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1、1.用主成分分析方法探讨城市工业主体结构。表1是某市工业部门13个行业8项指标的数据。表1 某市工业部门13个行业8项指标的数据年末固定资产净值（万元）职工人数（人）工业总产值（万元）全员劳动产率（元/人年）百元固定原资产值实现产值（元）资金利税率（）标准燃料消费量（吨）能源利用效果（万元/吨）1(冶金)90342524551010911927282.00016.1001974350.1722(电力)4903197320351031334.2007.1005920770.0033(煤炭)6735211393767178036.1008.2007263960.0034(化学)4945436241
2、815572250498.10025.9003482260.9855(机械)1391902035052158981060993.20012.6001395720.6286(建材)122151621910351638262.5008.7001458180.0667(森工)23726572810312329184.40022.200209210.1528(食品)11062230785493523804370.40041.000654860.2639(纺织)17111239075210821796221.50021.500638060.27610(缝纫)12063930612615586330.40
3、029.50018400.43711(皮革)21505704620010870184.20012.00089130.27412(造纸)525161551038316875146.40027.500787960.15113(文教艺术用品)1434113203193961469194.60017.80063541.5741）试用主成分分析方法确定8项指标的样本主成分（综合变量）；若要求损失信息不超过15，应取几个主成分；并对这几个主成分进行解释；2）利用主成分得分对13个行业进行排序和分类。解：先将给出的的数据导入到Spass软件对导入的数据进行因子分析得到KMO 與 Bartlett 檢定Kai
4、ser-Meyer-Olkin 測量取樣適當性。.463Bartlett 的球形檢定大約 卡方96.957df28顯著性.000首先进行KMO检验和巴特利球体检验，KMO检验系数=0.969570.5P值0.05，所以能进行因子分析。說明的變異數總計元件起始特徵值擷取平方和載入循環平方和載入總計變異的 %累加 %總計變異的 %累加 %總計變異的 %累加 %13.10538.81138.8113.10538.81138.8113.03237.90337.90322.89736.21875.0292.89736.21875.0292.97037.12775.02930.93011.62886.65
5、70.93011.62886.6570.93011.62886.65740.6428.02794.68450.3043.80198.48560.0871.08299.56770.0320.40299.96980.0020.031100.000擷取方法：主體元件分析。循环平方和载入，累加达到85%，所以取三个指标，即累加达到86.657%旋轉元件矩陣a元件123年末固定资产净值.975-.084.108职工人数.965-.093.044工业总产值.989.090.093全员劳动产率.121.822.204百元固定原资产值实现产值-.169.906-.181资金利税率-.088.931.021标准
6、燃料消费量-.020-.700-.289能源利用效果.141.139.961擷取方法：主體元件分析。 轉軸方法：具有 Kaiser 正規化的最大變異法。a. 在 4 疊代中收斂循環。由旋转矩阵分析可知，八个指标分为三类第一类：年末固定资产净值，职工人数，工业总产值第二类：全员劳动产率，百元固定原资产值实现产值，资金利税率，标准燃料消费量第三类：能源利用效果（2）对原始数据进行归一化处理,计算相应的得分，结果如下： 最后的结果如上表最后一列所示，根据数值的正负号分成两类，利用主成分得分对13个行业进行排序和分类如下：第一类：1(冶金) 4(化学) 5(机械) 8(食品) 13(文教)第二类：9(
7、纺织) 6(建材)7(森工)10(缝纫)11(皮革)12(造纸)2(电力) 3(煤炭)2. 下表是某年美国50州每10万人中各种类型犯罪的犯罪率数据，分析找出主要的犯罪类型 、列出主成分与原始变量的线性关系式，分析解释主成分及其特征，排序说明每州主要的犯罪类型。州名杀人罪强奸罪抢劫罪斗殴罪偷盗罪汽车犯罪ALABAMA14.225.296.8278.33017.4280.7ALASKA10.851.696.82844701.5753.3ARIZONA9.534.2138.2312.36813.5439.5ARKANSAS8.827.683.2203.42834.7183.4CALIFORNIA1
8、1.549.42873585639.2663.5COLORADO6.342170.7292.95838.4477.1CONNECTICUT4.216.8129.5131.83966.7593.2DELAWARE624.9157194.25361467FLORIDA10.239.6187.9449.15700.4351.4GEORGIA11.731.1140.5256.53521.3297.9HAWAII7.225.512864.15831.9489.4IDAHO5.519.439.6172.53650.4237.6ILLINOIS9.921.8211.32093913.5528.6INDIAN
9、A7.426.5123.2153.53584.9377.4IOWA2.310.641.289.83497.6219.9KANSAS6.622100.7180.54009.7244.3KENTUCKY10.119.181.1123.32534.3245.4LOUISIANA15.530.9142.9335.53635.4337.7MAINE2.413.538.71703603.8246.9MARYLAND834.8292.1358.94577.7428.5MASSACHUSETTS3.120.8169.1231.63843.51140.1MICHIGAN9.338.9261.9274.64681
10、.7545.5MINNESOTA2.719.585.985.83694343.1MISSISSIPPI14.319.665.7189.12155.5144.4MISSOURI9.628.3189233.53742.5378.4MONTANA5.416.739.2156.83578.1309.2NEBRASKA3.918.164.7112.73076.1249.1NEVADA15.849.1323.13556665.7559.2NEW HAMPSHIRE3.210.723.2763385.6293.4NEW JERSEY5.621180.4185.14210.3511.5NEW MEXICO8.
11、839.1109.6343.44427.3259.5NEW YORK10.729.4472.6319.14510745.8NORTH AROLINA10.61761.3318.33191.9192.1NORTH DAKOTA0.9913.343.82289.1144.7OHIO7.827.3190.5181.13912.8400.4OKLAHOMA8.629.273.82053516.3326.8OREGON4.939.9124.1286.95142.5388.9PENNSYLVANIA5.619130.31282501.6333.2RHODE ISLAND3.610.586.52014333
12、.6791.4SOUTH CAROLINA11.933105.9485.33956245.1SOUTH DAKOTA213.517.9155.72274.9147.5TENNESSEE10.129.7145.8203.93036.2314TEXAS13.333.8152.4208.24591.8397.6UTAH3.520.368.8147.34176.2334.5VERMONT1.415.930.8101.23549.2265.2VIRGINIA923.392.1165.73507.4226.7WASHINGTON4.339.6106.2224.84992.5360.3WEST VIRGINIA613.242.290.91939.1163.3WISCONSIN2.812.952.263.73461.1220.7WYOMING
