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年底非农农业工业客运货运地方财政城乡居民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工人数工资总额名称人口比余额（万人）（万元）（万元）（万人）（万吨）入（万元）（万人）（万元）(%)（万元）北京1 249.900.597 81 843 42719 999 70620 32345 5622 790 86326 806 646410.805 773 301天津910.170.580 91 501 13622 645 5023 25926 3171 128 07311 301 931202.682 254 34

2、3石家庄875.400.233 22 918 6806 885 7682 9291 911352 3487 095 87595.60758 877太原299.920.656 3236 0382 737 7501 93711 895203 2773 943 10088.65654 023呼和浩特207.780.441 2365 343816 4522 3512 623105 7831 396 58842.11309 337沈阳677.080.629 91 295 4185 826 7337 78215 412567 9199 016 998135.451 152 811大连545.310.494

3、 61 879 7398 426 38510 78019 187709 2277 556 79694.15965 922长春691.230.406 81 853 2105 966 3434 8109 532357 0964 803 744102.63884 447哈尔滨927.090.462 72 663 8554186 1236 7207 520481 4436 450 020172.791 309 151上海1 313.120.738 42 069 01954 529 0986 40644 4854 318 50025 971 200336.845 605 445南京537.440.534

4、 1989 19913 072 73714 26911 193664 2995 680 472113.811 357 861杭州616.050.355 61 414 73712 000 79617 88311 684449 5937 425 96796.901 180 947宁波538.410.254 71 428 23510 622 86622 21510 298501 7235 246 35062.15824 034合肥429.950.318 4628 7642 514 1254 8931 517233 6281 622 93147.27369 577福州583.130.273 32 15

5、2 2886 555 3518 8517 190467 5245 030 22069.59680 607厦门128.990.486 5333 3745 751 1243 7282 570418 7582 108 33146.93657 484南昌424.200.398 8688 2892 305 8813 6743 189167 7142 640 46062.08479 ,555济南557.630.408 51 486 3026 285 8825 91511 775460 6904 126 97083.31756 696青岛702.970.369 32 382 32011 492 03613

6、40817 038658 4354 978 045103.52961 704郑州615.360.342 4677 4255 287 60110 4336 768387 2525 135 33884.66696 848武汉740.200.586 91 211 2917 506 0859 79315 442604 6585 748 055149.201 314 766长沙582.470.310 71 146 3673 098 1798 7065 718323 6603 461 24469.57596 986广州685.000.621 41 600 73823 348 13922 00723 854

7、1 761 49920 401 811182.813 047 594深圳119.850.793 1299 66220 368 2958 7544 2741 847 9089 519 90091.261 890 338南宁285.870.406 4720 4861 149 6915 1303 293149 7002 190 91845.09371 809海口54.380.835 444 815717 4615 3452 356115 1741 626 80019.01198 138重庆3 072.340.206 74 168 7808 585 52552 44125 124898,9129 09

8、0 969223.731 606 804成都1 003.560.3351 935 5905 894 28940 14019 632561 1897 479 684132.891 200 671贵阳321.500.455 7362 0612 247 93415 7034 143197 9081 787 74855.28419 681昆明473.390.386 5793 3563 605 7295 60412 042524 2164 127 90088.11842 321西安674.500.409 4739 9053 665 94210 3119 766408 8965 863 980114.01

9、885 169州287.590.544 5259 4442 940 8841 8324 749169 5402 641 56865.83550 890西133.950.522 765 848711 3101 7461 46949 134855 05127.21219 251银川95.380.570 9171 603661 2262 1061 19374 758814 10323.72178 621乌鲁木齐158.920.824 478 5131 847 2412 6689 041254 8702 365 50855.27517 622解：为方便分析，分别将各个指标以x1,x2x10的形式出现,

10、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); xgxs=corrcoef(sj1);t1 t2=eig(xfc1)T1,T2=eig(xgxs)运行结果得:0.003900000000000.024000000000000.030700000000000.099100000000000.123200000000000.256600000000000.320700000000000.530000000000002.351400000000006.2602-0.13

11、670.2282-0.26280.19390.6371-0.21630.3176-0.1312-0.41910.2758-0.0329-0.02 仃0.00090.0446-0.1447-0.44370.4058-0.55620.54870.0593-0.0522-0.02800.2040-0.0492-0.5472-0.42250.34400.3188-0.44380.24010.0067-0.4176-0.2856-0.23890.1926-0.4915-0.41890.27260.20650.34030.0404-0.14080.08960.0380-0.1969-0.0437-0.48

12、88-0.6789-0.44050.1861-0.03430.23600.0640-0.82940.03770.26620.1356-0.12900.02780.37820.29810.47390.56850.23580.1465-0.1502-0.26310.12450.21520.36440.15670.3464-0.64850.2489-0.40430.2058-0.07040.04620.12140.38120.4879-0.57070.12 仃0.仃610.09870.35500.3280-0.01390.00710.3832-0.7894-0.16280.佃250.2510-0.0

13、4220.2694-0.03960.04560.16680.3799特征根和累计贡献率序号特征根方差贝献率%累计贝献率%16.260262.603362.603322.351423.514586.117830.53005.300191.417940.32073.207194.62550.25662.566097.19160.12321.232098.42370.09910.991099.41480.03070.307099.72190.02400.240099.961100.00390.0390100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

14、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1010.2758-0.4191-0.13120.3176-0.21630.63710.1939-0.26280.2282-0.136720.05930.5487-0.55620.4058-0.4437-0.14470.04460.0009-0.0217-0.032930.2401-0.44380.31880.344-0.4225-0.5472-0.04920.204-0.028-0.052240.34030.20650.272

15、6-0.4189-0.49150.1926-0.2389-0.2856-0.41760.006750.1861-0.4405-0.6789-0.4888-0.0437-0.19690.0380.0896-0.14080.040460.37820.0278-0.1290.13560.26620.0377-0.82940.0640.236-0.034370.36440.21520.1245-0.2631-0.15020.14650.23580.56850.47390.298180.38120.12140.0462-0.07040.2058-0.40430.2489-0.64850.34640.15

16、6790.38320.0071-0.01390.3280.3550.09870.17610.1217-0.57070.4879100.37990.1668-0.7894-0.7894-0.7894-0.7894-0.7894-0.7894-0.7894-0.78940.3812*x8Y1=0.2758*x1+0.0593*x2+0.3403*x3+0.1861*x4+0.3782*x5+0.3644*x6+0.3812*x7+0.3832*x9+0.3799*x10Y2=-0.4191*x1+0.5487 *x2-0.4438*x3+ 0.2065*x4 -0.4405*x5+ 0.0278*

17、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郑州武汉长沙广州深圳南宁海口重庆成都贵阳昆明西安兰州西宁银川乌鲁木齐输入程序：w=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 -13.088

18、0-6.6742 -9.4727 -11.0619-4.59690.3027 -6.79582.8034 -9.3362 24.20829.6413 -12.4012 -10.546511.83671.7517 -11.0433-5.3699-4.1079 -9.2339 -14.0791 -13.7901-6.2136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

19、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0.4587-1.09260.302413杭州0.1662-0.7794-0.792214长春-0.4299-0.5805-4.056215西安-0.5537-0.2729-4.10816济南-0.6083-0.3355-4.59717太原-1.28161.287-4.996818宁波-0.3045

20、-1.3474-5.074519昆明-0.8464-0.0304-5.370120石家庄-0.3245-1.7001-6.029121乌鲁木齐-1.72021.9375-6.21322福州-0.6022-1.2354-6.674823郑州-0.918-0.4461-6.795824兰州-1.7960.8549-9.233125长沙-1.1965-0.7851-9.336426厦门-1.81060.792-9.472427海口-2.37121.8282-10.545428贵阳-1.7169-0.1255-11.043229南昌-1.7517-0.0408-11.061930南宁-1.9685-0

21、.0329-12.400631合肥-1.9579-0.3534-13.087832呼和浩特-2.26910.381-13.309133银川-2.56220.9571-13.789434西宁-2.56150.8323-14.078435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、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

22、整，以使得社会经济指标提升。附件：sj =1.0e+007 *0.00010.00000.18432.00000.00200.00460.27912.68070.00000.57730.00010.00000.15012.26460.00030.00260.11281.13020.00000.22540.00010.00000.29190.68860.00030.00020.03520.70960.00000.07590.00000.00000.02360.27380.00020.00120.02030.39430.00000.06540.00000.00000.03650.08160.000

23、20.00030.01060.13970.00000.03090.00010.00000.12950.58270.00080.00150.05680.90170.00000.11530.00010.00000.18800.84260.00110.00190.07090.75570.00000.09660.00010.00000.18530.59660.00050.00100.03570.48040.00000.08840.00010.00000.26640.41860.00070.00080.04810.64500.00000.13090.00010.00000.20695.45290.000

24、60.00440.43192.59710.00000.56050.00010.00000.09891.30730.00140.00110.06640.56800.00000.13580.00010.00000.14151.20010.00180.00120.04500.74260.00000.11810.00010.00000.14281.06230.00220.00100.05020.52460.00000.08240.00000.00000.06290.25140.00050.00020.02340.16230.00000.03700.00010.00000.21520.65550.000

25、90.00070.04680.50300.00000.06810.00000.00000.03330.57510.00040.00030.04190.21080.00000.06570.00000.00000.06880.23060.00040.00030.01680.26400.00000.04800.00010.00000.14860.62860.00060.00120.04610.41270.00000.07570.00010.00000.23821.14920.00130.00170.06580.49780.00000.09620.00010.00000.06770.52880.001

26、00.00070.03870.51350.00000.06970.00010.00000.12110.75060.00100.00150.06050.57480.00000.13150.00010.00000.11460.30980.00090.00060.03240.34610.00000.05970.00010.00000.16012.33480.00220.00240.17612.04020.00000.30480.00000.00000.03002.03680.00090.00040.18480.95200.00000.18900.00000.00000.07200.11500.000

27、50.00030.01500.21910.00000.03720.00000.00000.00450.07170.00050.00020.01150.16270.00000.01980.00030.00000.41690.85860.00520.00250.08990.90910.00000.16070.00010.00000.19360.58940.00400.00200.05610.74800.00000.12010.00000.00000.03620.22480.00160.00040.01980.17880.00000.04200.00000.00000.07930.36060.000

28、60.00120.05240.41280.00000.08420.00010.00000.07400.36660.00100.00100.04090.58640.00000.08850.00000.00000.02590.29410.00020.00050.01700.26420.00000.05510.00000.00000.00660.07110.00020.00010.00490.08550.00000.02190.00000.00000.01720.06610.00020.00010.00750.08140.00000.01790.00000.00000.00790.18470.000

29、30.00090.02550.23660.00000.0518sj1 =1.1977 0.71490.5570 0.61250.4914 -1.4940-0.5940 1.0693-0.7678 -0.23390.1174 0.9093-0.1312 0.08960.1440 -0.44230.5889 -0.10361.3169 1.56670.66741.13900.30581.39901.8031-0.1495-1.0304-0.5571-0.8938-0.74590.0886-0.25360.70570.00190.6777-0.23981.5339-0.41480.90574.531

30、80.9189 3.1113-0.6652 1.3427-0.6958 -0.9003-0.7879 0.0172-0.7494 -0.8349-0.2453 0.34050.0330 0.6874-0.5212 -0.1999-0.3439 -0.3848-0.3730 3.01242.5079 3.26770.5439 0.7769 -0.3724 0.1012 -0.5484 -0.4053 -0.6636 -0.8144-0.1177 0.40980.0492 0.1752-0.3668 -0.2671-0.2199 -0.00264.3123 3.13353.6461 3.60181

31、.1365 0.8394-0.1547 -0.3345-0.2385 -0.4168-0.7997 -0.68730.3259 -0.0252-0.1721 -0.1719-0.0699 -0.23590.7761 0.09752.7543 3.47000.0649 0.1357-0.1460 0.3290 -0.2349 0.4584 0.3569 -0.0473 -0.0039 -0.12620.0022 -0.7525 0.2146 0.35310.6924 -0.0022 -0.25750.1542 -0.1390 -0.0032-0.1442-1.36380.22880.21771.

32、0945-0.1295-0.1959-0.1960-0.5580-0.2833-0.3487-0.9778-0.6156-0.5790-0.5135-0.9365-0.5126-0.7781-0.7374-0.6401-0.0598-1.25110.9936-0.1820-0.1461-0.4152-0.2363-0.2307-0.4683-0.3959-0.91640.0406-0.9276-0.2610-0.6216-0.8398-0.2939-0.7001-0.7415-0.4141-0.3596-0.4907-0.5527-0.5995-0.6266-0.7829-0.5905-0.6

33、146-0.5589-0.5537-0.1079-0.43200.2902-0.2084-0.41860.0062-0.2444-0.3758-0.3029-0.33620.1662-0.66951.23660.30310.27700.4899-0.0108-0.2391-0.0592-0.17530.0009-0.8324-0.5642-0.30650.0008-0.4540-0.3311-0.2138-0.2866-0.38320.23640.6488-0.0003-0.0886-0.05860.3432-0.0744-0.11540.49170.1019-0.0611-1.0245-0.

34、0689-0.5217-0.1595-0.5505-0.4063-0.4827-0.4685-0.46150.13230.85780.41101.46801.07521.11631.29212.23880.89691.4621-0.93361.8981-0.96321.1753-0.1551-0.68321.39410.4906-0.20700.5537-0.6205-0.4447-0.5187-0.7131-0.4915-0.7733-0.6117-0.6868-0.7637-0.6383-1.05712.1543-1.2324-0.7556-0.4715-0.8594-0.6525-0.7

35、774-1.0782-0.77464.6348-1.65463.12350.01753.90041.23300.27320.42171.39040.33110.7331-0.87730.7647-0.24692.75850.7283-0.12570.16280.29500.0123-0.5533-0.1460-0.8973-0.60520.4900-0.6952-0.5548-0.7516-0.6409-0.6007-0.2668-0.5653-0.4417-0.4718-0.44750.0307-0.1694-0.3756-0.2450-0.26900.1125-0.4265-0.4982-

36、0.4659-0.0105-0.1784-0.3056-0.09670.0673-0.2353-0.61720.3920-1.0057-0.5371-0.7976-0.6395-0.5883-0.6144-0.5136-0.4977-0.90700.2599-1.2102-0.7562-0.8056-0.9410-0.7305-0.9014-0.9793-0.7581-0.97970.5519-1.0985-0.7611-0.7722-0.9663-0.7003-0.9080-1.0214-0.7900-0.85992.0877-1.1968-0.6446-0.7200-0.2451-0.48

37、75-0.6588-0.6410-0.5238t1 =-0.13670.2282-0.26280.19390.6371-0.21630.3176-0.1312-0.41910.2758-0.0329-0.02170.00090.0446-0.1447-0.44370.4058-0.55620.54870.0593-0.0522-0.02800.2040-0.0492-0.5472-0.42250.34400.3188-0.44380.24010.0067-0.4176-0.2856-0.23890.1926-0.4915-0.41890.27260.20650.34030.0404-0.14080.08960.0380-0.1969-0.0437-0.4888-0.6789-0.44