级研究生《应用统计学》作业解答.docx

1、级研究生应用统计学作业解答2010级研究生应用统计学作业 作业1：多元线性回归P138例5.3题：中国民航客运的回归模型。为了研究我国民航客运量的变化趋势及其成因，我们以民航客运量作为因变量Y，以国民收入、消费额、铁路客运量、民航航线里程、来华旅游入境人数为影响民航客运量的主要因素。Y为民航客运量（万人），x1为国民收入（亿元）、x2为消费额（亿元）、x3为铁路客运量（万人）、x4为民航航线里程（万公里）、x5为来华旅游入境人数（万人）。根据1994年统计摘要获得1978-1993年统计数据，见表1。表1年份yx1x2x3x4x51978231.03010.01888.081491.014.8

2、9180.921979298.03350.02195.086389.016.0420.391980343.03688.02531.092204.019.53570.251981401.03941.02799.095300.021.82776.711982445.04258.03054.099922.023.27792.431983391.04736.03358.0106044.022.91947.71984554.05652.03905.0110353.026.021285.221985744.07020.04879.0112110.027.721783.31986997.07859.0555

3、2.0108579.032.432281.9519871310.09313.06386.0112429.038.912690.2319881442.011738.08038.0122645.037.383169.4819891283.013176.09005.0113807.047.192450.1419901660.014384.09663.095712.050.682746.219912178.016557.010969.095081.055.913335.6519922886.020223.012985.099693.083.663311.519933383.024882.015949.

4、0105458.096.084152.7第一步：做相关分析，设定理论模型。用SPSS软件计算增广相关阵，自变量的偏相关阵，输出结果见表2。表2Correlationsyx1x2x3x4x5yPearson Correlation1.989*.985*.227.987*.924*Sig. (2-tailed).000.000.398.000.000N161616161616x1Pearson Correlation.989*1.999*.258.984*.930*Sig. (2-tailed).000.000.335.000.000N161616161616x2Pearson Correlati

5、on.985*.999*1.289.978*.942*Sig. (2-tailed).000.000.278.000.000N161616161616x3Pearson Correlation.227.258.2891.213.504*Sig. (2-tailed).398.335.278.428.046N161616161616x4Pearson Correlation.987*.984*.978*.2131.882*Sig. (2-tailed).000.000.000.428.000N161616161616x5Pearson Correlation.924*.930*.942*.504

6、*.882*1Sig. (2-tailed).000.000.000.046.000N161616161616*. Correlation is significant at the 0.01 level (2-tailed).*. Correlation is significant at the 0.05 level (2-tailed).从相关阵看出，Y与x1、x2、 x4、x5的相关系数都在0.9以上，说明所选自变量是与y高度线性相关的，用Y与自变量做多元线性回归是适合的。Y与x3的相关系数ry3=0.227偏小，p值=0.199，x3是铁路客运量，这说明铁路客运量对民航客运量无显著影

7、响。但是仅凭简单的相关系数的大小是不能决定变量的取舍的，在初步建模时还是应该包括x3在内的。第二步：回归分析。第三步：回归诊断。回归方程：复相关系数R=0.999，决定系数R2=0.998，由决定系数看回归方程高度显著。方差分析表，F=1121.144，P=0.000，表明回归方程高度显著，x1、x2、x3 、x4、x5整体上对y有高度显著的线性影响。回归系数的显著性检验。自变量x1、x2、x3 、x4、x5对y均有显著影响，其中，x3铁路客运量的P值=0.006最大，但仍在1%的显著性水平上对Y高度显著，这说明在多元线性回归中不能仅凭简单相关系数的大小决定变量的取舍。作业2：主成分分析P33

8、5例12.1题：在企业经济效益的评价中，设计的指标往往很多。为了简化系统结构，抓住经济效益评价中的主要问题，我们可由原始数据矩阵出发求主成分。在我国部分省、市、自治区独立核算的工业企业的经济效益评价中，涉及9项指标，原始数据见表3.即样品数据n=28，变量数p=9。表3地区百万固定资产原值实现值()百元固定资产原值实现利税()百元资金实现利税()百元工业总产值实现利税()百元销售收入实现利税()每吨标准煤实现工业产值(元)每千瓦时电力实现工业产值(元)全员劳动生产率(元人年)百元流动资金实现产值(元)北京(1)119.2930.9829.9225.9715.4821783.4121006296

9、.7天津(2)143.9831.5930.2121.9412.2928524.2920254363.1河北(3)94.817.217.9518.149.3711672.0312607322.2山西(4)65.811.0811.0612.1516.848.821.6510166284.7内蒙(5)54.799.249.5416.866.278941.87564225.4辽宁(6)94.5121.1222.8322.3511.2814162.3613.386311.7吉林（7)80.4913.3613.7616.67.1413062.079400274.1黑龙江(8)75.8615.8216.67

10、20.8610.3712672.269830267上海(9)187.7945.939.7724.4415.0943464.1131246418.6江苏(10)205.9627.6522.5813.427.8132024.6923377407.2浙江(11)207.4633.0625.7815.949.2838114.1922054385.5安徽(12)110.7820.720.1218.696.614682.2312578341.1福建(13)122.7622.5219.9318.348.3522002.6312164301.2江西(14)94.9414.714.1815.496.691669

11、2.2410463274.4山东(15)117.5821.9320.8918.659.118202.817829331.1河南(16)85.9817.317.1820.127.6713061.8911247276.5湖北(17)103.9619.518.4818.779.1618292.7515745308.9湖南(18)104.0321.4721.2820.638.7212721.9813161309广东(19)136.4423.6420.8317.337.8529593.7116259334广西(20)100.7222.0420.921.889.6717322.1312441296.4四川

12、(21)84.7314.3514.1716.937.9613102.3411703242.5贵州(22)59.0514.4814.3524.538.0910681.329710206.7云南(23)73.7221.9122.729.729.3814471.9412517295.8陕西(24)78.0213.1312.5716.839.1917312.0811369220.3甘肃(25)59.6214.0716.2423.5911.349261.1313084246.8青海(26)51.668.328.2616.117.0510551.319246176.49宁夏(27)52.958.258.8

13、215.576.588341.1210406245.4新疆(28)60.2911.2613.1418.688.3910412.9109832661、 标准化原始数据。得到数据表4：表40.4235231.3384051.5902821.6875562.2396340.4819710.9547461.2603710.0488050.9951991.4096491.6314530.6672281.0658731.1887581.8553941.1338441.200166-0.143523-0.271001-0.109061-0.294868-0.008542-0.578208-0.457635-

14、0.1527880.490970-0.814993-0.985774-1.087213-1.8114352.740046-1.792728-0.846551-0.563494-0.159272-1.069921-1.200673-1.303002-0.618942-1.149187-0.864488-0.693032-1.001289-1.187521-0.1502370.1868270.5837370.7710330.694243-0.317096-0.119892-2.2717050.308902-0.474859-0.719486-0.703902-0.684770-0.829071-0

15、.432447-0.416696-0.692376-0.343074-0.582063-0.432176-0.2907790.3937900.359408-0.473344-0.222238-0.620028-0.4661862.0095833.0809562.9886561.3001862.0961332.7554331.6711712.9832842.1625242.4302940.9494850.548246-1.489892-0.5825441.5557832.2647801.6592991.9648512.4650251.5813351.002539-0.851871-0.04165

16、72.1944081.7530481.4367001.5885780.2264810.1377740.199007-0.155617-1.027764-0.262566-0.252942-0.1576680.8186910.5038680.3503370.172033-0.244231-0.3838510.5050410.156444-0.2273240.126834-0.140281-0.562984-0.644276-0.965803-0.994648-0.051789-0.242707-0.513523-0.3378720.3839290.2814290.308322-0.165745-

17、0.1078880.1065570.3304330.7258300.645294-0.347742-0.259322-0.2183750.206435-0.634057-0.432447-0.600920-0.381613-0.3014580.068569-0.002378-0.033819-0.135363-0.0858110.1159940.2792600.3751900.2603510.0701900.2277050.3636890.335558-0.247709-0.468101-0.508808-0.0595760.2620850.8206170.4811450.299804-0.4

18、99946-0.5678261.3009631.2617850.4616730.695579-0.0064500.2942770.3097410.6520370.1018430.014276-0.355288-0.1807180.043603-0.376685-0.603861-0.645696-0.601220-0.527351-0.428252-0.140361-0.304889-0.891011-0.971284-0.588678-0.6201421.322972-0.479518-0.682024-1.184294-0.640218-1.511775-0.6316120.2790930

19、.5652822.636993-0.004862-0.284588-0.549747-0.1679310.033199-0.532050-0.746349-0.872843-0.626538-0.0747730.013227-0.406462-0.361086-1.275954-0.958086-0.636563-0.3518241.0849800.716320-0.830932-1.378753-0.072531-0.816450-1.142393-1.308123-1.484720-0.808830-0.862186-0.695657-1.194529-0.718287-2.035609-

20、1.112524-1.316298-1.405218-0.945549-1.035123-0.927407-1.388987-0.523114-0.840725-0.942573-0.964751-0.791922-0.158149-0.369133-0.7103380.432779-0.426032-0.4835262、将标准化数据进行主成分分析。由Total Variance Explained表我们可以看到前面两个主成分y1,y2的方差和占全部方差的比例为84.7%。故选取y1为第一主成分，y2为第二主成分，且这两个主成分之方差和占全部方差的84.7%，即基本上保留了原来指标的信息，这样

21、由原来的9个指标转化为2个新指标，起到了降维的作用。由该表得到前2个主成分y1，y2的线性组合为：作业3：判别分析P335例12.1题：2005年全国城镇居民月平均消费状况可划分为两类，分类后的数据见表3.试建立费歇线性判别函数，并将广东、西藏两个待判省区归类。x1人均粮食支出，x2人均副食支出，x3 人均烟、酒、饮料支出，x4人均其他副食支出，x5人均衣着支出，x6人均日用杂品支出，x7人均水电燃料支出，x8人均其他非商品支出。表5 2005年31个省、市、自治区城镇居民月平均消费类型划分数据序号地区x1x2x3x4x5x6x7x8Group1北京21.3124.8935.4373.9893

22、.0120.5843.97433.7312上海21.13168.6940.8170.1274.3215.4650.9422.7413浙江19.96142.2443.3350.74101.7712.9253.44394.5514天津21.5122.3929.0851.6455.0411.354.88288.1325河北18.2590.2124.4532.4462.487.4547.5178.8426山西21.8466.3818.0561.3274.488.1934.97177.4527内蒙古21.3767.0820.2835.2781.0710.9439.46182.228辽宁22.74115.

23、8828.2142.4458.079.6348.65194.8529吉林20.2288.9418.5435.6365.728.8150.29186.52210黑龙江21.3375.51429.5669.298.2442.08165.9211江苏18.61122.5127.0742.563.4715.3836.14240.92212安徽19.61107.1332.8535.7761.437.5334.6142.23213福建25.56171.6522.340.5357.1312.654.03225.08214江西18.75104.6815.5535.6151.811.1836.27142.722

24、15山东18.2788.3419.0743.1972.9712.5942.16200.18216河南19.0773.1818.0129.3864.518.9138.14155.45217湖北18.76102.6721.8730.4764.3311.9942.14168.17218湖南20.25104.4520.7238.1562.9812.6739.16213.56219广西18.7131.3511.6932.0641.5410.8442.77178.51220海南16.16139.9212.9823.5824.8710.7632.35144.21221重庆18.18120.3926.1837

25、.9468.1611.6438.48246.37222四川18.53109.9521.4933.0450.9810.8833.96183.85223贵州18.3392.4325.3832.1956.321438.57144.82224云南22.399.0833.3632.0152.067.0432.85190.04225陕西20.0370.7519.7534.9553.2910.5538.2189.41226甘肃18.6872.7423.7238.6962.419.6535.26170.12227青海20.3375.6420.8833.8553.8110.0632.82171.32228宁夏19.7570.2418.6736.7161.7510.0840.26165.2222