应用统计学试题20036(A)

应用统计学试题20036(A)

华东理工大学2002---2003学年第二学期(A)《应用统计学》试题(工商经济学院00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.（30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。nx1x2x3yRx1Rx2Rx3Ry18027894216.516.511.517.028027883716.516.59.515.537525903715.015.013.015.546222871811.510.07.011.556223871811.511.57.011.566224931911.513.516.013.076224932011.513.516.014.08582387157.511.57.09.09581889147.52.511.57.010581788137.51.09.56.011581993127.55.016.05.01250188672.52.55.01.01350197282.55.01.02.51450197982.55.02.02.51550208092.58.03.04.016562082155.08.04.09.0177020911514.08.014.09.0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:Y7\n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:RY①利用SPSS计算结果，建立y关于x1，x2，x3的逐步回归方程7\n②利用SPSS计算结果，建立Rｙ关于Rｘ1、Rｘ2、Rｘ3及它们的平方项Rx11,Rx22,Rx33,相互乘积项Rx12,Rx13,Rx23的R逐步回归方程。③试用上面所求得的两个回归方程，比较第3点、第12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。1.（30分）为了研究中国九十年代的经济发展状况，搜集了1989年---2002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1989199019911992199319941995指数(%)104.1103.8109.2114.2113.5112.6110.5年份1996199719981999200020012002指数(%)109.6108.8107.8107.1107.8107.3108.0资料来源：根据“中国统计摘要1999”(中国统计出版社)整理7\n①请将下列直径D(i,j)表中的括号填上，(无计算过程,不给分)。D(i,j)123456789101112131410.00020.0450.000318.42014.5800.000472.60854.10712.5000.000598.37268.84814.6600.2450.0006109.41373.55214.7281.2870.4050.0007110.16073.57317.5407.7404.7402.2050.0008110.16974.48922.34015.4289.8104.7400.4050.0009110.86976.97529.06024.39315.8608.0471.4470.3200.00010113.74982.42039.17536.34024.39313.3523.9681.6270.5000.00011118.60089.98951.18049.64934.10919.7007.4123.6281.4600.2450.00012120.39793.30557.10956.18938.28921.8948.1803.8481.4680.3270.2450.00013123.33297.89064.28763.81643.46224.9599.6294.5531.7320.3800.2600.2450.00014124.16499.57267.44067.16745.34025.7409.7794.5571.7800.5800.5300.2600.1250.000②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)。e[P(i,j)]234567891011121320.00030.0450.000412.5450.0450.000514.7050.2900.0450.000614.7731.3320.2900.0450.000717.5857.7851.3320.2900.0450.000822.38515.1781.7370.6950.2900.0450.000929.10516.2192.7781.6520.6100.2900.0450.0001039.22018.7405.2992.2371.1950.6100.2900.0450.0001151.22521.2138.7443.0231.8970.8550.5350.2900.0450.0001257.15421.4339.5123.1051.9780.9370.6170.3720.2900.0450.0001364.33222.13810.9603.1582.0320.9900.6700.4250.3050.2600.0450.0001467.48522.14211.1103.3582.2321.1900.8700.6250.5750.3050.1700.0457\n③试给出k=4的分类情况。试用经济理论和知识，解释取k=4分类的合理性。1.简答题（12分）①岭估计和主成分估计的共性。②简要说明在“Bayes判别”中，如何使达到最小的问题得到简化的。2.（28分）7\n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x510.9489.8964.51357773.0822.5892.3255.41298168.65313.4690.7138.20114819.08412.4690.0445.12112427.6858.9490.4641.83108036.1262.8090.1750.64201150.8678.9191.4346.32138342.6588.8290.7847.33162847.1790.8091.4762.36482266.23105.9490.3140.85169621.24112.6092.4235.14171732.81127.0787.9729.5193317.901314.4488.7129.04131321.361415.2489.4331.0594320.40153.1691.2137.85137227.34169.0488.7639.7188015.521712.0287.2838.76124828.911811.1589.1336.3397618.231922.4687.7238.38184536.772024.3484.8631.0779815.102133.2183.7939.44119324.05224.7890.5731.2690320.252321.5686.0022.3865418.932414.0980.9621.4995614.722532.3187.607.7086512.592611.1889.7141.0193021.492713.8086.3329.6993822.042825.3481.5631.30110027.352920.8481.4534.59102425.723039.6064.9038.47137431.91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:PrincipalComponentAnalysis.表(2)ComponentMatrixa7\nComponent12多孩率%(x1)-.762.554综合节育率%(x2).568-.768初中以上文化程度的人口比例%(x3).892.255人均国民收入(x4).870.347城镇人口比例%(x5).891.370ExtractionMethod:PrincipalComponentAnalysis.a：2componentsextracted.表(3)RotatedComponentMatrixaComponent12多孩率%(x1)-.354-.873综合节育率%(x2)7.635E-02.953初中以上文化程度的人口比例%(x3).892.255人均国民收入(x4).922.166城镇人口比例%(x5).952.157ExtractionMethod:PrincipalComponentAnalysis.RotationMethod:VarimaxwithKaiserNormalization.a:Rotationconvergedin3iterations.①请写出前两个特征值和对应的两个主成分，并给出它们的贡献率。②能否对未经旋转的主成分与旋转后的因子作比较，对这两个主成分的意义作一个合理的解释，并给两个主成分命名。③请指出这里的因子分析所采用的方法。④能否讨论一下：为什么在SPSS软件中主成分分析仅仅是因子分析的一种提取因子的方法？7