统计问题7个人解答.docx
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统计问题7个人解答.docx
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统计问题7个人解答
对问题中的表格进行matlab操作如下:
A=[42.4,10.2,116.8,4.8,43.6,13.3,61.1,99.3,139.3,55.5,68.3,83.4,90,18.8,47.6,99.6,100.1,80.6,90,100.8,146.1,55.1;
12,19.4,24.6,28.8,24.7,28.3,18.7,18.3,9.4,8.1,3.5,5.7,12.8,19.4,22.8,21,23,2.8,21.2,15.1,8.4,6.7;
24,18.4,12.5,1,2.8,1.8,8.8,13.7,18.7,22.6,26.7,27.5,23.7,17.4,13.3,9.5,3.6,2.6,6.8,14.2,19.6,22.4;
22.7,15.1,12.1,4.4,5.4,4.7,8.5,11.8,17.9,22.3,29.1,29.4,23.6,15.1,12.3,10.6,6.7,6.2,8.3,13.7,18.6,21.2];
协方差>>cov(A)
ans=
1.0e+003*
Columns1through7
0.1592-0.04840.5422-0.10420.1338-0.05410.2550
-0.04840.0172-0.17910.0258-0.04990.0100-0.0852
0.5422-0.17912.5537-0.09450.87520.11091.2599
-0.10420.0258-0.09450.16420.06710.1441-0.0229
0.1338-0.04990.87520.06710.36170.12980.4465
-0.05410.01000.11090.14410.12980.14160.0767
0.2550-0.08521.2599-0.02290.44650.07670.6252
0.4699-0.15312.1413-0.10860.71560.06601.0522
0.7303-0.23523.0873-0.25660.97030.00281.5019
0.2522-0.07860.9104-0.14580.2428-0.06390.4324
0.3381-0.10591.1513-0.22020.2853-0.11400.5411
0.4139-0.13071.5073-0.23410.4068-0.09910.7167
0.4268-0.13641.7265-0.17840.5211-0.03070.8346
0.00110.00030.04640.01450.02570.01710.0256
0.1546-0.05200.81720.00550.30210.06860.4086
0.4625-0.15382.1859-0.07760.75140.09801.0788
0.4623-0.15662.2825-0.04160.80910.13871.1322
0.4413-0.14551.9214-0.13390.62030.02540.9381
0.4099-0.13761.9925-0.04850.69870.10980.9866
0.4908-0.15972.1735-0.13630.71050.04291.0640
0.7725-0.24843.2480-0.27811.0158-0.00461.5789
0.2572-0.07950.9210-0.15150.2431-0.06830.4369
Columns8through14
0.46990.73030.25220.33810.41390.42680.0011
-0.1531-0.2352-0.0786-0.1059-0.1307-0.13640.0003
2.14133.08730.91041.15131.50731.72650.0464
-0.1086-0.2566-0.1458-0.2202-0.2341-0.17840.0145
0.71560.97030.24280.28530.40680.52110.0257
0.06600.0028-0.0639-0.1140-0.0991-0.03070.0171
1.05221.50190.43240.54110.71670.83460.0256
1.80102.61430.78350.99681.29551.46820.0364
2.61433.85961.20091.55211.98282.18990.0406
0.78351.20090.40360.53670.66390.69640.0043
0.99681.55210.53670.72210.88290.90770.0002
1.29551.98280.66390.88291.09321.14860.0068
1.46822.18990.69640.90771.14861.25000.0187
0.03640.04060.00430.00020.00680.01870.0036
0.67900.95560.26580.32720.44110.52630.0192
1.83212.64040.77750.98331.28791.47610.0395
1.90562.72250.78470.98431.30211.51370.0447
1.62172.38080.73070.94111.20881.34600.0263
1.66592.38710.69320.87181.14931.32970.0382
1.83252.67750.81421.04271.34581.50970.0334
2.75194.06781.26911.64182.09502.30960.0419
0.79351.21800.41080.54650.67520.70690.0043
Columns15through21
0.15460.46250.46230.44130.40990.49080.7725
-0.0520-0.1538-0.1566-0.1455-0.1376-0.1597-0.2484
0.81722.18592.28251.92141.99252.17353.2480
0.0055-0.0776-0.0416-0.1339-0.0485-0.1363-0.2781
0.30210.75140.80910.62030.69870.71051.0158
0.06860.09800.13870.02540.10980.0429-0.0046
0.40861.07881.13220.93810.98661.06401.5789
0.67901.83211.90561.62171.66591.83252.7519
0.95562.64042.72252.38082.38712.67754.0678
0.26580.77750.78470.73070.69320.81421.2691
0.32720.98330.98430.94110.87181.04271.6418
0.44111.28791.30211.20881.14931.34582.0950
0.52631.47611.51371.34601.32971.50972.3096
0.01920.03950.04470.02630.03820.03340.0419
0.26990.69990.73930.59950.64290.68281.0035
0.69991.87151.95531.64461.70641.85962.7777
0.73931.95532.05271.70281.78821.92822.8621
0.59951.64461.70281.47471.49041.65802.5079
0.64291.70641.78821.49041.55891.68732.5101
0.68281.85961.92821.65801.68731.86952.8198
1.00352.77772.86212.50792.51012.81984.2875
0.26820.78620.79240.74000.70040.82491.2874
Column22
0.2572
-0.0795
0.9210
-0.1515
0.2431
-0.0683
0.4369
0.7935
1.2180
0.4108
0.5465
0.6752
0.7069
0.0043
0.2682
0.7862
0.7924
0.7400
0.7004
0.8249
1.2874
0.4183
特征根,特征向量>>[d,v]=eig(cov(A))
d=
Columns1through6
-0.14580.1445-0.01190.0549-0.02480.2330
0.0663-0.13260.04970.23170.01230.0185
-0.66400.00730.1710-0.09380.10350.1751
0.0815-0.0642-0.0798-0.20880.08590.2708
0.09210.10650.11820.0789-0.3854-0.3188
0.09890.0011-0.0055-0.11160.01450.1632
0.18120.1648-0.2594-0.41860.0708-0.1071
0.08720.56700.0640-0.08030.0148-0.0054
0.5159-0.00410.26600.0846-0.12420.0801
-0.07250.29860.0599-0.13710.10840.0954
-0.1563-0.07670.03770.08380.1789-0.5222
-0.09810.13830.0612-0.3738-0.34910.1528
-0.0333-0.43330.1106-0.20640.11530.2852
0.0314-0.06630.03580.16190.06260.0249
-0.08610.0514-0.0260-0.29180.1068-0.4910
0.1298-0.33740.0011-0.23560.3533-0.1566
-0.06520.05800.53620.34150.1466-0.0248
0.15270.2482-0.35390.30690.31300.1943
-0.2078-0.1628-0.25530.1365-0.5778-0.0258
-0.17320.0099-0.52650.28030.1147-0.0416
0.1861-0.2844-0.14940.0155-0.16170.0038
-0.02980.04660.07300.00740.0097-0.0405
Columns7through12
-0.12560.83800.2179-0.05230.06910.0014
0.0531-0.10000.3840-0.5680-0.00150.4200
-0.2455-0.2176-0.18630.0109-0.02070.1479
-0.0714-0.11820.65450.0853-0.2042-0.1021
-0.05670.16190.03580.1231-0.16910.4060
0.20480.0672-0.2172-0.32570.70080.1157
-0.35430.0663-0.12940.0930-0.06310.4580
0.03930.0073-0.0058-0.08580.0003-0.2888
-0.1017-0.1764-0.0335-0.00140.0192-0.0474
-0.1707-0.24450.3496-0.06790.2412-0.0546
-0.2551-0.02200.2125-0.09580.25450.0974
0.4582-0.09680.08280.0167-0.00540.2035
0.12630.1665-0.04160.0453-0.11500.1540
0.1039-0.03240.23170.71030.47960.1739
0.41810.15360.1660-0.0212-0.0140-0.1583
-0.05130.1115-0.0336-0.05670.0277-0.2313
0.17910.09470.01490.0442-0.13640.0035
-0.01490.0459-0.08890.0231-0.05060.0777
-0.2072-0.00270.0902-0.05430.1593-0.3244
0.3853-0.11940.01750.0155-0.11950.1157
-0.03450.01920.00470.00080.0241-0.0811
0.01580.0060-0.02710.0106-0.0203-0.0007
Columns13through18
0.0189-0.0079-0.07240.0168-0.26650.0823
0.04380.13180.2836-0.00570.0868-0.0078
0.03810.1517-0.0017-0.2701-0.22850.0282
0.21950.0923-0.2228-0.0648-0.0811-0.1431
-0.0744-0.40340.0488-0.4010-0.0099-0.0773
0.0410-0.0443-0.2195-0.0406-0.0334-0.1207
-0.03900.1636-0.06230.45810.09110.0073
0.4574-0.12680.0459-0.11720.40170.0352
-0.04970.1674-0.3109-0.1471-0.33950.2290
-0.5775-0.43040.01580.07540.04140.0227
0.33750.0852-0.1910-0.03480.10800.1003
0.17350.09880.31700.1156-0.14750.0799
-0.0894-0.1365-0.2197-0.17820.60290.0810
0.09280.07060.1791-0.02180.06150.0041
-0.37790.3734-0.1185-0.1955-0.00410.0299
0.1140-0.32610.51380.0252-0.24440.0079
-0.10280.0589-0.00220.52580.0970-0.0139
-0.20490.31350.3019-0.30350.1229-0.0467
-0.11880.13830.11060.16510.22920.0181
0.1005-0.3495-0.32360.1651-0.18470.0944
-0.02450.02220.01710.0148-0.0285-0.1725
0.01760.0172-0.08690.0161-0.0484-0.9120
Columns19through22
-0.02590.10310.16310.0711
-0.06430.3857-0.0361-0.0232
0.07350.1637-0.18720.3118
0.0549-0.2585-0.3794-0.0209
0.0313-0.1736-0.30280.1011
0.0595-0.2023-0.36470.0049
-0.05610.1125-0.15000.1524
0.04670.2917-0.08720.2631
-0.31120.11440.11820.3854
0.0492-0.01790.20470.1178
0.0038-0.37100.34810.1513
-0.0421-0.29790.32320.1947
-0.1743-0.00520.15100.2176
-0.05000.2791-0.04470.0046
-0.00180.1823-0.14730.0976
-0.2180-0.0223-0.16710.2667
0.1019-0.2135-0.26830.2763
-0.0332-0.37630.01450.2385
-0.3124-0.0585-0.20570.2418
-0.12640.1106-0.02430.2687
0.76950.13170.14370.4059
-0.27980.08120.21600.1194
v=
1.0e+004*
Columns1through6
-0.000000000
0-0.00000000
00-0.0000000
000-0.000000
0000-0.00000
00000-0.0000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
Columns7through12
000000
000000
000000
000000
000000
000000
-0.000000000
0-0.00000000
00-0.0000000
000-0.000000
00000.00000
000000.0000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
Columns13through18
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
000000
0.000000000
00.00000000
000.0000000
0000.000000
00000.00000
000000.0000
000000
000000
000000
000000
Columns19through22
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0.0000000
00.001300
000.10560
0002.5890
特征根为:
0.0013
0.1056
2.5890
特征值从大到小排列2.58900.10560.0013
如果我们只取一个主成分,则贡献率为2.5890/(0.0013+0.1056+2.5890)=0.96>0.85,所以只取这一个主成分。
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