应用统计学试题2000.2

1华东理工大学2000---2001学年第一学期《应用统计学》试题(工商经济学院98级)班级_________姓名__________学号___________成绩__________注意：本试卷为开卷考试题，所有的计算都要给出计算过程，否则不给分。1.（20分）在把氨氧化成硝酸的生产过程中，希望求得氨的损失率ｙ关于空气流速ｘ１，冷却水温度ｘ２，吸收液中硝酸的浓度ｘ３的回归方程，现收集到17组数据，见下表。nx1x2x3yRx1Rx2Rx3Ry18027894216.516.511.517.028027883716.516.59.515.537525903715.015.013.015.546222871811.510.07.011.556223871811.511.57.011.566224931911.513.516.013.076224932011.513.516.014.08582387157.511.57.09.09581889147.52.511.57.010581788137.51.09.56.011581993127.55.016.05.01250188672.52.55.01.01350197282.55.01.02.51450197982.55.02.02.51550208092.58.03.04.016562082155.08.04.09.0177020911514.08.014.09.0①利用SPSS计算结果，建立y关于x1，x2，x3的逐步回归方程②利用SPSS计算结果，建立Rｙ关于Rｘ1、Rｘ2、Rｘ3及它们的平方Rx11,Rx22,Rx33,相互乘积项的回归Rx12,Rx13,Rx23的R逐步回归方程③试用两个回归方程，比较第5点、第14点的残差。④试利用Ｒ回归方程求出x1=60,x2=25,x3=81时，ｙ的预测值。附表：SPSS计算结果表(1)VariablesEntered/RemovedaModelVariablesEnteredVariablesRemovedMethod1X1.Stepwise(Criteria:Probability-of-F-to-enter=.090,Probability-of-F-to-remove=.100).2X2.Stepwise(Criteria:Probability-of-F-to-enter=.090,Probability-of-F-to-remove=.100).aDependentVariable:Y表(2)ANOVAcModelSumofSquaresdfMeanSquareFSig.1Regression1588.74811588.748108.229.000aResidual220.1931514.680Total1808.941162Regression1665.3282832.66481.171.000bResidual143.6131410.258Total1808.94116a:Predictors:(Constant),X1b:Predictors:(Constant),X1,X2c:DependentVariable:Y2表(3)CoefficientsaModelUnstandardizedCoefficientsBStd.ErrortSig.1(Constant)-43.9966.037-7.288.000X11.013.09710.403.0002(Constant)-50.6055.596-9.043.000X1.721.1345.366.000X21.141.4182.732.016a:DependentVariable:Y表(4)VariablesEntered/RemovedaModelVariablesEnteredVariablesRemovedMethod1RX12.Stepwise(Criteria:Probability-of-F-to-enter=.090,Probability-of-F-to-remove=.100).2RX1.Stepwise(Criteria:Probability-of-F-to-enter=.090,Probability-of-F-to-remove=.100).3RX11.Stepwise(Criteria:Probability-of-F-to-enter=.090,Probability-of-F-to-remove=.100).a:DependentVariable:RY表(5)ANOVAdModelSumofSquaresdfMeanSquareFSig.1Regression350.8641350.86498.124.000aResidual53.636153.576Total404.500162Regression361.4612180.73058.789.000bResidual43.039143.074Total404.500163Regression385.2463128.41586.705.000cResidual19.254131.481Total404.50016a:Predictors:(Constant),RX12b:Predictors:(Constant),RX12,RANKofX1c:Predictors:(Constant),RX12,RANKofX1,RX11d:DependentVariable:RANKofY表(6)CoefficientsaModelUnstandardizedCoefficientsBStd.ErrortSig.1(Constant)3.976.6845.814.000RX125.083E-02.0059.906.0002(Constant)2.3011.1032.087.056RX123.099E-02.0122.649.019RANKofX1.404.2181.857.0853(Constant)-.8611.099-.784.447RX125.970E-02.0115.513.000RANKofX11.356.2814.817.000RX11-7.919E-02.020-4.007.001a:DependentVariable:RY32.（30分）为了研究中国九十年代的经济发展状况，搜集了1989年---1999年中国国内生产总值(GDP)指数(上年=100)，列表如下(本表按不变价格计算)：年份19891990199119921993199419951996199719981999指数104.1103.8109.2114.2113.5112.6110.5109.6108.8107.8107.1资料来源：“中国统计摘要1999”，中国统计出版社①请将下列直径D(i,j)表中的括号填上，(无计算过程,不给分)。1234567891020.045318.4214.584(……)54.10712.5598.37268.84814.660.2456109.41373.552(……)1.2870.4057110.1673.57317.547.744.742.2058110.16974.48922.3415.4289.814.740.4059110.86976.97529.0624.39315.868.0481.447(…….)10113.74982.4239.17536.3424.39313.3523.9681.6270.511118.689.98951.1849.64934.10919.77.4123.6281.460.245②请将下列最小目标函数e［P（i,j）］表中的括号填上，(无计算过程,不给分)。234567891030.045(3)4(……..)0.045(4)514.705(3)0.29(4)0.045(5)614.773(3)1.332(4)0.29(6)0.045(6)717.585(3)7.785(4)(……)0.29(7)0.045(7)822.385(3)15.178(7)1.737(7)0.855(7)0.29(8)0.045(8)929.105(3)16.22(7)2.779(7)1.652(8)0.77(8)0.29(8)0.045(9)1039.22(3)18.741(7)5.3(7)2.237(9)1.355(9)(……)0.29(10)0.045(10)1151.225(3)21.213(7)8.744(7)3.024(10)1.897(10)0.855(10)0.535(10)0.29(10)0.045(10)③试给出不同k值的分类情况。④试用经济理论和知识，解释取k=4分类的合理性。3.简答题（24分）①岭估计和主成分估计的共性。②R估计能用来解决什么统计问题？其基本思路是什么？③系统聚类法与有序样品聚类法的主要不同点。④简要说明在“Bayes判别”中，如何使G1gG1hgG21)gh(P)gh(Lq)D,,D,D(I达到最小的问题得到简化的。44.（26分）这是一个生育率因素分析的课题。生育率受社会、经济、文化、计划生育政策等很多因素影响。现选择的变量有：人均国民收入、城镇人口比例、初中以上文化程度的人口比例、多孩率、综合节育率。现给出1990年中国30个省、自治区、直辖市的数据。No.多孩率x1综合节育率x2初中以上文化程度的人口比例x3人均国民收入x4城镇人口比例x51.9489.8964.51357773.0822.5892.3255.41298168.65313.4690.7138.20114819.08412.4690.0445.12112427.6858.9490.4641.83108036.1262.8090.1750.64201150.8678.9191.4346.32138342.6588.8290.7847.33162847.179.8091.4762.36482266.23105.9490.3140.85169621.24112.6092.4235.14171732.81127.0787.9729.5193317.901314.4488.7129.04131321.361415.2489.4331.0594320.40153.1691.2137.85137227.34169.0488.7639.7188015.521712.0287.2838.76124828.911811.1589.1336.3397618.231922.4687.7238.38184536.772024.3484.8631.0779815.102133.2183.7939.44119324.05224.7890.5731.2690320.252321.5686.0022.3865418.932414.0980.9621.4995614.722532.3187.607.7086512.592611.1889.7141.0193021.492713.8086.3329.6993822.042825.3481.5631.30110027.352920.8481.4534.59102425.723039.6064.9038.47137431.91经SPSS软件计算的结果如下：表(1)TotalVarianceExplainedComponentInitialEigenvaluesTotal%ofVarianceCumulative%ExtractionSumsofSquaredLoadingsTotal%ofVarianceCumulative%13.25065.00665.0063.25065.00665.00621.22024.39689.4011.22024.39689.4013.2504.99394.3944.1813.62098.01459.928E-021.986100.000ExtractionMethod:Prin