应用统计学试题20056(B)(参考答案).doc

华东理工大学20042005学年第二学期 应用统计学 课程期末考试试卷 B 2005.6开课学院： 商学院 ，考试形式：开卷，所需时间： 120 分钟考生姓名： 学号： 专业： 班级 题序一二 三总 分得分评卷人一、花菜留种培养试验（30分）对花菜留种的生产条件进行研究，目的是提高花菜种子的亩产量，现考察四个二水平因子，选取因素水平表如下。试验除考察四个因素的作用外，还要考察AC的交互作用。因素水平A浇水次数B喷药次数C施肥方法D进室时间1浇1至2次随时喷开花期施肥11月初2随时浇定期施四次肥11月中选用L 8 ( 2 7 ) 表安排试验，试验计划和试验结果见表1。表1 试验计划和试验结果列号试验号ABCACD亩产量（斤/亩）1234567yi11111111350.0021112222325.0031221122425.0041222211425.0052121212200.0062122121250.0072211221275.0082212112375.00经SPSS软件的计算，列表如下，请根据计算结果表格进行分析。表2 ANOVNSourceType III Sum of SquaresdfMean SquareFSig.A22578.125157.8000.017B17578.125117578.12545.0000.022C1953.12511953.1250.155D178.12500.2000.698A * C3828.12513828.1259.8000.089Error781.2502390.625Total46796.8757表3 Estimated Marginal MeansAMeanStd. Error1.00381.2509.8822.00275.0009.882BMeanStd. Error1.00281.2509.8822.00375.0009.882 CMeanStd. Error1.00312.5009.8822.00343.7509.882DMeanStd. Error1.00325.0009.8822.00331.2509.882ACMeanStd. Error1.001.00387.50013.9752.00375.00013.9752.001.00237.50013.9752.00312.50013.975（1）表2中有些数据没给出，请根据方差分析表的原理将其计算出来，给出计算过程。来源于因子D的误差平方和46796.87522578.12517578.1251953.1253828.125781.25078.125均方和VA=22578.125/1=22578.125FC=1953.125/390.6255（2）由表2分析哪些因子是显著的，给出理由。因子A是显著的，因为其P=0.0170.1因子B是显著的，因为其P0.0220.1因子A*C是显著的，因为其P0.0890.1（3）由表2和表3分析出花菜留种的最优生产条件，给出理由。花菜留种的最优生产条件是：A取因子水平1，B取因子水平2，C取因子水平1，D取任意水平因子。因为在因子A和C的组合中，最大因子D不显著，可取任意水平。（4）根据表1，得出在最优生产条件下，花菜种子的亩产量为多少，给出理由。在最优生产条件下，花菜种子的亩产量为425斤/亩，因为因子A、B和C的水平分别取1、2和1时所对应的试验结果为425斤/亩。二、数学家的年工资研究（30分）某科学基金会的管理人员希望估价从事数学研究工作的中等或较高水平的数学家的年工资额Y与他们的研究成果（论文、著作）的质量指标X1，从事研究工作的时间X2以及能成功获得资助的指标X3之间的关系，为此按一定的试验设计方法调查了24位此类型的数学家，得到下列数据：nX1X2X3YRX1RX2RX3RY13.509.004.0033.202.0003.0002.0003.00025.3020.006.0040.3012.0008.00012.50014.00035.1018.005.9038.7011.0007.00011.00012.00045.8033.006.4046.8015.00017.50015.50022.00054.2031.005.0041.406.00016.0007.00017.00066.0013.006.7037.5017.0005.00017.0009.00076.8025.007.5039.0021.00012.50021.00013.00085.5030.006.0040.7013.00015.00012.50016.00093.105.003.5030.101.0001.0001.0001.000107.2047.008.0052.9023.00024.00023.00024.000114.5025.005.0038.207.50012.5007.00011.000124.9011.005.8031.8010.0004.00010.0002.000138.0023.008.3043.3024.00010.50024.00019.000146.5035.007.0044.1019.00020.50018.50020.000156.6039.007.4042.8020.00022.00020.00018.000163.7021.004.3033.603.0009.0003.0004.000176.207.007.0034.2018.0002.00018.5005.000187.0040.007.6048.0022.00023.00022.00023.000194.0035.004.9038.005.00020.5005.00010.000204.5023.005.0035.907.50010.5007.0007.000215.9033.006.4040.4016.00017.50015.50015.000225.6027.006.1036.8014.00014.00014.0008.000234.8034.005.5045.209.00019.0009.00021.000243.9015.004.4035.104.0006.0004.0006.000经SPSS软件的计算，得到下列计算结果：表4 Variables Entered/Removed(a)ModelVariables EnteredVariables RemovedMethod1X2.Stepwise (Criteria: Probability-of-F-to-enter = 0.100).2X1.Stepwise (Criteria: Probability-of-F-to-enter =0 .100).a: Dependent Variable: Y表5 ANOVA(c)ModelSum of SquaresdfMean SquareFSig.1Regression508.0691508.06961.6890.000(a)Residual181.191228.236Total689.260232Regression570.5272285.26350.4540.000(b)Residual118.733215.654Total689.26023a: Predictors: (Constant), X2; b: Predictors: (Constant), X2, X1; c: Dependent Variable: Y表6 Coefficients(a)ModelUnstandardized CoefficientstSig.BStd. Error1(Constant)29.0481.45419.9780.000X2.419.0537.8540.0002(Constant)23.2512.12010.9690.000X2.341.0506.8310.000X11.443.4343.3240.003a: Dependent Variable: Y表7 Variables Entered/Removed(a)ModelVariables EnteredVariables RemovedMethod1RX2*RX3.Stepwise (Criteria: Probability-of-F-to-enter = 0.100).2RX2.Stepwise (Criteria: Probability-of-F-to-enter = 0.100).3RX3.Stepwise (Criteria: Probability-of-F-to-enter = 0.100).4.RX2*RX3Stepwise (Criteria: Probability-of-F-to-enter =0.100).a: Dependent Variable: RY表8 ANOVA(e)ModelSum of SquaresdfMean SquareFSig.1Regression790.5921790.59248.3930.000(a)Residual359.4082216.337Total1150.000232Regression863.7332431.86731.6810.000(b)Residual286.2672113.632Total1150.000233Regression904.5863301.52924.5730.000(c)Residual245.4142012.271Total1150.000234Regression904.5702452.28538.6990.000(d)Residual245.4302111.687Total1150.00023a: Predictors: (Constant),RX2*RX3; b: Predictors: (Constant), RX2*RX3, RX2; c: Predictors: (Constant), RX2*RX3, RX2, RX3; d: Predictors: (Constant), RX2, RX3; e: Dependent Variable: RY表9 Coefficients(a)ModelUnstandardized CoefficientstSig.BStd. Error1(Constant)5.9871.2484.7980.000RX2*RX30.0370.0056.9570.0002(Constant)3.2911.6292.0200.056RX2*RX30.0200.0092.3730.027RX20.4480.1942.3160.0313(Constant)-0.3982.545-0.1570.877RX2*RX3-0.0010.014-0.0360.972RX20.6750.2223.0450.006RX30.3640.1991.8250.0834(Constant)-0.3301.640-0.2010.843RX20.6690.1135.9330.000RX30.03580.1133.1720.005a: Dependent Variable: RY（1）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，计算第3点、第24点的残差。由得则第3点残差第22点残差根据计算残差第3点对应的，则，其对应的则第3点残差第24点对应的，则，其对应的则第24点残差（4）试利用R回归方程 ，求出X1=5.5，X2=46，X3=4.0时，Y的预测值。X1=5.5，X2=46，X3=4.0对应的则，其预测值为三、主成分回归分析（40分）某医院管理工作者希望了解病人对医院工作的满意程度Y和病人的年龄X1、病情的严重程度X2和忧虑程度X3之间的关系。他们随机选取了23位病人，得到下表所列数据：nX1X2X3YnX1X2X3Y150.0051.002.3048.001338.0055.002.2047.00236.0046.002.3057.001434.0051.002.3051.00340.0048.002.2080.001553.0054.002.2057.00441.0044.001.8090.001636.0049.002.0066.00528.0043.001.8060.001733.0056.002.5079.00649.0054.002.9036.001829.0046.001.9088.00742.0050.002.2046.001933.0049.002.1080.00845.0048.002.4054.002055.0051.002.4049.00952.0062.002.9026.002129.0052.002.3077.001029.0050.002.1077.002244.0058.002.9052.001129.0048.002.4089.002343.0050.002.3060.001243.0053.002.4067.00经SPSS软件的计算，得到下列计算结果：表10 Descriptive StatisticsNMinimumMaximumMeanStd. DeviationX12328.0055.0039.618.47X22343.0062.0050.784.44X3231.802.902.300.30Y2326.0090.0062.4317.55表11 Total Variance ExplainedComponentInitial EigenvaluesExtraction Sums of Squared LoadingsTotal% of VarianceCumulative %Total% of VarianceCumulative %12.18672.88372.8832.18672.88372.88320.60920.30093.1830.60920.30093.18330.2056.817100.000Extraction Method: Principal Component Analysis.表12 Component Matrix(a)Component12X10.2630.965X20.9220.226X30.9040.276Extraction Method: Principal Component Analysis; a: 2 components extracted.表13 Component Score Coefficient MatrixComponent12X1-0.3071.118X20.612-0.198X30.571-0.123Extraction Method: Principal Component Analysis. Component Scores.表14 Variables Entered/Removed(b)ModelVariables EnteredVariables RemovedMethod1REGR factor score 2 for analysis 1, REGR factor score 1 for analysis 1(a).Entera: All requested variables entered.; b: Dependent Variable: Zscore(Y)表15 ANOVA(b)ModelSum of SquaresdfMean SquareFSig.1Regression11.70225.85111.3630.001(a)Residual10.298200.515Total22.00022a: