, we use round off: We use the eqution to solve totl mount of medls in 0 is:70. Model Solution We respectively predict from three spects, but medl prediction covers so extensive fields, whose ctul vlue cnnot be correctly predicted by just one isolted spect. So, we utilize weighted summtion method to synthesize these three spects to let our predicting work to be more ccurte, specifics re s following: We mke sttistics of ll predicted vlues s following Tble : Input bove Tble dt into eqution y = x + x + 3 x = : It solves: = = = Therefore, we get finl medl prediction model formul: Y = X + X X Model Test Then we will use prediction formul to clculte Chin obtined totl mount of medls in 0 Olympic Gmes, 3 nd then compre with ctul vlue of Chin obtined totl mount of medls in 0, test formul ccurcy. Input yer 0 X = 4, X = 5, X 3 = 70 into formul, it solves predicted vlue of totl mount of medls in 0 is 4, while ctul totl mount of medls in 0 is, there is 4 pieces difference, on whole, it is supposed tht prediction model ccurcy is higher. Model Applictions Use model to predict unknown Chin chievble totl mount of medls in 06 Olympic Gmes, nd then it needs Chinese prticipnts mount in 06 nd Chinese per cpit GDP in 06 these two unknown quntities (Fig. 4). Therefore, we further conduct scientific prediction on the two quntities, specific process is s following: Prediction on Per Cpit GDP in 06: Per Cpit GDP Fig. (4). Curve figure of per cpit chnges with time. Per Cpit GDP Above Fig. (4) is per cpit GDP chnges with time, from the figure, it is cler tht figure roughly shows qudrtic function type, nd then we use qudrtic regression eqution to predict per cpit GDP in 06, specific process is s following:

6 734 The Open Cybernetics & Systemics Journl, 05, Volume 9 Tng nd Li Tble. Predicted vlue sttisticl tble. X X X Y Tble 9. Prediction tble of per cpit GDP in 06. Yer Yer code x Per cpit GDP ( y x x 3 x 4 xy x y SUB Tble 0. Prediction tble of Chinese prticipnts mount in 06 Olympic Gmes. Yer Yer code x Amount of Chinese prticipnts y x xy xi^4 + bxi^3 + cxi^ = xi^3 + b xi^ + b xi^ + c xi + c = xi = yi xi^ yi xi yi Input Tble 9 dt into lest squre method formul, it gets: b + 04c = b + 36c 577 = b + c 733 = 0 By excel MDETERM function, it solves the threevrible liner eqution nd gets: = 9.4 b = 37. c = And further it gets y = 9.4x Input x = 9 nd get: y = Therefore, we get Chin per cpit GDP in 06 is Yun

7 Regression Anlysis-bsed Chinese Olympic Gmes Competitive Sports The Open Cybernetics & Systemics Journl, 05, Volume Prediction on Number of Chinese Prticipnts in 06 Olympic Gmes: We use liner regression to predict Chinese prticipnts mount: 6 xi * yi 6xy = 6 xi^ 6x^ ; b = y x Input Tble 0 dt into formul nd clculte, then get: = 4. b = 4.6 Therefore, Chinese prticipnts mount prediction formul is: Y = 4.6x + 4. Input x = 9 nd get Y = 439 Therefore Chin will hve 439 thletes in 06 Olympic Gmes. Predict Totl Amount of Medls of Chin in 06 Olympic Gmes Apply we obtined three prediction formuls, we input per cpit GDP in 06 nd prticipnts in 06 respectively into prediction formuls, nd get medl predicted vlue in 06 x = 5, x = 54, x3 = 7 Finlly, we input x, x, x 3 in 06 into Y = x x x 3, nd get y = 9, so we get the number of medls in 06 is 9. Rtio between golden medls mount nd medls mount is round 40%~50%, therefore golden medls mount in 06 Rio de Jneiro should be mong 44~46. CONCLUSION A country or region comprehensive sports performnce suffers significnt influences from popultion scle, economic strength, income level, host effect, fondness nd focus on sports, system s well s geogrphic loction nd other objective fctors, which hs internl regulrities, so it should tret sports performnces with correct ttitude nd not blindly compre oneself with others. To chieve greter results in comprehensive sports, Chin should dhere to objective lw nd work from foundtion, from which the key points re continuing to strive for improving Chinese overll economic strength nd people income level, insisting on the whole ntion system, incresing investment to impel ntionwide fitness undertking development, strengthening ntionl fitness consciousness, fostering sports enthusism, focusing on helthy ntionl culture. The pper pplies weighted ccumultive method to predict on Chin previous Olympic Gmes medls totl mount nd nlyzes golden medls totl mount floting chnge rule, mkes objective evlution on Chinese comprehensive sports level, which is of certin guiding significnce. CONFLICT OF INTEREST The uthors confirm tht this rticle content hs no conflict of interest. ACKNOWLEDGEMENTS Declred none. REFERENCES [] L. Ci, nd J. Ji, The role of locl government in MICE, Journl of Huzhong University of Science nd Technology(Socil Science Edition), vol., no. 5, pp , 007. [] J. Dong, Existing minly problems, resons nd countermesures bout Chin host meg sport events, Sports & Science, vol. 33, no. 3, pp. 4-5, 0. [3] H, Guo, nd Y. Zhu, Anlysis nd strtegic reserch on Chins current sports industry development, Fujin Sports Science nd Technology, vol. 0, no. 3, pp. 3-5, 03. [4] X. Hung, nd W. Zeng, Reserch on the commercilized opertion of Chinese lrge physicl gmes with the public welfre, Sci- Tech Informtion Development & Economy, vol. 7, no., pp. 37-3, 007. [5] L. Zhou, X. Chen, nd X. Zhou, Sttus nd role of government in sport event exhibition industry-tking shnghi s n exmple, Sports Science Reserch, vol., no. 4, pp. 4-5, 007. Received: My 6, 05 Revised: July 4, 05 Accepted: August 0, 05 Tng nd Li; Licensee Benthm Open. This is n open ccess rticle licensed under the terms of the ( which permits unrestricted, noncommercil use, distribution nd reproduction in ny medium, provided the work is properly cited.