数学实验论文.

1、城市空气污染数据的真实性判别及分析研究1.摘要空气质量问题始终是政府、环境保护部门和全国人民关注的热点问题。2016年的两会上,全国政协常委、环境保护部副部长吴晓青表示，政府工作报告中提出的今后五年地级市及以上城市空气质量优良天数比率超过80的目标必须完成。其中，优良天数比率指的是：区域内城镇空气质量优良以上的监测天数占全年监测总天数的比例。针对此，我们小组刚好找到了浙江舟山的相关数据，AQI指数与影响空气质量的污染物（PM2.5、PM10、CO、NO2、SO2）并用matlab对此进行分析。关键词：多元线性回归模型；散点图；层次分析；残差分析；相关性分析2.模型建立2.1问题分析针对按照常识

2、，空气污染指数随影响空气质量的污染物（PM2.5、PM10、CO、NO2、SO2）的上升而增大。空气质量指数AQI为y，PM2.5的含量为x1，PM10的含量为x2，CO的含量为x3，NO2的含量为x4，SO2的含量为x5。利用matlab分别作出y对x1、 x2、x3、x4、x5的散点图，如后图所示， 所以假设y与x1、x2、x3、x4、x5的关系为线性关系。图2-1- Error! Main Document Only.Y对x1的散点图图2-1- Error! Main Document Only.Y对x1的散点图图2-1 Error! Main Document Only.Y对x2的散点

3、图Y对x2的散点图2.2符号假设r:残差向量rint：r的置信区间b:参数估计值bint：b的置信区间：复相关系数F:检验统计量P：F统计量对应的概率：剩余平方和State：回归模型的检验统计量：回归系数向量 =（，）Y：空气质量指数向量X1:PM2.5的含量（直径小于2.5um可吸入颗粒）X2：PM10的含量(直径小于10um的可吸入颗粒)X3:CO的含量（CO为一氧化碳）X4：NO2的含量（NO2为二氧化氮）X5：SO2的含量（SO2为二氧化硫）：随机误差p：相关系数矩阵2.3模型建立模型一的建立空气质量指数AQI为y与PM2.5的含量为x1，PM10的含量为x2，CO的含量为x3，NO2

4、的含量为x4，SO2的含量为x5之间的多元线性回归模型为y=+x1+x2+x3+x4+x5+其中，是带估计的回归系数，是随机误差。3.模型计算31 问题一的计算利用matlab命令：b,bint,r,rint,s=regress(y,X)，rcoplot(r,rint)得到残差分析表图2-1- 3再由残差置信区间得出异常数据第8、25、26、31、33、36、37、38、39、40、50、51、56、57、79、223、229、276组得到回归模型的系数（置信区间95%）表3- 1回归系数回归系数估计值回归系数置信区间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有表中数据可知的置信区间包含零点，所以这个系数的解释是不可靠的。再用matlab中的corrcoef命令直接得到相关系数矩阵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又表中数据可知X1与X2关系显著，所以X1多余，应当去掉。去掉X1后再用上述方法得到残差分析表图2-1- 4由残差置信区间得出异常数据第8、25、26、31、33、36、37、38、39、40、50、51、56、57、79、223、229、276，321组得到回归模型的系数（置信区间95%）表3-

7、2回归系数回归系数估计值回归系数置信区间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得到线性回归方程y=15.0105+0.7207x2+15.4721x3-0.2314x4-0.3380x5数据真实性判定:表3- 3组数AQI指数PM2.5PM10CONO2SO2异常点（为0异常）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 问题二的计算由表中数据观测出有些组的数据与其它组的数据相差过大，视为不真实数据，其中不真实数据有第8、25、26、31、33、36、37、38、39、40、50、51、56、57、79、223、22

11、9、276，321组数据严重性检验表3- 4组数AQI指数PM10CONO2SO2异常点（为0异常）残差置信区间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残差置信区间到原点最小值0-2020-50>50严重程度轻微中等严重轻微严重的有第8、31、33、39、40、50、79、223、229、321组中等严重的有第25、26、36、38、51、56、57、276组强烈严重的有第37组3.3问题三的计算3.2.1数据不真实的类型和原因（1）各级发布数据存在差异，各自自成体系（2）实时空气质量指数评价滞后（3）城市空气质量无评价方法3.2.2为环境保护和政策制定提供的对策（1）国家、省、市三级业务平台实现统一数据（2）用均值

14、法计算城市各污染物浓度（3）调整空气实时报发布方式4 .模型推广41问题四的计算相关性分析：舟山市月平均AQI指数与钢材产量表3- 5时间AQI指数钢材产量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命令直接得到相关系数矩阵1.0000 0.13010.1301 1.0000一般认为，两个变量的相关系数超过0.85时才具有显著的相关关系因为0.1301<0.85所以AQI与钢材产量相关性不显著所以舟山不能用空气质量数据的变化来展示工业生产（例如钢产量）等数据的实际情况参考文献1 环境空气质量标准, 中华人民共和国国家标准，GB 3095-20122 环境空气质量指数（AQI）技术规定（试行）：中华人民共和国国家环境保护标准，HJ 633-20123资源节约与环保2013年，第十二期4方开泰：实用多元统计分析.上海：华东师范大学出版社，1989。

16、5高惠璇：应用多元统计分析.背景：北京大学出版社，20056王学民：应用多元分析（第二版）.上海：上海财经大学出版社，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科学计算（第二版）.北京：机械工业出版社，20069董维国，深入浅出MATLAB7.x混合编程

17、.北京：机械工业出版设，200610龚纯，王正林.MATLAB语言常用算法程序集（第二版）.北京：电子工业出版社，200811张志刚等.MATLAB与数学实验（第二版）。北京：中国铁道出版社，200312姜启源等.数学模型（第四版）。北京：高等教育出版社，2011附录舟山市的空气质量和气候数据表3- 6组数AQI指数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