一组空气污染数据的主成分分析

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1、一组空气污染数据的主成分分析【说明】下面的多元统计分析练习题摘自R.A.Johnson等编写的《应用多元统计分析（第五版）》，原书为：RichardA.JohnsonandDeanW.Wichern.AppliedMultivariateStatisticalAnalysis(5thEd).PearsonEducation,Inc.2003。我看的是中国统计出版社（ChinaStatisticsPress）2003年发行的影印本。第一题为原书第1.6题，即第1章的第6题，第二题为原书第8.12题，即第8章的第12题。第二题用的是第一题的数据。1习题1.6.ThedatainTa

2、ble1.5are42measurementsonair-pollutionvariablesrecordedat12:00noonintheLosAngelesareaondifferentdays.(a)Plotthemarginaldotdiagramsforallthevariables.(b)Constructthe,Sn,andRarrays,andinterprettheentriesinR.TABLE1.5AIR-POLLUTIONDATAWind(x1)Solarradiation(x2)CO(x3)NO(x4)NO2(x5)O3(x6)HC(x7)89872

3、1282710743953710343563108852815469142810389052121249847412155572642114478251111138645213946715410336914212737727418103107042117310724181039774191038764177387153164496742132396933953106253144414988427638804213114530335236835110234884327636784211113879217103662439831037317238714110737524112845

4、48658436754110243103541692885419102586316122586721318277974925377952862668621114384043652Source:DatacourtesyofProfessorG.C.Tiao.8.12.Considertheair-pollutiondatalistedinTable1.5.Yourjobistosummarizethesedatainfewerthanp=7dimensionsifpossible.Conductaprincipalcomponentanalysisofthedatausingbo

5、ththecovariancematrixSandthecorrelationmatrixR.Whathaveyoulearned?Doesitmakeanydifferencewhichmatrixischosenforanalysis?Canthedatabesummarizedinthreeorfewerdimensions?Canyouinterprettheprincipalcomponents?2部分解答2.1部分统计参数利用Excel计算的平均值（）和标准差　WindSolarradiationCONONO2O3HCAverage7.573.8571434.547

6、6192.190476210.0476199.40476193.0952381Stdev1.581138817.3353881.23372091.08735743.37098375.56583450.6917466Excel给出的协方差矩阵S　WindSolarCONONO2O3HC14radiationWind2.4404762Solarradiation-2.714286293.36054CO-0.3690483.81632651.4858277NO-0.452381-1.3537410.65759641.154195NO2-0.5714296.60204082.25963

7、721.062358311.092971O3-2.17857130.0578232.7545351-0.7913833.052154230.24093HC0.16666670.60884350.1383220.17233561.01927440.58049890.4671202Excel给出相关系数矩阵R　WindSolarradiationCONONO2O3HCWind1Solarradiation-0.1014421CO-0.1938030.18279341NO-0.269543-0.0