Iris数据判别分析.doc

1、Iris数据判别分析一、提出问题R.A.Fisher 在 1936年发表的 Iris 数据中，研究某植物的萼片长、宽及花瓣长、宽。x1 ：萼片长， x2：萼片宽， x3：花瓣长， x4：花瓣宽。取自3 个种类 G1，G2，G3，每个种类50 个样品，共150 个样品。数据如下表所示。序号类别x1x2x34x11603314223642856223265284615436731562453632851156146341437369315123826222451592593248181014636102112613046141226027511613365305220142562539111536

2、530551816358275119173683259231815133175192572845132036234542321377386722222633347162336733572524376306621253492545172615535132273673052232827032471429264324515302612840133114831162323593051183325524381134363255019353643253233615234142371493614138254304515393793864204014432132413673357214215035166432

3、582640124414430132453772867204636327491847147321624825526441249250233310503723260285114830143521513816253361304918541483419255150301625615032122573612656145836428562159143301116015840122611513819462267314414633622848186414930142651513514266256304515672582741106815034164691463214270260294515712572635

4、107215744154731503614274377306123753633456247635827511977257194213783723058167915434154801524215181371305921823643155188336030481884363295618852492433108625627421387257304212881554214289149311529037726692391360225015921543917493266294613942522739149526034451696150341529714419142982502035109925524371

5、010025827391210114732132102146311521033693257231042622943131053742861191062593042151071513415210815035133109356284920110260224010111373296318112367255818113149311511142673147151152632344131161543715211725630411311826325491511926128471212026429431312125125301112225728411312336530582212436931542112515

6、43913412615135143127372366125128365325120129261294714130256293613131269314915132364275319133368305521134255254013135148341621361483014113714523133138357255020139157381731401513815314125523401314226630441414326828481414415434172145151371541461523515214735828512414826730501714936333602515015337152（ 1）

7、 进行 Bayes 判别，并用回代法与交叉确认法判别结果；（ 2） 计算每个样品属于每一类的后验概率；（ 3） 进行逐步判别，并用回代法与交叉确认法验证判别结果。二、判别分析用距离判别法，总体 G1， G2， G3 的协方差矩阵计算各个总体之间的马氏平方距离形成的矩阵，其中线性判别函数是2.1 Bayes 判别先验概率按比例分配，即求得的线性判别函数中关于变量的系数以及常数项均与上面结果相同。广义平方距离函数，后验概率以下是 SPSS软件判别分析结果。分析觀察值處理摘要未加權的觀察值N百分比有效150100.0已排除遺漏或超出範圍群組代碼0.0至少一個遺漏區別變數0.0遺漏或超出範圍群組代碼及

8、0.0至少一個遺漏區別變數總計0.0總計150100.0群組統計資料有效的 N (listwise)类别平均數標準偏差未加權加權1x150.263.7955050.000x234.104.3395050.000x314.621.7375050.000x42.461.0545050.0002x159.365.1625050.000x227.503.3645050.000x342.604.6995050.000x413.261.9785050.0003x165.886.3595050.000x229.743.2255050.000x355.525.5195050.000x420.462.93650

9、50.000總計x158.508.253150150.000x230.454.571150150.000x337.5817.653150150.000x412.067.718150150.000群組平均值的等式檢定Wilks Lambda( )Fdf1df2顯著性x1.393113.3142147.000x2.63841.6762147.000x3.0591180.1612147.000x4.075902.5042147.000聯合組內矩陣 ax1x2x3x4共變異x127.1599.78316.7094.225x29.78313.5145.6103.464x316.7095.61018.51

10、94.571x44.2253.4644.5714.547相關x11.000.511.745.380x2.5111.000.355.442x3.745.3551.000.498x4.380.442.4981.000a. 共變異數矩陣具有147 自由度。共變異數矩陣 a类别x1x2x3x41x114.40010.9731.509.939x210.97318.8271.304.994x31.5091.3043.016.607x4.939.994.6071.1112x126.6439.00018.2905.578x29.00011.3168.3884.173x318.2908.38822.0827.3

11、10x45.5784.1737.3103.9113x140.4349.37630.3296.158x29.37610.4007.1385.224x330.3297.13830.4595.797x46.1585.2245.7978.621總計x168.104-3.050125.84951.862x2-3.05020.893-31.831-11.530x3125.849-31.831311.628131.066x451.862-11.530131.06659.574a. 共變異數矩陣總計具有 149自由度。變數已輸入 / 已移除 a,b,c,dWilks Lambda ( )確切 F步驟已輸入統計

12、資料df1df2df3統計資料df1df2顯著性1x3.05912147.0001180.1612147.000.0002x2.03922147.000297.9004292.000.0003x4.02732147.000243.5026290.000.0004x1.02542147.000191.1338288.000.000在每一個步驟中，輸入最小化整體Wilks Lambda的變數。a. 步驟的數目上限為8 。b.要輸入的局部F 下限為 3.84 。c. 要移除的局部 F 上限為 2.71 。d. F 層次、容差或 VIN 不足，無法進行進一步計算。分析中的變數Wilks Lambda步

13、驟允差要移除的 F( )1x31.0001180.1612x3.8741129.588.638x2.87437.484.0593x3.72941.949.043x2.78144.975.044x4.67129.889.0394x3.37944.010.040x2.64817.172.031x4.66022.391.033x1.3696.615.027不在分析中的變數Wilks Lambda步驟允差最低 允差要輸入的 F( )0x11.0001.000113.314.393x21.0001.00041.676.638x31.0001.0001180.161.059x41.0001.000902.

14、504.0751x1.445.44532.824.040x2.874.87437.484.039x4.752.75223.296.0442x1.375.37512.776.033x4.671.67129.889.0273x1.369.3696.615.025Wilks Lambda ()確切 F步驟變數數目Lambda ( )df1df2df3統計資料df1df2顯著性11.059121471180.1612147.000.00022.03922147297.9004292.000.00033.02732147243.5026290.000.00044.02542147191.1338288.

15、000.000分類處理摘要已處理150已排除遺漏或超出範圍群組代碼0至少一個遺漏識別變數0已在輸出中使用150群組的事前機率分析中使用的觀察值类别在前未加權加權1.3335050.0002.3335050.0003.3335050.000總計1.000150150.000Bayes判别（用回代法）的结果见下表。分類結果a預測的群組成員資格类别123總計原始計數150005020500503005050%1100.0.0.0100.02.0100.0.0100.03.0.0100.0100.0a. 100.0%個原始分組觀察值已正確地分類。下表是 Bayes判别（交叉确认法）的结果。分類函數係數

16、类别123x12.3641.5101.167x21.834.558.320x3-1.524.6651.417x4-1.521.4191.747（常數）-78.767-70.541-101.501費雪 (Fisher)線性區別函數分類結果 a預測的群組成員資格类别123總計原始計數150005020482503014950%1100.0.0.0100.02.096.04.0100.03.02.098.0100.0a. 98.0%個原始分組觀察值已正確地分類。2.2逐步判别逐步判别的主要计算步骤如下：第一步：输入原始数据矩阵第二步：计算变量的总均值、组均值、总离差、组内离差。第三步：给定挑选变量F

17、检验门坎值（临界值）。第四步： 逐步挑选变量。 逐步挑选变量的思想与逐步回归中一样，现假设迭代已进行了S 步，引进了 r 个变量，这 r 个变量号构成的集合为，剩下的 m-r 个变量号构成的集合为。第五步：求判别函数。设迭代h 步后，挑选变量结束，共选入r 个变量进入判别式。其中， qk 为第 k 个总体的先验概率。判别系数的计算为其中，表示为 k 个总体的第i 个变量的均值。第六步：判别归类。 将已知样本进行回判，并算出错判概率，然后将待判样本进行归类。得到结果如下表：逐觀察值統計資料個實最高群組第二高群組區別評分案際預測P(Dd |重心的馬氏重心的馬氏編群的群G=g)P(G=g(Mahal

18、anobis)群P(G=g(Mahalanobis)號組組pdf| D=d)距離平方組| D=d)距離平方函數 1函數 2原111.58321.0001.0782.000102.251-8.352.071始233.68021.000.7712.00024.2046.471.577322.7822.996.4913.00411.3692.354-.416433.34521.0002.1292.00027.3876.3201.779532*.1412.7303.9223.2705.9113.691-.998611.91221.000.1842.00076.125-6.926.377733.2092

19、.9993.1272.00116.8394.7372.059822.2872.9772.5003.0239.9633.132-1.460923*.1312.7604.0632.2406.3713.625.9351011.47821.0001.4742.000103.912-8.335.8911122.8322.997.3693.00312.1112.237-.399122*.1622.8323.6382.1686.8414.337-.92131333.6552.995.8462.00511.3154.722.8021422.54421.0001.2193.00025.639.960-1.524

20、1533.6452.992.8772.00810.5444.921-.1371633.8122.998.4162.00212.9595.261-.0391733.44921.0001.5992.00027.5486.5501.3421811.44321.0001.6272.00062.661-6.086.5281922.7792.998.4993.00212.7022.375-1.0152033.24321.0002.8332.00024.4305.7142.1922133.42121.0001.7282.00028.0116.5801.3842222.2932.9792.4523.02110

21、.1812.409.6792333.11821.0004.2672.00032.7306.5532.3432433.20721.0003.1472.00029.7687.168-.3082533.3282.9352.2322.0657.5734.468-.4672611.56421.0001.1462.000103.265-8.360.4892733.45021.0001.5982.00018.6635.2751.7352822.73321.000.6213.00017.9901.388-.0212922.5122.9991.3393.00114.9401.731.4263022.64721.

22、000.8723.00023.337.853-.4073111.48821.0001.4332.00068.257-6.533-.6803233.5612.9801.1572.0208.9284.558.2293322.49921.0001.3903.00026.151.944-1.6123433.5552.9861.1772.0149.7384.809-.2353533.35221.0002.0892.00021.7635.5411.9573611.91921.000.1692.00090.235-7.729.1533711.82721.000.3802.00094.309-7.940.18

23、33822.4052.9471.8093.0537.5952.904-.0773933.7642.999.5392.00115.6275.2111.1384011.85721.000.3092.00075.989-6.973-.2124133.82521.000.3852.00018.2245.5691.1324211.30321.0002.3882.00067.317-6.2201.3014322.77421.000.5113.00022.6201.129-1.1214411.60721.000.9982.00071.573-6.730-.5844533.06521.0005.4522.00

24、031.1877.302-1.0814633.2742.8492.5872.1516.0364.090-.0544711.57521.0001.1082.00068.776-6.562-.5074822.5712.9991.1213.00115.1582.328-1.6044922.19121.0003.3163.00034.340.133-1.6105033.00921.0009.3902.00047.3777.6392.7965111.67021.000.8012.00069.948-6.626-.3415211.85621.000.3102.00090.123-7.662.6615333

25、.2422.8452.8372.1556.2293.912.4785411.42721.0001.7022.00063.049-6.207-.4555511.43921.0001.6482.00069.334-6.598-.8395611.88321.000.2492.00090.552-7.761-.0235733.0182.9317.9852.06913.1815.024-2.2555833.79721.000.4532.00021.2306.225.2755911.66921.000.8042.00082.308-7.344-.6786011.04021.0006.4552.000130

26、.836-9.4761.5696111.54221.0001.2232.00070.142-6.479.9336222.58621.0001.0693.00020.4121.098.0876333.2032.7463.1922.2545.3473.831.2306411.65421.000.8502.00075.585-6.965-.6306511.90521.000.2002.00091.111-7.758.3266622.4862.9731.4423.0278.6002.718-.0516722.40421.0001.8123.00028.207.745-1.6516811.73321.0

27、00.6222.00070.758-6.591.5106911.80921.000.4232.00075.140-6.929-.2977022.6552.991.8453.00910.2722.467-.1857122.09021.0004.8253.00039.077-.421-1.1837211.02521.0007.3922.000119.382-8.6862.5727311.86421.000.2922.00092.048-7.786.4997433.67121.000.7992.00024.5306.417.8667533.15921.0003.6772.00030.2506.327

28、2.2857633.8122.998.4162.00212.9595.261-.0397722.1542.9983.7383.00216.1632.778-2.3557833.1732.8843.5112.1167.5714.468-.9847911.89421.000.2232.00081.567-7.193.6738011.22821.0002.9562.000112.943-8.7171.2278133.90821.000.1932.00019.7246.022.4048233.6972.993.7222.00710.5984.892.0368333.1902.7843.3202.216

29、5.8953.774.5768433.6172.999.9652.00113.9845.458-.4608522.20921.0003.1343.00033.948.105-1.4378622.97521.000.0513.00015.6021.899-.8808722.86221.000.2983.00020.6201.196-.6128811.08721.0004.8762.000120.483-8.9801.6808911.66421.000.8192.00073.727-6.856-.5559033.00321.00011.5482.00049.2118.743-.7679133.02

30、02.6717.7982.3299.2234.468-2.0429211.50921.0001.3492.00086.699-7.3401.3819322.99321.000.0153.00017.3681.648-.8239422.9052.999.1993.00114.8581.827-.2979522.1912.9903.3093.01012.4622.1061.0489611.97921.000.0412.00082.315-7.313.0169711.00121.00013.4272.00051.548-5.164-2.7419822.18821.0003.3453.00029.93

31、3.958-2.3909922.25421.0002.7383.00031.658.468-1.80310022.63321.000.9143.00025.003.777-.82410111.92421.000.1592.00080.961-7.252-.17310211.54421.0001.2192.00069.006-6.577-.59510333.52321.0001.2952.00023.5515.9971.57810422.90721.000.1963.00019.3141.329-.54110533.41921.0001.7382.00017.8565.954-.75610622

32、.5742.9991.1103.00114.8371.748.32210711.97921.000.0432.00084.024-7.406.02910811.83421.000.3632.00090.065-7.649.72610933.8822.999.2522.00113.3415.111.64611022.16921.0003.5583.00030.446.936-2.44411133.23221.0002.9222.00019.6016.140-1.10811233.1532.9993.7512.00118.9376.032-1.37411311.54621.0001.2092.00

33、077.998-7.102-.85811422.7002.998.7143.00212.8922.034.05611522.53121.0001.2653.00016.7082.195-1.75511611.70821.000.6922.00097.452-8.050.62611722.79921.000.4503.00018.9331.305-.21111822.1462.8563.8463.1447.4133.595-1.33411922.6672.999.8113.00115.4092.218-1.48812022.82321.000.3893.00020.8801.143-.51512

34、122.05921.0005.6623.00040.180-.647-.58912222.95121.000.1013.00018.3171.455-.57012333.59121.0001.0512.00025.8526.595.74012433.6692.998.8042.00213.7144.9361.12012511.17821.0003.4572.000106.319-8.2611.82512611.90421.000.2032.00087.234-7.512.62812733.07721.0005.1362.00034.7526.6452.52112833.3002.9822.4082.0