數(shù)學(xué)實驗論文.

1、城市空氣污染數(shù)據(jù)的真實性判別及分析研究1.摘要空氣質(zhì)量問題始終是政府、環(huán)境保護(hù)部門和全國人民關(guān)注的熱點問題。2016年的兩會上,全國政協(xié)常委、環(huán)境保護(hù)部副部長吳曉青表示，政府工作報告中提出的今后五年地級市及以上城市空氣質(zhì)量優(yōu)良天數(shù)比率超過80的目標(biāo)必須完成。其中，優(yōu)良天數(shù)比率指的是：區(qū)域內(nèi)城鎮(zhèn)空氣質(zhì)量優(yōu)良以上的監(jiān)測天數(shù)占全年監(jiān)測總天數(shù)的比例。針對此，我們小組剛好找到了浙江舟山的相關(guān)數(shù)據(jù)，AQI指數(shù)與影響空氣質(zhì)量的污染物（PM2.5、PM10、CO、NO2、SO2）并用matlab對此進(jìn)行分析。關(guān)鍵詞：多元線性回歸模型；散點圖；層次分析；殘差分析；相關(guān)性分析2.模型建立2.1問題分析針對按照常識

2、，空氣污染指數(shù)隨影響空氣質(zhì)量的污染物（PM2.5、PM10、CO、NO2、SO2）的上升而增大?？諝赓|(zhì)量指數(shù)AQI為y，PM2.5的含量為x1，PM10的含量為x2，CO的含量為x3，NO2的含量為x4，SO2的含量為x5。利用matlab分別作出y對x1、 x2、x3、x4、x5的散點圖，如后圖所示， 所以假設(shè)y與x1、x2、x3、x4、x5的關(guān)系為線性關(guān)系。圖2-1- Error! Main Document Only.Y對x1的散點圖圖2-1- Error! Main Document Only.Y對x1的散點圖圖2-1 Error! Main Document Only.Y對x2的散點

3、圖Y對x2的散點圖2.2符號假設(shè)r:殘差向量rint：r的置信區(qū)間b:參數(shù)估計值bint：b的置信區(qū)間：復(fù)相關(guān)系數(shù)F:檢驗統(tǒng)計量P：F統(tǒng)計量對應(yīng)的概率：剩余平方和State：回歸模型的檢驗統(tǒng)計量：回歸系數(shù)向量 =（，）Y：空氣質(zhì)量指數(shù)向量X1:PM2.5的含量（直徑小于2.5um可吸入顆粒）X2：PM10的含量(直徑小于10um的可吸入顆粒)X3:CO的含量（CO為一氧化碳）X4：NO2的含量（NO2為二氧化氮）X5：SO2的含量（SO2為二氧化硫）：隨機誤差p：相關(guān)系數(shù)矩陣2.3模型建立模型一的建立空氣質(zhì)量指數(shù)AQI為y與PM2.5的含量為x1，PM10的含量為x2，CO的含量為x3，NO2

4、的含量為x4，SO2的含量為x5之間的多元線性回歸模型為y=+x1+x2+x3+x4+x5+其中，是帶估計的回歸系數(shù)，是隨機誤差。3.模型計算31 問題一的計算利用matlab命令：b,bint,r,rint,s=regress(y,X)，rcoplot(r,rint)得到殘差分析表圖2-1- 3再由殘差置信區(qū)間得出異常數(shù)據(jù)第8、25、26、31、33、36、37、38、39、40、50、51、56、57、79、223、229、276組得到回歸模型的系數(shù)（置信區(qū)間95%）表3- 1回歸系數(shù)回歸系數(shù)估計值回歸系數(shù)置信區(qū)間16.043411.9930 20.09380.0819-0.0395 0.

5、20330.67500.5878 0.762213.94807.8771 20.0189-0.2308-0.3666 -0.0951-0.3412-0.5515 -0.1309R2= 0.8221 F= 439.0060 p< 0.0001 s2 = 171.8599有表中數(shù)據(jù)可知的置信區(qū)間包含零點，所以這個系數(shù)的解釋是不可靠的。再用matlab中的corrcoef命令直接得到相關(guān)系數(shù)矩陣1.0000 0.9310 0.7222 0.7294 0.7094 0.8542 0.9310 1.0000 0.6662 0.7714 0.7543 0.8948 0.7222 0.6662 1.0

6、000 0.5731 0.5147 0.6670 0.7294 0.7714 0.5731 1.0000 0.7183 0.6412 0.7094 0.7543 0.5147 0.7183 1.0000 0.6194 0.8542 0.8948 0.6670 0.6412 0.6194 1.0000又表中數(shù)據(jù)可知X1與X2關(guān)系顯著，所以X1多余，應(yīng)當(dāng)去掉。去掉X1后再用上述方法得到殘差分析表圖2-1- 4由殘差置信區(qū)間得出異常數(shù)據(jù)第8、25、26、31、33、36、37、38、39、40、50、51、56、57、79、223、229、276，321組得到回歸模型的系數(shù)（置信區(qū)間95%）表3-

7、2回歸系數(shù)回歸系數(shù)估計值回歸系數(shù)置信區(qū)間15.010511.2579 18.76310.72070.6658 0.775615.47219.8331 21.1111-0.2314-0.3672 -0.0955-0.3380-0.5484 -0.1276R2= 0.8214 F= 547.4489 p< 0.0001 s2 = 172.1328得到線性回歸方程y=15.0105+0.7207x2+15.4721x3-0.2314x4-0.3380x5數(shù)據(jù)真實性判定:表3- 3組數(shù)AQI指數(shù)PM2.5PM10CONO2SO2異常點（為0異常）3015531490.75174321555110

8、.544303475527540.711752106431570.791452296415200.548404156434750.9939104616434620.81882565431600.76192401156544631.32872438562741.0516331861071621.32614304668762940.9326820988599312582238950600.62311302768918280.6612303678959880.6831834991071411.3463114010242681.1235220137103771060.9557245110537560.

9、9328180416106771241.135425208108801471.123818501091381841.5756560561091592131.826959060109731151.316130408109681310.954225391101201571.7445290811152640.762140207111661041.243715431115861411.5359315711627510.9526150129116871201.43816470124931341.1721826125602170.9742200373126921400.993418458133981351

10、.3382733134781171.24381903813865901.183180641381021661.2782414331511141811.768340361542812792.2168300651611201831.436644321801602191.636433791861431841.19312604321951482311.99341373581252842.436618032 問題二的計算由表中數(shù)據(jù)觀測出有些組的數(shù)據(jù)與其它組的數(shù)據(jù)相差過大，視為不真實數(shù)據(jù)，其中不真實數(shù)據(jù)有第8、25、26、31、33、36、37、38、39、40、50、51、56、57、79、223、22

11、9、276，321組數(shù)據(jù)嚴(yán)重性檢驗表3- 4組數(shù)AQI指數(shù)PM10CONO2SO2異常點（為0異常）殘差置信區(qū)間8111640.76214018.8768169.7542425651600.7619240-89.0618-40.0897261252170.9742200-69.5421-20.330831861621.3261430-62.6926-12.3918331341171.24381905.13386156.25462361542792.2168300-94.2584-46.5631373582842.4366180100.6592143.466838138901.18318024.

12、4333475.05522391101571.7445290-50.2250.48330340102681.123522010.7595961.61226501091841.5756560-55.7525-6.3049451105560.932818022.4651273.14018561092131.8269590-76.169-27.382557116510.952615035.4853785.75471791861841.193126010.8292461.0235322389600.62311307.16951758.2708322964200.548403.81654155.0298

13、427689280.66123021.9795372.7969732155110.544300.0227251.26964殘差置信區(qū)間到原點最小值0-2020-50>50嚴(yán)重程度輕微中等嚴(yán)重輕微嚴(yán)重的有第8、31、33、39、40、50、79、223、229、321組中等嚴(yán)重的有第25、26、36、38、51、56、57、276組強烈嚴(yán)重的有第37組3.3問題三的計算3.2.1數(shù)據(jù)不真實的類型和原因（1）各級發(fā)布數(shù)據(jù)存在差異，各自自成體系（2）實時空氣質(zhì)量指數(shù)評價滯后（3）城市空氣質(zhì)量無評價方法3.2.2為環(huán)境保護(hù)和政策制定提供的對策（1）國家、省、市三級業(yè)務(wù)平臺實現(xiàn)統(tǒng)一數(shù)據(jù)（2）用均值

14、法計算城市各污染物濃度（3）調(diào)整空氣實時報發(fā)布方式4 .模型推廣41問題四的計算相關(guān)性分析：舟山市月平均AQI指數(shù)與鋼材產(chǎn)量表3- 5時間AQI指數(shù)鋼材產(chǎn)量2013年12月164.48198.12013年11月111.93178.12014年12月100.24194.82014年11月74.61163.22014年10月68.52167.72014年9月60.9187.42014年8月60.07198.42014年7月68.81196.72014年6月66.37200.52014年5月94.23204.52014年4月76.932002014年3月82.5204.72014年2月89.2419

15、1.3用matlab中的corrcoef命令直接得到相關(guān)系數(shù)矩陣1.0000 0.13010.1301 1.0000一般認(rèn)為，兩個變量的相關(guān)系數(shù)超過0.85時才具有顯著的相關(guān)關(guān)系因為0.1301<0.85所以AQI與鋼材產(chǎn)量相關(guān)性不顯著所以舟山不能用空氣質(zhì)量數(shù)據(jù)的變化來展示工業(yè)生產(chǎn)（例如鋼產(chǎn)量）等數(shù)據(jù)的實際情況參考文獻(xiàn)1 環(huán)境空氣質(zhì)量標(biāo)準(zhǔn), 中華人民共和國國家標(biāo)準(zhǔn)，GB 3095-20122 環(huán)境空氣質(zhì)量指數(shù)（AQI）技術(shù)規(guī)定（試行）：中華人民共和國國家環(huán)境保護(hù)標(biāo)準(zhǔn)，HJ 633-20123資源節(jié)約與環(huán)保2013年，第十二期4方開泰：實用多元統(tǒng)計分析.上海：華東師范大學(xué)出版社，1989。

16、5高惠璇：應(yīng)用多元統(tǒng)計分析.背景：北京大學(xué)出版社，20056王學(xué)民：應(yīng)用多元分析（第二版）.上海：上海財經(jīng)大學(xué)出版社，20047 Ghanem, D., & Zhang, J. (2014). Effortless perfection: Do Chinese cities manipulate air pollution data. Journal of Environmental Economics and Management, 68(2), 203-225.8王正林等.精通MATLAB科學(xué)計算（第二版）.北京：機械工業(yè)出版社，20069董維國，深入淺出MATLAB7.x混合編程

17、.北京：機械工業(yè)出版設(shè)，200610龔純，王正林.MATLAB語言常用算法程序集（第二版）.北京：電子工業(yè)出版社，200811張志剛等.MATLAB與數(shù)學(xué)實驗（第二版）。北京：中國鐵道出版社，200312姜啟源等.數(shù)學(xué)模型（第四版）。北京：高等教育出版社，2011附錄舟山市的空氣質(zhì)量和氣候數(shù)據(jù)表3- 6組數(shù)AQI指數(shù)PM2.5PM10CONO2SO215421420.5110224420330.5214234828490.5921145132530.6415254824500.5624266258950.924447113981330.744111811152640.7621494924340

18、.62202103721340.62131114623470.56144124015280.5119713297230.43142143728590.7133615951001331.31433316132951741.15492617112571540.83027187035750.712727196851920.954630207653921.044820216741690.84369226344710.8388236744780.77236246130500.942872565431600.76192426125602170.97422027112611550.9542202873276

19、60.772520295929650.792822306046720.92411331861071621.326143321801602191.63643333134781171.24381934991071411.34631135119781071.274910361542812792.216830373581252842.4366183813865901.18318391101201571.7445294010242681.1235224172641121.084633427440780.92402343826611314731447222530.67258456150850.682116

20、466017300.612447333110.59141484017350.6274496961850.983119501091381841.5756565110537560.932818524427430.76237534626450.74206546468921.152223559050771.042412561091592131.8269595711627510.952615586047821.0443315984811311.31564160109731151.316130618558971.116730627659990.96623637647770.7652156413810216

21、61.278241651611201831.436644665026540.732710673918420.75305685835680.92497695227430.73023704418420.34107715529600.52010724022390.41154736140540.5297748051770.61101275378210.3363764215310.3975776344690.72277788561840.854012791861431841.193126808562860.942112811771361951.374342827033850.76191783532556

22、0.722012843811210.551158598701040.892213865020430.697387328260.64174883618370.75268893718320.71186907856731.0627991128961161.26178923517250.89183939067791.37245945230481.1372953712290.7933963510250.755197326160.84519829360.8771994424330.95741004328400.99441013617260.853210240253611251033315240.93821

23、044415260.92411054421361621064315250.95821073710190.961211083925301.33191093511151.18811106139481.35218111118881131.572833112108801041.4624221135936521.422141147151721.341971156544631.32871164313210.972211173522261.152861185337501.092021199268841.252281204211161.18911215326481.34961225315381.0463123

24、4010280.881121245121430.93731254313310.8762126438240.99421274811151.24711285325401.11195129116871201.438161304921360.982191313716290.642971324420390.431661336542760.5538151347140660.526131355931550.482281366242630.57318137103771060.9557241386041620.683041396436720.571761404711430.371431414617440.412

25、561424418370.431841433217310.513561446645650.862791455533430.721731463517240.652841473825330.852641489267901.0423111497352680.872471504631410.773051515235500.743261524018280.621731535521550.632571546931700.692481554412360.521021564212270.541631574627460.672671584524340.711721595131430.68195160602840

26、0.651121615635490.843151625834450.861651636528420.71731645726410.741741654620360.712451667049720.893381677953811.143171684217260.781411694518270.741011704728430.781521715726380.811421725536560.892751734931470.922421744516300.79102175418220.77721764624291.161751776042510.981371787144661.0325121795532

27、500.93281806141600.9431618161406513081826841800.951651835731630.942141845223510.791121855621520.781741865320430.851531879245861.0925131886638720.951421894823400.911121903113200.971121917248631.4528101927144571.2729101937145571.352781949657791.281981956736781.042981966227491.021631975417270.919719846

28、26400.8520101997848621.0522122006941610.8926102015228380.781962024413250.691032034312270.68832043317280.8304205118881151.442310206121901141.432311207111661041.243715208108801471.12381820988599312582106431570.791452114718330.791232126334491.061052136333430.941172147348681.072192154720360.851332164819

29、310.661452174116210.491172183818260.5942193517240.64732205235440.57692214221370.36732226140550.461652238950600.6231132247852560.512392255221400.431152264119240.43832274933330.751942285615190.46632296415200.54842304220170.571932315535250.5415212324111140.51622333823220.59132234429170.542119235516120.

30、521322365231380.6720102373416170.621682383615240.592032393319290.642572404329320.661642413721270.681122424628310.81722438562741.051632448249570.891032453511120.62622466242490.891032477039540.88104248419140.7332493921350.75722505840600.963372515235450.872962525235480.8625425339232811322544512180.9472

31、2554933380.922552562313160.72124257179150.6753258167140.68622592110190.71103260178130.72123261156110.794262167120.71842633410270.68432643512340.54422653717360.61822662812230.591132673414260.641332683313290.692042692710150.611342704012230.6289271187170.6122272205180.62222733317270.83732744020300.8718

32、32755931420.851132768918280.66123277196160.641342782511240.621252793614270.66832805931500.911452816214190.72532825722190.65642834912210.74642843214240.86113285509170.8932864218290.861732874324350.891632883515210.95183289318130.88193290357120.781162915924400.831042923718310.671432933519320.6510329458

33、36481.031442957644621.08832965629380.91032974829410.792242986243660.83242994820310.661033004414300.591143015531490.751743027539530.8715173033618300.661543048259840.921683058150640.791353064425330.58733074722340.54743085026390.59953094628360.621443104529410.62843115113240.531653124014280.561563134017

34、320.751943144413250.5374315428200.46543165014270.53743174723330.641093184617250.6653194910150.62733204711220.68134321555110.5443322376140.5523323219160.872053243518320.851753255920390.661253266332520.881553275025370.81763283911230.761453295631580.972483304418330.921343314312340.681343325122500.85166

35、3336933580.891363345613340.61943356717580.69853366928610.79973376020380.71053385313310.73953395115340.79133404915350.6453415419440.61353425620530.62443436025580.68873446226690.77181534583491070.962518346112791411.1537253475527540.71175348379230.571443493614320.621663503919360.641463517749800.942293524717330.66733535118440.651343544213280.631743553913290.611653565427570.712073576029570.731053584913400.651133594616440.731743604214330.71593613716350.732763625335511.464073634631451.032383644317360.691773654517420.6721536643183