应用统计学试题2002(a)

应用统计学试题2002(a)

华东理工大学2001---2002学年第二学期《应用统计学》试题(A)班级_________姓名__________学号___________成绩__________案例：Croq’Pain公司（续）Croq’Pain是法国一家有名的快餐连锁店。MichelBoutillon在这里担任运作部经理的工作，其主要任务是在新连锁店建成以前完成开张的所有准备工作。上个月，公司要求他完成一项研究任务，即建立一套选择新店址的分析系统，并希望这套系统最好以统计分析模型为基础。Michel运用“逐步回归”方法建立了新店址选择的分析系统。公司总裁，JeanGerard，认为该系统对原有信息的利用率太低，丢失了一些有价值的信息。Gerard要求Michel重新审查该系统。Michel苦苦思考了两周，提出了新的思路。在提交给Gerard以前，请你帮助审查一下。1.（20分）表1.DescriptiveStatisticsNMinimumMaximumMeanStd.Deviation毛利60-43.00399.20142.950091.3341Zscore(毛利)60-2.035932.805634.406198E-161.0000000毛利率60-.039.416.17799.11075(1)根据表l提供的资料，请你给出“Zscore(毛利)”的计算公式，该指标的特征是什么？(2)根据“毛利率=毛利/资本”，请你估算一下，该公司的60家已开业的餐馆毛利率超过26%家数（要提供依据）。7\n2.（40分）以下是Michel运用“逐步回归”方法建立了新店址选择的分析系统：表2.VariablesEntered/RemovedModelVariablesEnteredVariablesRemovedMethod1P15.Stepwise2月租金.Stepwise3平均收入.Stepwise4非餐企业.StepwiseaDependentVariable:毛利率表3.ANOVAModelSumofSquaresdfMeanSquareFSig.4Regression.5734.14352.183.000Residual.151552.744E-03Total.72459eDependentVariable:毛利率表4.CoefficientsModelUnstandardizedCoefficientsBStd.ErrorStandardizedCoefficientsBetatSig.4(Constant)-.291.070-4.164.000P155.216E-05.000.5608.959.000月租金-7.518E-03.001-.403-6.536.000平均收入1.262E-02.002.3735.971.000非餐企业1.362E-03.000.2784.485.000aDependentVariable:毛利率表5.ExcludedVariablesModelBetaIntSig.PartialCorrelation4投资.036.441.661.060店堂面积.058.918.363.124雇员人数-.026-.406.686-.055P25.034.496.622.067P35.111.330.743.045P45-.320-1.412.164-.189P55.062.710.481.096TOTAL.086.368.715.050餐馆数-.019-.292.771-.040非竞争餐-.018-.279.781-.038生活指数-.047-.684.497-.093eDependentVariable:毛利率(1)请指出表3用的是什么方法？其中有几个数据已模糊不清了，请你帮忙算算。7\n(2)请写出Michel的新店址选择系统，并说明该系统能运用的依据。(3)请预测一下，“Calais”、“Toulouse”的毛利率；判断一下由选址专家提供的2处备选地点是否可行。表6.选址专家提供的2处备选方案餐馆投资店堂面积P15P25P35P45P55Total平均收入餐馆数非竞争餐非餐企业月租金生活指数Calais6605460025704306901440671038451822131Toulouse836245340030002570120013501135037586213136(4)表5告诉了你什么信息？其中“餐馆数”的“Sig.=0.771”的含义是什么？7\n3.（40分）以下所提供的资料是Michel苦苦思考了两周后提出的新思路。表7.TotalVarianceExplainedComponentInitialEigenvaluesTotal%ofVarianceCumulative%RotationSumsofSquaredLoadingsTotal%ofVarianceCumulative%14.81432.09532.0954.79931.99531.99522.39715.97748.0722.09713.98045.97631.4429.61557.6871.53710.24756.22341.2848.55766.2441.50310.02166.2445.9396.26272.5066.8705.80178.3077.8315.54083.8478.7835.21789.0649.7024.68193.74410.5133.42097.16511.3602.40299.567122.992E-02.19999.767131.930E-02.12999.895141.124E-027.492E-0299.970154.476E-032.984E-02100.000ExtractionMethod:PrincipalComponentAnalysis.表8.RotatedComponentMatrixComponent1234投资-3.772E-02.901-.292.169店堂面积-5.625E-02.8763.416E-02-1.469E-02雇员人数-.1313.215E-02.281.580P15.972-1.618E-036.769E-02-3.020E-02P25.544-.1221.330E-02.109P35.9731.328E-025.018E-02-5.842E-02P45.9519.993E-025.846E-02-3.586E-02P55.762.103-.1761.049E-02TOTAL.9941.522E-02-8.370E-04-1.922E-03平均收入.132.477.458.111餐馆数-.157-.372.4779.689E-02非竞争餐Í7.960E-025.629E-02.7026.798E-02非餐企业6.356E-02-3.796E-025.418E-02-.662月租金4.235E-02.330-.624.360生活指数.2524.793E-02-9.201E-02.725ExtractionMethod:PrincipalComponentAnalysis.RotationMethod:VarimaxwithKaiserNormalization.7\n表9.VariablesEnteredModelVariablesEnteredVariablesRemovedMethod1REGRfactorscore1foranalysis1.Stepwise2REGRfactorscore3foranalysis1.Stepwise3REGRfactorscore4foranalysis1.StepwiseaDependentVariable:毛利率表10.ModelSummaryModelRRSquareAdjustedRSquareStd.ErroroftheEstimate1.597.356.3458.9646E-022.753.568.5527.4103E-023.826.682.6656.4077E-02aPredictors:(Constant),REGRfactorscore1foranalysis1bPredictors:(Constant),REGRfactorscore1foranalysis1,REGRfactorscore3foranalysis1cPredictors:(Constant),REGRfactorscore1foranalysis1,REGRfactorscore3foranalysis1,REGRfactorscore4foranalysis1dDependentVariable:毛利率表11.ANOVAModelSumofSquaresdfMeanSquareFSig.1Regression.2581.25832.054.000Residual.466588.036E-03Total.724592Regression.4112.20537.397.000Residual.313575.491E-03Total.724593Regression.4943.16540.088.000Residual.230564.106E-03Total.72459aPredictors:(Constant),REGRfactorscore1foranalysis1bPredictors:(Constant),REGRfactorscore1foranalysis1,REGRfactorscore3foranalysis1cPredictors:(Constant),REGRfactorscore1foranalysis1,REGRfactorscore3foranalysis1,REGRfactorscore4foranalysis1dDependentVariable:毛利率7\n表12.CoefficientsModelUnstandardizedCoefficientsBStd.ErrorStandardizedCoefficientsBetatSig.1(Constant).178.01215.380.000REGRfactorscore1foranalysis16.608E-02.012.5975.662.0002(Constant).178.01018.606.000REGRfactorscore1foranalysis16.608E-02.010.5976.849.000REGRfactorscore3foranalysis15.094E-02.010.4605.280.0003(Constant).178.00821.517.000REGRfactorscore1foranalysis16.608E-02.008.5977.921.000REGRfactorscore3foranalysis15.094E-02.008.4606.107.000REGRfactorscore4foranalysis1-3.752E-02.008-.339-4.498.000aDependentVariable:毛利率表13.ExcludedVariablesModelBetaIntSig.PartialCorrelation1REGRfactorscore2foranalysis1.068.645.521.085REGRfactorscore3foranalysis1.4605.280.000.573REGRfactorscore4foranalysis1-.339-3.516.001-.4222REGRfactorscore2foranalysis1.068.782.437.104REGRfactorscore4foranalysis1-.339-4.498.000-.5153REGRfactorscore2foranalysis1.068.906.369.121aPredictorsintheModel:(Constant),REGRfacorscore1foranalysis1bPredictorsintheModel:(Constant),REGRfactorscore1foranalysis1,REGRfactorscore3foranalysis1cPredictorsintheModel:(Constant),REGRfactorscore1foranalysis1,REGRfactorscore3foranalysis1,REGRfactorscore4foranalysis1dDependentVariable:毛利率7\n表14.ResidualsStatisticsMinimumMaximumMeanStd.DeviationNPredictedValue-5.78791E-02.33533.177999.1484E-0260Residual-.14566.11362-2.03541E-176.2426E-0260Std.PredictedValue-2.5781.720.0001.00060Std.Residual-2.2731.773.000.97460aDependentVariable:毛利率(1)请指出Michel提出的新思路是采用的什么方法？(2)请写出前四个特征根，并算出它们的贡献率和累计贡献率。试分别给所对应的四个综合指标命名。(3)请写出Michel按新思路建立的选址模型，并说明该模型能运用的依据。(4)请利用Michel提出的新思路再预测一下，“Calais”、“Toulouse”的毛利率；判断一下由选址专家提供的2处备选地点是否可行。(5)Michel提出的这两个模型是否有差异，如有的话，请说明原因。7