应用统计学试题2002(A)(参考答案).doc

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：CroqPain公司（续）CroqPain 是法国一家有名的快餐连锁店。Michel Boutillon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，Jean Gerard，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. Descriptive StatisticsNMinimumMaximumMeanStd. 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？参考答案：Zscore(毛利)是“毛利”的标准化值，其特征是均值为0，方差为1。“Zscore(毛利)”的计算公式：(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）。参考答案：利用“3”原则，而，所以该公司的60家已开业的餐馆毛利率超过26%家数不少于0.1660=10家。2. （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. Variables Entered/RemovedModelVariables EnteredVariables RemovedMethod1P15.Stepwise2月租金.Stepwise3平均收入.Stepwise4非餐企业.Stepwisea Dependent Variable:毛利率表3. ANOVAModelSum of SquaresdfMean SquareFSig.4Regression.5734.143552.183.000Residual.151552.744E-03Total.72459e Dependent Variable: 毛利率表4. CoefficientsModelUnstandardized CoefficientsBStd. ErrorStandardized CoefficientsBetatSig.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-03.000.2784.485.000a Dependent Variable: 毛利率表5. Excluded VariablesModelBeta IntSig.Partial Correlation4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-.093e Dependent Variable: 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。 参考答案：表3用的是方差分析方法。ST-SE=SR 0.724-0.151=0.573，fT-fR=fE 59-4=55，F=MSR/MSE 0.143/0.002744=52.183(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。参考答案：新店址选择系统为：毛利率=-.291+0.00005216 P15-0.007518月租金+0.01262平均收入+0.001362非餐企业由于该回归模型的总的回归检验显著，而且各回归系数的偏回归检验也显著，所以该系统能运用。(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Calais6605460025704306901440671038451822131Toulouse836245340030002570120013501135037586213136参考答案：毛利率=-.291+0.00005216 P15-0.007518月租金+0.01262平均收入+0.001362非餐企业Calais毛利率=-.291+0.00005216600-0.00751822+0.0126238+0.00136218=Toulouse毛利率=-.291+0.000052163400-0.00751813+0.0126237+0.0013628=(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？参考答案：表5告诉了我们有11个指标沒有能进入该回归模型，主要原因是这些指标与回归模型中的4个指标存在着一定的相关性。“Sig.= 0.771 ”是显著性概率，即P(T-0.292 )= 0.771 ,“餐馆数”指标由于不显著而剔除在模型之外。3. （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. Total Variance ExplainedComponentInitial EigenvaluesTotal% of VarianceCumulative %Rotation Sums of Squared LoadingsTotal% of VarianceCumulative %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-02100.000Extraction Method: Principal Component Analysis.表8. Rotated Component Matrix Component 1234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7.960E-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-02.725Extraction Method: Principal Component Analysis. Rotation Method: Varimax with Kaiser Normalization.表9. Variables EnteredModelVariables EnteredVariables RemovedMethod1REGR factor score 1 for analysis 1.Stepwise2REGR factor score 3 for analysis 1.Stepwise3REGR factor score 4 for analysis 1.Stepwisea Dependent Variable: 毛利率表10. Model SummaryModelRR SquareAdjusted R SquareStd. Error of the Estimate1.597.356.3458.9646E-022.753.568.5527.4103E-023.826.682.6656.4077E-02a Predictors: (Constant), REGR factor score 1 for analysis 1b Predictors: (Constant), REGR factor score 1 for analysis 1 , REGR factor score 3 for analysis 1c Predictors: (Constant), REGR factor score 1 for analysis 1 , REGR factor score 3 for analysis 1 , REGR factor score 4 for analysis 1d Dependent Variable: 毛利率表11. ANOVAModelSum of SquaresdfMean SquareFSig.1Regression.2581.25832.054.000Residual.466588.036E-03Total.724592Regression.4112.20537.397.000Residual.313575.491E-03Total.724593Regression.4943.16540.088.000Residual.230564.106E-03Total.72459a Predictors: (Constant), REGR factor score 1 for analysis 1b Predictors: (Constant), REGR factor score 1 for analysis 1 , REGR factor score 3 for analysis 1c Predictors: (Constant), REGR factor score 1 for analysis 1 , REGR factor score 3 for analysis 1 , REGR factor score 4 for analysis 1d Dependent Variable: 毛利率表12. CoefficientsModelUnstandardized CoefficientsBStd. ErrorStandardized CoefficientsBetatSig.1(Constant).178.01215.380.000REGR factor score 1 for analysis 16.608E-02.012.5975.662.0002(Constant).178.01018.606.000REGR factor score 1 for analysis 16.608E-02.010.5976.849.000REGR factor score 3 for analysis 15.094E-02.010.4605.280.0003(Constant).178.00821.517.000REGR factor score 1 for analysis 16.608E-02.008.5977.921.000REGR factor score 3 for analysis 15.094E-02.008.4606.107.000REGR factor score 4 for analysis 1-3.752E-02.008-.339-4.498.000a Dependent Variable: 毛利率表13. Excluded VariablesModelBeta IntSig.Partial Correlation1REGR factor score 2 for analysis 1.068.645.521.085REGR factor score 3 for analysis 1.4605.280.000.573REGR factor score 4 for analysis 1-.339-3.516.001-.4222REGR factor score 2 for analysis 1.068.782.437.104REGR factor score 4 for analysis 1-.339-4.498.000-.5153REGR factor score 2 for analysis 1.068.906.369.121a Predictors in the Model: (Constant), REGR fac or score 1 for analysis 1b Predictors in the Model: (Constant), REGR factor score 1 for analysis 1 , REGR factor score 3 for analysis 1c Predictors in the Model: (Constant), REGR factor score 1 for analysis 1 , REGR factor score 3 for analysis 1 , REGR factor score 4 for analysis 1d Dependent Variable: 毛利率表14. Residuals StatisticsMinimumMaximumMeanStd. DeviationNPredicted Value-5.78791E-02.33533.177999.1484E-0260Residual-.14566.11362-2.03541E-176.2426E-0260Std. Predicted Value-2.5781.720.0001.00060Std. Residual-2.2731.773.000.97460a Dependent Variable: 毛利率(1) 请指出Michel提出的新思路是采用的什么方法？参考答案：Michel提出的新思路是采用的先进行“因子分析，再由新的综合因子进行回归建模”的方法提取因子采