spss的试题答案结果

1、 统计复习题目一.某公司管理人员为了解某化妆品在一个城市的月销售量Y（单位：箱）与该城市中适合使用该化妆品的人数（单位：千人）以及他们 人均月收入（单位：元）之间的关系，在某个月中对15个城市做调查，得上述各量的观测值如表A1所示.假设Y与，之间满足线性回归关系 其中独立同分布于.(1)求回归系数的最小二乘估计值和误差方差的估计值，写出回归方程并对回归系数作解释；analyze-regression-linear,y to dependent,x1 x2 to indepents ,statistics-confidence intervals,save-unstandardized. Pre

2、diction individual-individual.ok CoefficientsaModelUnstandardized CoefficientsStandardized CoefficientstSig.95% Confidence Interval for BBStd. ErrorBetaLower BoundUpper Bound1(Constant)3.4532.4311.420.181-1.8438.749x1.496.006.93481.924.000.483.509x2.009.001.1089.502.000.007.011a. Dependent Variable:

3、 yANOVAbModelSum of SquaresdfMean SquareFSig.1Regression53844.716226922.3585.679E3.000aResidual56.884124.740Total53901.60014a. Predictors: (Constant), x2, x1b. Dependent Variable: y回归系数的最小二乘估计值和误差方差的估计值分别为：3.453,0.496,0.009和=4.740. 回归方程为y=0.496*x1+0.009*x2+3.453 回归系数解释：3.453可理解为化妆品的月基本销售量，当人均月收入固定时，

4、适合使用该化妆品的人数每提高一个单位，月销售量Y将增加0.496个单位；当适合使用该化妆品的人数固定时，人均月收入每提高一个单位，月销售量 Y将增加0.009个单位(2)求出方差分析表，解释对线性回归关系显著性检验的结果.求复相关系数的平方的值并解释其意义；ANOVAbModelSum of SquaresdfMean SquareFSig.1Regression53844.716226922.3585.679E3.000aResidual56.884124.740Total53901.60014a. Predictors: (Constant), x2, x1b. Dependent Var

5、iable: yModel SummaryModelRR SquareAdjusted R SquareStd. Error of the Estimate1.999a.999.9992.17722a. Predictors: (Constant), x2, x1由于P值=0.000<0.05，所以回归关系显著.值=0.999，说明Y与，之间的线性回归关系是高度显著的(3)分别求和的置信度为的置信区间；coefficients的后面部分.和的置信度为的置信区间分别为（0.483，0.509），（0.007,0.011）(4)对，分别检验人数及收入对销量Y的影响是否显著；由于系数，对应的检

6、验P值分别为0.000，0.000都小于0.05，所以适合使用该化妆品的人数和人均月收入 对月销售量Y的影响是显著的(5)该公司欲在一个适宜使用该化妆品的人数，人均月收入的新城市中销售该化妆品，求其销量的预测值及置信为0.95的置信区间.Y的预测值及置信度为0.95的置信区间分别为：135.5741和（130.59977，140.54305）在数据表中直接可以看见二、某班42名男女学生全部参加大学英语四级水平考试，数据如下：（数据表为A2）不合格1合格2男生1262女生286问男女生在英语学习水平上有无显著差异？单击weight cases-weight cases by-x, ok, ana

7、lyze-descriptive statistics-crosstabs,(列联表分析)sex to rows,score to column, exact-exact, statistics chi-square ,ok.Chi-Square TestsValuedfAsymp. Sig. (2-sided)Exact Sig. (2-sided)Exact Sig. (1-sided)Point ProbabilityPearson Chi-Square7.721a1.005.010.010Continuity Correctionb5.5781.018Likelihood Ratio7

8、.3691.007.037.010Fisher's Exact Test.010.010Linear-by-Linear Association7.537c1.006.010.010.010N of Valid Cases42a. 1 cells (25.0%) have expected count less than 5. The minimum expected count is 2.67.b. Computed only for a 2x2 tablec. The standardized statistic is 2.745.原假设不显著，看这个（Asymp. Sig. (2

9、-sided)）。Pearson Chi-Square（卡方检验） and Likelihood Ratio（似然比） all <0.05 男女生在英语学习水平上差异是显著的三、将一块耕地等分为24个小区，今有3种不同的小麦品种(d)和2种不同的肥料(B1,B2)，现将各小麦品种与各种肥料进行搭配，对每种搭配都在4个小区上试验，测得每个小区产量的数据如表A3所示.（1）假设所给数据服从方差分析模型，建立方差分析表，A与B的交互效应在下是否显著？3.0Analyze-general linear model-univariate,x to dependent variable,a and

10、b to fixed factor, ok Tests of Between-Subjects EffectsDependent Variable:xSourceType III Sum of SquaresdfMean SquareFSig.Corrected Model263.333a552.66721.545.0003650.66713650.6671.493E3.000a190.333295.16738.932.000b54.000154.00022.091.000a * b19.00029.5003.886.040Error44.000182.444Total3958.00024Co

11、rrected Total307.33323a. R Squared = .857 (Adjusted R Squared = .817)由于交互效应检验P值=0.04<0.05，所以小麦(A)与肥料(B)之间的交互效应是显著的.（2）若A与B的交互效应显著，分别就B的各水平，给出在A的各水平上的均值的置信度为0.95 的置信区间以及两两之差的置信度不小于0.95的Bonferroni同时置信区间.3.1.Analyze-general linear model-univariate,x to dependent variable,a to fixed factor,post hoc-a

12、 to post hoc tests for, bonferroni,options-a to display means for.ok aDependent Variable:xaMeanStd. Error95% Confidence IntervalLower BoundUpper Bound19.000.6877.44510.555210.000.6878.44511.555313.500.68711.94515.055Multiple ComparisonsxBonferroni(I) a(J) aMean Difference (I-J)Std. ErrorSig.95% Conf

13、idence IntervalLower BoundUpper Bound12-1.00.972.991-3.851.853-4.50*.972.004-7.35-1.65211.00.972.991-1.853.853-3.50*.972.017-6.35-.65314.50*.972.0041.657.3523.50*.972.017.656.35Based on observed means. The error term is Mean Square(Error) = 1.889.*. The mean difference is significant at the .05 leve

14、l.固定肥料的水平，的置信度为0.95的置信区间分别为(7.445,10.555),(8.445,11.555),(11.945,15.055);的置信度不小于0.95的Bonferroni同时置信区间分别为（-3.85,1.85）,（-7.35,-1.65）,（-6.35,-0.65）2. Analyze-general linear model-univariate, x to dependent variable,a to fixed factor,post hoc-a to post hoc tests for,bonferroni,options-a to display means

15、 for,.ok aDependent Variable:xaMeanStd. Error95% Confidence IntervalLower BoundUpper Bound110.500.8668.54112.459212.000.86610.04113.959319.000.86617.04120.959Multiple ComparisonsxBonferroni(I) a(J) aMean Difference (I-J)Std. ErrorSig.95% Confidence IntervalLower BoundUpper Bound12-1.501.225.755-5.09

16、2.093-8.50*1.225.000-12.09-4.91211.501.225.755-2.095.093-7.00*1.225.001-10.59-3.41318.50*1.225.0004.9112.0927.00*1.225.0013.4110.59Based on observed means. The error term is Mean Square(Error) = 3.000.*. The mean difference is significant at the .05 level.固定肥料的水平，的置信度为0.95的置信区间分别(8.541,12.459),(10.0

17、41,13.959),(17.041,20.959)的置信度不小于0.95的Bonferroni同时置信区间分别为（-5.09,2.09）,（-12.09,-4.91）,（-10.59,-3.41）四、数据表A4给出了我国31个省市自治区的的经济发展状况，所考察的八个指标为：地区生产总值；：居民消费水平；：基本建设投资；职工平均工资； ：居民消费价格指数；：商品零售价格指数；：货物周转量；：工业总产值。(1)从样本相关系数矩阵出发做主成分分析，求各主成分的贡献率及前三个主成分的累计贡献率；求出前三个主成分的表达式。Analyze-data-reduction-factor将八个成分全部选入va

18、riables，extraction-extract-number of factors-8,okTotal Variance ExplainedComponentInitial EigenvaluesExtraction Sums of Squared LoadingsTotal% of VarianceCumulative %Total% of VarianceCumulative %13.74146.76146.7613.74146.76146.76122.39429.92676.6872.39429.92676.6873.7389.23185.918.7389.23185.9184.4

19、806.00691.9235.4375.46697.3896.1421.77699.1657.060.74599.9108.007.090100.000Extraction Method: Principal Component Analysis.Component MatrixaComponent12345678地区生产总值.814.556-.116.031-.035-.028-.094-.061居民消费水平.766-.493.195-.076.212-.285.005.006基本建设投资.785.558-.141.085-.083-.013.196.003职工平均工资.604-.572.0

20、16.465.264.149-.002-.002居民消费价格指数-.314.599.666.298-.091-.051-.007.001商品零售价格指数-.397.721-.006-.131.552.029.013.000货物周转量.761-.181.458-.380-.005.185.017-.004工业总产值.823.540-.116.020-.042.019-.109.058Undefined error #11401 - Cannot open text file "F:SPSSspsslangenspss.err": No such file or direa.

21、8 components extracted.各主成分的贡献率分别为46.761%，29.926%，9.231%，6.006%，5.466%，1.776%，0.745%，0.09%.前三个主成分的累计贡献率为85.918%.y1=0.814x1+0.766x2+0.785x3+0.604x4-0.314x5-0.397x6+0.761x7+0.823x8y2=0.556x1-0.493x2+0.558x3-0.572x4+0.599x5+0.721x6-0.181x7+0.540x8(2)本相关系数矩阵出发做因子分析，提取三个公共因子F1，F2，F3，说明每个公共因子各由哪些指标解释，并解释每

22、个公共因子的具体意义。1.求出三个公共因子F1，F2，F3的表达式。Analyze-data-reduction-factor将八个成分全部选入variables，extraction-extract-number of factors-3,descriptives-correlation matrix- coefficients, rotation-method- varimax, scores-save as variables,display factor score coefficient matrix, okComponent Score Coefficient MatrixComp

23、onent123地区生产总值.341-.075-.062居民消费水平-.031.380.092基本建设投资.343-.097-.089职工平均工资-.036.258-.125居民消费价格指数-.085.220.910商品零售价格指数.114-.254.157货物周转量-.021.468.460工业总产值.339-.069-.065Undefined error #11401 - Cannot open text file "F:SPSSspsslangenspss.err": No such file or dire Undefined error #11408 - Can

24、not open text file "F:SPSSspsslangenspss.err": No such file or direF1=0.341x1-0.031x2+0.343x3-0.036x4-0.085x5+0.114x6-0.021x7+0.339x82.根据三个公共因子F1，F2，F3的得分，对31个省市自治区进行分层聚类分析，要求样本间用欧氏平方距离，类间用类内平均连接法，如果聚为4类，写出每一类成员。Analyze-classify-hierarchical cluster,F1.F2.F3 to variables,地区 to label cases

25、by, statistics-cluster member ship-single solution-number of cluster-4. method-cluster method-median clustering,save- cluster member ship-single solution-number of cluster-4.ok 分类在表的最后一列可以读出。五、表B1给出了煤净化过程的一组数据，Y为净化后煤溶液中所含杂质的重量，这是衡量净化效率的指标，X1表示输入净化过程的溶液所含的煤与杂质的比，X2是溶液的PH值，X3是溶液的流量。假设Y与，和之间满足线性回归关系 其中

26、独立同分布于.(1) 求回归系数的最小二乘估计值和误差方差的估计值，写出回归方程并对回归系数作解释；analyze-regression-linear,y to dependent,x1 x2 x3to independent ,statistics-confidence intervals, save-unstandardized. Prediction individual-individual .ok CoefficientsaModelUnstandardized CoefficientsStandardized CoefficientstSig.95% Confidence Inte

27、rval for BBStd. ErrorBetaLower BoundUpper Bound1(Constant)397.08762.7576.327.000252.370541.805x1-110.75014.762-.841-7.502.000-144.792-76.708x215.5834.921.3553.167.0134.23626.931x3-.058.026-.255-2.274.053-.117.001a. Dependent Variable: yANOVAbModelSum of SquaresdfMean SquareFSig.1Regression31156.0243

28、10385.34123.827.000aResidual3486.8928435.862Total34642.91711a. Predictors: (Constant), x3, x2, x1b. Dependent Variable: y回归系数的最小二乘估计值和误差方差的估计值分别为:397.087,-110.75,15.583,-0.058和435.862y=-110.750*x1+15.583*x2-0.058*x3+397.087回归系数解释：397.087可理解为杂质的基本重量，当PH值和溶液流量固定时，输入净化过程的溶液所含的煤与杂质的比 每提高一个单位，杂质的重量 Y将减少1

29、10.75个单位；当输入净化过程的溶液所含的煤与杂质的比和溶液流量固定时，PH值每提高一个单位，杂质的重量Y将增加15.583个单位；当输入净化过程的溶液所含的煤与杂质的比和PH值固定时，溶液流量每提高一个单位，杂质的重量Y将减少0.058个单位。(2)求出方差分析表，解释对线性回归关系显著性检验的结果.求复相关系数的平方的值并解释其意义；ANOVAbModelSum of SquaresdfMean SquareFSig.1Regression31156.024310385.34123.827.000aResidual3486.8928435.862Total34642.91711a. Pr

30、edictors: (Constant), x3, x2, x1b. Dependent Variable: yModel SummaryModelRR SquareAdjusted R SquareStd. Error of the Estimate1.948a.899.86220.87730a. Predictors: (Constant), x3, x2, x1由于P值=0.000<0.05，所以回归关系显著.值=0.899，说明Y与，之间的线性回归关系是显著的(3)分别求，和的置信度为的置信区间；coefficients的后面部分，和的置信度为的置信区间分别为（-144.792，

31、-76.708），（4.236，26.931），（-0.117，0.001）(4)对，分别检验， 和对Y的影响是否显著；由于系数，对应的检验P值分别为0.000，0.013都小于0.05，所以和 对Y的影响是显著的.而对应的检验P值为0.053大于0.05，所以对Y的影响是不显著的。(5)若有，的值，求Y的预测值及置信度为0.95的置信区间.Y的预测值及置信度为0.95的置信区间分别为：218.64484和（166.93687，270.35282）在数据表中直接可以看见六、考察四种不同催化剂对某一化工产品得率的影响，在四种不同催化剂下分别做了6次实验，得数据如表B2所示.假定各种催化剂下产品的

32、得率服从同方差的正态分布，试在下，检验四种不同催化剂对该化工产品的得率有无显著影响.要写出方差分析表。方差分析表:Analyzecompare means -one-way anova,x to dependent list,a to factor ,okANOVAxSum of SquaresdfMean SquareFSig.Between Groups.0063.0021.306.300Within Groups.03020.001Total.03623由于检验P值=0.300>0.05，所以认为四种不同催化剂对该化工产品的得率在水平0.05下无显著差异。 七、为了研制一种治疗枯草

33、热病的药物，将两种成分（A和B）各按三种不同剂量（低、中、高）混合，将36位自愿受试患者随机分为9组，每组4人服用各种剂量混合下的药物，记录其病情缓解的时间（单位：小时）数据如表B3所示.（1）假设所给数据服从方差分析模型，建立方差分析表，A与B的交互效应在下是否显著？B3.0.Analyze-general linear model-univariate,x to dependent variable,a and b to fixed factor, okTests of Between-Subjects EffectsDependent Variable:xSourceType III S

34、um of SquaresdfMean SquareFSig.Corrected Model373.105a846.638774.910.0001857.61011857.6103.086E4.000a220.0202110.0101.828E3.000b123.660261.8301.027E3.000a * b29.42547.356122.227.000Error1.62527.060Total2232.34036Corrected Total374.73035a. R Squared = .996 (Adjusted R Squared = .994)交互效应检验P值=0.000<

35、;0.05，所以成分 (A)与成分(B)之间的交互效应是显著的（2）若A与B 的交互效应显著，分别就A的各水平，给出在B的各水平上的均值的置信度为0.95 的置信区间以及两两之差的置信度不小于0.95的Bonferroni同时置信区间.B3.1.Analyze-general linear model-univariate,x to dependent variable,a to fixed factor,post hoc-a to post hoc tests for, bonferroni,options-a to display means for.okbDependent Variab

36、le:xbMeanStd. Error95% Confidence IntervalLower BoundUpper Bound12.475.1102.2262.72424.600.1104.3514.84934.575.1104.3264.824Multiple ComparisonsxBonferroni(I) b(J) bMean Difference (I-J)Std. ErrorSig.95% Confidence IntervalLower BoundUpper Bound12-2.1250*.15546.000-2.5810-1.66903-2.1000*.15546.000-2

37、.5560-1.6440212.1250*.15546.0001.66902.58103.0250.155461.000-.4310.4810312.1000*.15546.0001.64402.55602-.0250.155461.000-.4810.4310Based on observed means. The error term is Mean Square(Error) = .048.*. The mean difference is significant at the .05 level.固定成分(A)的水平，的置信度为0.95的置信区间分别为(2.226,2.724),(4.

38、351,4.849),(4.326,4.824);的置信度不小于0.95的Bonferroni同时置信区间分别为（-2.581,-1.669）,（-2.556,-1.644）,（-0.431,0.481）B3.2.Analyze-general linear model-univariate,x to dependent variable,a to fixed factor,post hoc-a to post hoc tests for, bonferroni,options-a to display means for.okbDependent Variable:xbMeanStd. Er

39、ror95% Confidence IntervalLower BoundUpper Bound15.450.1275.1625.73828.925.1278.6379.21339.125.1278.8379.413Multiple ComparisonsxBonferroni(I) b(J) bMean Difference (I-J)Std. ErrorSig.95% Confidence IntervalLower BoundUpper Bound12-3.4750*.18028.000-4.0038-2.94623-3.6750*.18028.000-4.2038-3.1462213.

40、4750*.18028.0002.94624.00383-.2000.18028.888-.7288.3288313.6750*.18028.0003.14624.20382.2000.18028.888-.3288.7288Based on observed means. The error term is Mean Square(Error) = .065.*. The mean difference is significant at the .05 level.固定成分(A)的水平，的置信度为0.95的置信区间分别为(5.162,5.738),(8.637,9.213),(8.837,

41、9.413)；的置信度不小于0.95的Bonferroni同时置信区间分别为（-4.0038,-2.9462）,（-4.2038,-3.1462）,（-0.7288,0.3288）B3.3.Analyze-general linear model-univariate,x to dependent variable,a to fixed factor,post hoc-a to post hoc tests for, bonferroni,options-a to display means for.okbDependent Variable:xbMeanStd. Error95% Confi

42、dence IntervalLower BoundUpper Bound15.975.1305.6826.268210.275.1309.98210.568313.250.13012.95713.543Multiple ComparisonsxBonferroni(I) b(J) bMean Difference (I-J)Std. ErrorSig.95% Confidence IntervalLower BoundUpper Bound12-4.3000*.18333.000-4.8378-3.76223-7.2750*.18333.000-7.8128-6.7372214.3000*.1

43、8333.0003.76224.83783-2.9750*.18333.000-3.5128-2.4372317.2750*.18333.0006.73727.812822.9750*.18333.0002.43723.5128Based on observed means. The error term is Mean Square(Error) = .067.*. The mean difference is significant at the .05 level.固定成分(A)的水平，的置信度为0.95的置信区间分别为(5.682,6.268),(9.982,10.568),(12.9

44、57,13.543);的置信度不小于0.95的Bonferroni同时置信区间分别为（-4.8378,-3.7622）,（-7.8128,-6.7372）,（-3.5128,-2.4372）. 八、表B4给出了1991年我国30个省、区、市城镇居民的月平均消费数据，所考察的八个指标如下（单位均为元/人）：人均粮食支出；：人均副食支出；：人均烟酒茶支出；人均其他副食支出； ：人均衣着商品支出；：人均日用品支出；：人均燃料支出；：人均非商品支出（1）从出发做主成分分析，求各主成分的贡献率及前两个主成分的累计贡献率； Analyze-data-reduction-factor将八个成分全部选入var

45、iables，extraction-extract-number of factors-2,okTotal Variance ExplainedComponentInitial EigenvaluesExtraction Sums of Squared LoadingsTotal% of VarianceCumulative %Total% of VarianceCumulative %13.09638.70438.7043.09638.70438.70422.36729.59068.2942.36729.59068.2943.92011.50079.7944.7068.82488.6185.

46、4986.23194.8486.2302.87497.7227.1311.63599.3578.051.643100.000Extraction Method: Principal Component Analysis.第一，第二,第八主成分的贡献率分别为：38.704%，29.59%，11.5%，8.824%，6.231%，2.874%，1.635%，0.635%. 前两个主成分的累计贡献率68.294%.(2)求出前两个主成分并解释其意义.Component MatrixaComponent12x1.439-.371x2.914-.058x3-.033.731x4.447.828x5.038.885x6.867.207x7.558-.401x8.896-.134Undefined error #11401 - Cannot open text file "C:Program Files