主成分分析练习

1、中国大陆35个大城市某年的10项社会经济统计指标数据见下表对其进行分析。非农城乡居民年底农业工业客运货运地方财政在岗职在岗职工城市业年底储蓄总人口总产值总产值总量总量预算内收余额工人数工资总额名称人口比（万人）（万元）（万元）（万人）（万吨）入（万元）（万人）（万元）(%)（万兀）北京1249.900.59781843427199997062032345562279086326806646410.805773301天津910.170.5809150113622645502325926317112807311301931202.682254343石家庄875.400.23322918680688

2、576829291911352348709587595.60758877太原299.920.65632360382737750193711895203277394310088.65654023呼和浩特207.780.441236534381645223512623105783139658842.11309337沈阳677.080.6299129541858267337782154125679199016998135.451152811大连545.310.4946187973984263851078019187709227755679694.15965922长春691.230.406818532

3、105966343481095323570964803744102.63884447哈尔滨927.090.462726638554186123672075204814436450020172.791309151上海1313.120.7384206901954529098640644485431850025971200336.845605445南京537.440.53419891991307273714269111936642995680472113.811357861杭州616.050.35561414737120007961788311684449593742596796.901180947

4、宁波538.410.25471428235106228662221510298501723524635062.15824034合肥429.950.3184628764251412548931517233628162293147.27369577福州583.130.27332152288655535188517190467524503022069.59680607厦门128.990.4865333374575112437282570418758210833146.93657484南昌424.200.3988688289230588136743189167714264046062.08479,55

5、5济南557.630.408514863026285882591511775460690412697083.31756696青岛702.970.369323823201149203613408170386584354978045103.52961704郑州615.360.34246774255287601104336768387252513533884.66696848武汉740.200.5869121129175060859793154426046585748055149.201314766长沙582.470.31071146367309817987065718323660346124469

6、.57596986广州685.000.62141600738233481392200723854176149920401811182.813047594深圳119.850.793129966220368295875442741847908951990091.261890338南宁285.870.4064720486114969151303293149700219091845.09371809海口54.380.83544481571746153452356115174162680019.01198138重庆3072.340.2067416878085855255244125124898,9129

7、090969223.731606804成都1003.560.3351935590589428940140196325611897479684132.891200671贵阳321.500.45573620612247934157034143197908178774855.28419681昆明473.390.38657933563605729560412042524216412790088.11842321西安674.500.409473990536659421031197664088965863980114.01885169兰州287.590.54452594442940884183247491

8、69540264156865.83西宁133.950.522765848711310174614694913485505127.21银川95.380.5709171603661226210611937475881410323.72乌鲁木齐158.920.824478513184724126689041254870236550855.27550890219251178621517622解：为方便分析，分别将各个指标以x1,x2x10的形式出现,将数据保存为txt格式，存入matlab，输入命令：clearsj=load(shuju.txt)sj1=zscore(sj)xfc1=cov(sj1);

9、xgxs=corrcoef(sj1);t1t2=eig(xfc1)T1,T2=eig(xgxs)运行结果得：0.0039000000.0240000000.0307000000.0991000000.1232000000000000000000000000000000000000000000000000000.2566000000.3207000000.5300000002.3514000006.2602-0.13670.2282-0.26280.19390.6371-0.21630.3176-0.1312-0.41910.2758-0.0329-0.02170.00090.0446-0.14

10、47-0.44370.4058-0.55620.54870.0593-0.0522-0.02800.2040-0.0492-0.5472-0.42250.34400.3188-0.44380.24010.0067-0.4176-0.2856-0.23890.1926-0.4915-0.41890.27260.20650.34030.0404-0.14080.08960.0380-0.1969-0.0437-0.4888-0.6789-0.44050.1861-0.03430.23600.0640-0.82940.03770.26620.1356-0.12900.02780.37820.2981

11、0.47390.56850.23580.1465-0.1502-0.26310.12450.21520.36440.15670.3464-0.64850.2489-0.40430.2058-0.07040.04620.12140.38120.4879-0.57070.12170.17610.09870.35500.3280-0.01390.00710.3832-0.7894-0.16280.19250.2510-0.04220.2694-0.03960.04560.16680.3799特征根和累计贡献率序号特征根方差贝献率累计贝献率16.260262.603362.603322.351423.

12、514586.117830.53005.300191.417940.32073.207194.62550.25662.566097.19160.12321.232098.42370.09910.991099.41480.03070.307099.72190.02400.240099.961100.00390.0390100易知累计贡献率达到一个较高的百分数（如85以上）的成分为主成分，由上表可知x9,x10为主要成分，即在岗职工人数与在岗职工工资总额这两个指标为主要成分。特征向量表特征向量1特征向量2特征向量3特征向量4特征向量5特征向量6特征向量7特征向量8特征向量9特征向量1010.275

13、8-0.4191-0.13120.3176-0.21630.63710.1939-0.26280.2282-0.136720.05930.5487-0.55620.4058-0.4437-0.14470.04460.0009-0.0217-0.032930.2401-0.44380.31880.344-0.4225-0.5472-0.04920.204-0.028-0.052240.34030.20650.2726-0.4189-0.49150.1926-0.2389-0.2856-0.41760.006750.1861-0.4405-0.6789-0.4888-0.0437-0.19690.

14、0380.0896-0.14080.040460.37820.0278-0.1290.13560.26620.0377-0.82940.0640.236-0.034370.36440.21520.1245-0.2631-0.15020.14650.23580.56850.47390.298180.38120.12140.0462-0.07040.2058-0.40430.2489-0.64850.34640.156790.38320.0071-0.01390.3280.3550.09870.17610.1217-0.57070.4879100.37990.1668-0.7894-0.7894-

15、0.7894-0.7894-0.7894-0.7894-0.7894-0.7894Y1=0.2758*x1+0.0593*x2+0.3403*x3+0.1861*x4+0.3782*x5+0.3644*x6+0.3812*x7+0.3812*x8+0.3832*x9+0.3799*x10Y2=-0.4191*x1+0.5487*x2-0.4438*x3+0.2065*x4-0.4405*x5+0.0278*x6+0.2152*x7+0.1214*x8+0.0071*x9+0.1668*x10Y1Y2北京天津石家庄太原呼和浩特沈阳大连长春哈尔滨上海南京杭州宁波合肥福州厦门南昌济南青岛输入程序：w

16、=T2(10,10),T2(9,9);h=t1(:,10),t1(:,9);h1=sj1*h;g1=h1*w得出综合得分：47.558517.0746-6.0283-4.9972-13.30953.25561.7705-4.05590.428859.79031.6455-0.7918-5.0739-13.0880-6.6742-9.4727-11.0619-4.59690.3027-6.79582.8034-9.336224.20829.6413-12.4012-10.546511.83671.7517-11.0433-5.3699-4.1079-9.2339-14.0791-13.7901-

17、6.2136各地区主成分得分及综合得分与排名Y1Y2综合得分排名上海8.42522.996459.78921北京7.19331.074147.55712广州3.53130.893524.20763天津2.37220.945617.07394重庆4.0471-5.741711.83465深圳0.56262.60279.6426沈阳0.3330.49813.25597武汉0.34840.26462.80328大连0.3588-0.20211.77099成都1.1725-2.3771.750810南京0.15430.2891.645511哈尔滨0.4272-0.95510.428512青岛0.458

18、71.09260.302413杭州0.16620.77940.792214长春0.42990.58054.056215西安0.55370.27294.10816济南0.60830.33554.59717太原1.28161.2874.996818宁波0.30451.34745.074519昆明0.84640.03045.370120石家庄0.32451.70016.029121乌鲁木齐1.72021.9375-6.21322福州0.60221.23546.674823郑州0.9180.44616.795824兰州1.7960.85499.233125长沙1.19650.78519.336426厦

19、门1.81060.7929.472427海口2.37121.828210.545428贵阳1.71690.125511.043229南昌1.75170.040811.061930南宁1.96850.032912.400631合肥1.95790.353413.087832呼和浩特2.26910.38113.309133银川2.56220.957113.789434西宁2.56150.832314.078435因此可以得出结论，若是城市中在岗职工人数与在岗职工工资总额数值越高，则该城市的经济指标就越好。在这方面，我们可以看出上海、北京、广州、天津、重庆、深圳、沈阳、武汉、大连、成都、南京、哈尔滨、

20、青岛这几个城市的社会经济统计指标相对较好，而海口、贵阳、南昌、南宁、合肥、呼和浩特、银川、西宁这些城市则相对较弱，需要在在岗职工人数与在岗职工工资总额这两个方面做出更多调整，以使得社会经济指标提升。附件：sj=1.0e+007*0.00010.00000.18432.00000.00200.00460.27912.68070.00000.57730.00010.00000.15012.26460.00030.00260.11281.13020.00000.22540.00010.00000.29190.68860.00030.00020.03520.70960.00000.07590.0000

21、0.00000.02360.27380.00020.00120.02030.39430.00000.06540.00000.00000.03650.08160.00020.00030.01060.13970.00000.03090.00010.00000.12950.58270.00080.00150.05680.90170.00000.11530.00010.00000.18800.84260.00110.00190.07090.75570.00000.09660.00010.00000.18530.59660.00050.00100.03570.48040.00000.08840.0001

22、0.00000.26640.41860.00070.00080.04810.64500.00000.13090.00010.00000.20695.45290.00060.00440.43192.59710.00000.56050.00010.00000.09891.30730.00140.00110.06640.56800.00000.13580.00010.00000.14151.20010.00180.00120.04500.74260.00000.11810.00010.00000.14281.06230.00220.00100.05020.52460.00000.08240.0000

23、0.00000.06290.25140.00050.00020.02340.16230.00000.03700.00010.00000.21520.65550.00090.00070.04680.50300.00000.06810.00000.00000.03330.57510.00040.00030.04190.21080.00000.06570.00000.00000.06880.23060.00040.00030.01680.26400.00000.04800.00010.00000.14860.62860.00060.00120.04610.41270.00000.07570.0001

24、0.00000.23821.14920.00130.00170.06580.49780.00000.09620.00010.00000.06770.52880.00100.00070.03870.51350.00000.06970.00010.00000.12110.75060.00100.00150.06050.57480.00000.13150.00010.00000.11460.30980.00090.00060.03240.34610.00000.05970.00010.00000.16012.33480.00220.00240.17612.04020.00000.30480.0000

25、0.00000.03002.03680.00090.00040.18480.95200.00000.18900.00000.00000.07200.11500.00050.00030.01500.21910.00000.03720.00000.00000.00450.07170.00050.00020.01150.16270.00000.01980.00030.00000.41690.85860.00520.00250.08990.90910.00000.16070.00010.00000.19360.58940.00400.00200.05610.74800.00000.12010.0000

26、0.00000.03620.22480.00160.00040.01980.17880.00000.04200.00000.00000.07930.36060.00060.00120.05240.41280.00000.08420.00010.00000.07400.36660.00100.00100.04090.58640.00000.08850.00000.00000.02590.29410.00020.00050.01700.26420.00000.05510.00000.00000.00660.07110.00020.00010.00490.08550.00000.02190.0000

27、0.00000.01720.06610.00020.00010.00750.08140.00000.01790.00000.00000.00790.18470.00030.00090.02550.23660.00000.0518sj1=1.19770.71490.66741.13900.91893.11132.50793.26773.64613.60180.55700.61250.30581.3990-0.66521.34270.54390.77691.13650.83940.4914-1.49401.8031-0.1495-0.6958-0.9003-0.37240.1012-0.1547-

28、0.3345-0.59401.0693-1.0304-0.5571-0.78790.0172-0.5484-0.4053-0.2385-0.4168-0.7678-0.2339-0.8938-0.7459-0.7494-0.8349-0.6636-0.8144-0.7997-0.68730.11740.90930.0886-0.2536-0.24530.3405-0.11770.40980.3259-0.0252-0.13120.08960.70570.00190.03300.68740.04920.1752-0.1721-0.17190.1440-0.44230.6777-0.2398-0.

29、5212-0.1999-0.3668-0.2671-0.0699-0.23590.5889-0.10361.5339-0.4148-0.3439-0.3848-0.2199-0.00260.77610.09751.31691.56670.90574.5318-0.37303.01244.31233.13352.75433.4700-0.14600.3290-0.23490.45840.3569-0.0473-0.0039-0.12620.06490.1357-0.1442-1.36380.22880.21771.0945-0.1295-0.1959-0.1960-0.5580-0.2833-0

30、.3487-0.9778-0.6156-0.5790-0.5135-0.9365-0.5126-0.7781-0.7374-0.6401-0.0598-1.25110.9936-0.1820-0.1461-0.4152-0.2363-0.2307-0.4683-0.3959-0.91640.0406-0.9276-0.2610-0.6216-0.8398-0.2939-0.7001-0.7415-0.4141-0.3596-0.4907-0.5527-0.5995-0.6266-0.7829-0.5905-0.6146-0.5589-0.5537-0.1079-0.43200.2902-0.2

31、084-0.41860.0062-0.2444-0.3758-0.3029-0.33620.1662-0.66951.23660.30310.27700.4899-0.0108-0.2391-0.0592-0.17530.0009-0.8324-0.5642-0.30650.0008-0.4540-0.3311-0.2138-0.2866-0.38320.23640.6488-0.0003-0.0886-0.05860.3432-0.0744-0.11540.49170.1019-0.0611-1.0245-0.0689-0.5217-0.1595-0.5505-0.4063-0.4827-0

32、.4685-0.46150.13230.85780.41101.46801.07521.11631.29212.23880.89691.4621-0.93361.8981-0.96321.1753-0.1551-0.68321.39410.4906-0.20700.5537-0.6205-0.4447-0.5187-0.7131-0.4915-0.7733-0.6117-0.6868-0.7637-0.6383-1.05712.1543-1.2324-0.7556-0.4715-0.8594-0.6525-0.7774-1.0782-0.77464.6348-1.65463.12350.017

33、53.90041.23300.27320.42171.39040.33110.7331-0.87730.7647-0.24692.75850.7283-0.12570.16280.29500.0123-0.5533-0.1460-0.8973-0.60520.4900-0.6952-0.5548-0.7516-0.6409-0.6007-0.2668-0.5653-0.4417-0.4718-0.44750.0307-0.1694-0.3756-0.2450-0.26900.1125-0.4265-0.4982-0.4659-0.0105-0.1784-0.3056-0.09670.0673-

34、0.2353-0.61720.3920-1.0057-0.5371-0.7976-0.6395-0.5883-0.6144-0.5136-0.4977-0.90700.2599-1.2102-0.7562-0.8056-0.9410-0.7305-0.9014-0.9793-0.7581-0.97970.5519-1.0985-0.7611-0.7722-0.9663-0.7003-0.9080-1.0214-0.7900-0.85992.0877-1.1968-0.6446-0.7200-0.2451-0.4875-0.6588-0.6410-0.52380.0022-0.75250.214

35、60.35310.6924-0.0022-0.25750.1542-0.1390-0.0032t1=-0.13670.2282-0.26280.19390.6371-0.21630.3176-0.1312-0.41910.2758-0.0329-0.02170.00090.0446-0.1447-0.44370.4058-0.55620.54870.0593-0.0522-0.02800.2040-0.0492-0.5472-0.42250.34400.3188-0.44380.24010.0067-0.4176-0.2856-0.23890.1926-0.4915-0.41890.27260.20650.34030.0404-0.14080.08960.0380-0.1969-0.0437-0.4888-0.6789-0.44050.1861-0.03430.23600.0640-0.82940.03770.26620.1356-0.12900.02780.37820.29810.47390.568