1、多元统计习题程序第一章一、均值向量、协方差阵、离差阵例2-1 行业公司简称净资产收益率%总资产报酬率%资产负债率%总资产周转率流动资产周转率已获利息倍数销售增长率%资本积累率%电力、煤气及水的生产和供应业深能源16.8512.35 42.32 0.37 1.78 7.18 45.73 54.54 深南电2215.30 46.51 0.76 1.77 15.67 48.11 19.41 富龙热力8.977.98 30.56 0.17 0.58 10.43 17.80 9.44 穗恒运10.258.99 40.44 0.46 2.46 5.06 11.06 1.09 粤电力20.8120.00 3
2、5.87 0.43 1.25 34.89 24.77 12.67 韶能股份8.867.52 27.59 0.24 0.84 20.59 -3.50 54.02 惠天热电10.987.94 49.30 0.36 0.69 12.43 16.88 3.52 原水股份8.858.88 36.20 0.13 0.41 8.53 -11.49 2.44 大连热电9.037.41 46.89 0.28 0.79 6.86 16.23 -1.52 龙电股份12.078.70 16.81 0.28 0.68 29.75 4.11 63.06 华银电力6.856.12 41.93 0.24 0.65 4.38
3、11.20 3.80 房地行业长春经开9.8510.50 31.23 0.34 0.40 17.13 18.05 7.18 兴业房产1.071.52 66.91 0.21 0.24 1.53 -31.93 1.08 金丰投资19.447.01 73.34 0.26 0.30 7.02 71.22 12.73 新 黄 浦7.615.92 39.64 0.16 0.17 4.20 14.77 7.91 浦东金桥4.243.99 37.30 0.20 0.25 3.98 -9.24 4.69 外 高 桥1.6731.92 49.05 0.03 0.05 1.06 -21.74 0.24 中华企业8.
4、786.28 57.42 0.17 0.19 3.58 75.29 2.93 渝开发0.22.24 63.40 0.09 0.15 1.07 -12.56 0.29 辽 房 天8.123.98 69.10 0.10 0.72 2.65 -35.83 3.16 粤宏远0.421.16 37.42 0.09 0.15 1.59 19.18 0.43 ST中福5.176.62 65.48 0.16 0.21 1.33 -19.91 23.74 倍特高新0.722.76 65.39 0.30 0.42 1.24 8.40 0.70 三木集团5.994.53 65.17 0.74 0.88 4.14 7
5、5.36 0.87 寰岛实业0.420.20 24.03 0.02 0.03 -8.18 -71.33 0.42 中 关 村9.324.48 67.76 0.32 0.37 16.42 -29.42 4.09 信息技术业中兴通讯18.7811.09 69.15 0.93 1.08 4.79 80.80 23.27 长城电脑14.949.48 45.53 1.14 1.85 9.51 34.47 35.93 青鸟华光9.7888.70 36.67 0.28 0.39 13.11 28.36 7.87 清华同方15.919.08 34.19 0.85 1.19 15.61 98.92 95.66
6、永鼎光缆9.48.67 32.75 0.79 1.25 13.49 41.75 6.33 宏图高科14.577.96 65.86 0.76 0.94 3.95 54.45 15.71 海星科技4.063.35 36.49 0.48 0.60 4.64 -16.28 1.69 方正科技27.4816.69 57.13 2.51 2.87 7.40 63.27 32.02 复华实业5.584.10 44.24 0.28 0.41 3.77 12.92 2.30 1向量分析：analyze-descriptive statistics-descriptiwes-optionsvariance.得如下
7、表：Descriptive StatisticsMeanStd. DeviationN净资产收益率9.696.70835总资产报酬率7.244.36935资产负债率47.1215.20035总资产周转率.43.45635流动资产周转率.77.68135已获利息倍数8.318.42335销售增长率18.0038.03235资本积累率14.6821.86735Correlations净资产收益率总资产报酬率资产负债率总资产周转率流动资产周转率已获利息倍数销售增长率资本积累率净资产收益率Pearson Correlation1.891*.054.688*.721*.518*.651*.485*Sig
8、. (2-tailed).000.757.000.000.001.000.003Sum of Squares and Cross-products1530.003888.140188.40171.612112.056995.3495646.6032420.424Covariance45.00026.1225.5412.1063.29629.275166.07771.189N3535353535353535总资产报酬率Pearson Correlation.891*1-.158.572*.708*.665*.528*.405*Sig. (2-tailed).000.364.000.000.000
9、.001.016Sum of Squares and Cross-products888.140648.891-357.16938.77071.585831.4642985.0211316.995Covariance26.12219.085-10.5051.1402.10524.45587.79538.735N3535353535353535资产负债率Pearson Correlation.054-.1581.143-.043-.407*.161-.281Sig. (2-tailed).757.364.412.805.015.356.102Sum of Squares and Cross-pr
10、oducts188.401-357.1697855.26133.764-15.200-1770.1543162.159-3171.244Covariance5.541-10.505231.037.993-.447-52.06393.005-93.272N3535353535353535总资产周转率Pearson Correlation.688*.572*.1431.782*.142.547*.342*Sig. (2-tailed).000.000.412.000.417.001.044Sum of Squares and Cross-products71.61238.77033.7647.08
11、18.26718.524323.012115.963Covariance2.1061.140.993.208.243.5459.5003.411N3535353535353535流动资产周转率Pearson Correlation.721*.708*-.043.782*1.272.452*.389*Sig. (2-tailed).000.000.805.000.114.006.021Sum of Squares and Cross-products112.05671.585-15.2008.26715.76853.024398.330196.981Covariance3.2962.105-.4
12、47.243.4641.56011.7165.794N3535353535353535已获利息倍数Pearson Correlation.518*.665*-.407*.142.2721.228.458*Sig. (2-tailed).001.000.015.417.114.189.006Sum of Squares and Cross-products995.349831.464-1770.15418.52453.0242412.3522478.0902868.946Covariance29.27524.455-52.063.5451.56070.95272.88584.381N353535
13、3535353535销售增长率Pearson Correlation.651*.528*.161.547*.452*.2281.402*Sig. (2-tailed).000.001.356.001.006.189.017Sum of Squares and Cross-products5646.6032985.0213162.159323.012398.3302478.09049178.72611379.256Covariance166.07787.79593.0059.50011.71672.8851446.433334.684N3535353535353535资本积累率Pearson C
14、orrelation.485*.405*-.281.342*.389*.458*.402*1Sig. (2-tailed).003.016.102.044.021.006.017Sum of Squares and Cross-products2420.4241316.995-3171.244115.963196.9812868.94611379.25616257.569Covariance71.18938.735-93.2723.4115.79484.381334.684478.164N3535353535353535*. Correlation is significant at the
15、0.01 level (2-tailed).*. Correlation is significant at the 0.05 level (2-tailed).2方差阵为： 3差阵为： 第二章Tests of NormalityKolmogorov-SmirnovaShapiro-WilkStatisticdfSig.StatisticdfSig.净资产收益率.15235.039.94435.077总资产报酬率.13735.095.94235.064资产负债率.14435.065.93935.052总资产周转率.23535.000.68335.000流动资产周转率.15935.026.850
16、35.000已获利息倍数.17235.011.88035.001销售增长率.11635.200*.98235.836资本积累率.25235.000.69535.000a. Lilliefors Significance Correction*. This is a lower bound of the true significance.此表给出了对每个变量进行正态性检验的结果，由sig.值可以看到净资产收益率、总资产报酬率、资产负债率、销售增长率的P值均大于0.05，则接受原假设，显然遵从正态分布。我们只对这四个指标进行比较。多元正态分布有关均值与方差的检验：analyzegeneral l
17、inear modelmultivariate,将净资产收益率、总资产报酬率、资产负债率、销售增长率这四个指标选入dependent列表框，将行业指标选入fixde factor框，点击OK运行，则输出结果：Between-Subjects FactorsN行业电力、煤11房地行业15信息技术9Multivariate TestscEffectValueFHypothesis dfError dfSig.InterceptPillais Trace.9471.303E2a4.00029.000.000Wilks Lambda.0531.303E2a4.00029.000.000Hotellin
18、gs Trace17.9691.303E2a4.00029.000.000Roys Largest Root17.9691.303E2a4.00029.000.000行业Pillais Trace.7124.1498.00060.000.001Wilks Lambda.3884.387a8.00058.000.000Hotellings Trace1.3174.6118.00056.000.000Roys Largest Root1.0778.079b4.00030.000.000a. Exact statisticb. The statistic is an upper bound on F
19、 that yields a lower bound on the significance level.c. Design: Intercept + 行业由Sig.可以看到，三个行业的运营能力（净资产收益率，总资产报酬率，资产负债率，销售增长率这四个指标的整体来看）是有显著差别的。也就是说，不同行业的运营能力是不同的。Tests of Between-Subjects EffectsSourceDependent VariableType III Sum of SquaresdfMean SquareFSig.Corrected Model净资产收益率458.258a2229.1296.84
20、1.003总资产报酬率250.101b2125.05010.034.000资产负债率1728.665c2864.3334.515.019销售增长率9467.268d24733.6343.814.033Intercept净资产收益率3633.32913633.329108.483.000总资产报酬率1987.13211987.132159.453.000资产负债率71640.788171640.788374.189.000销售增长率15289.807115289.80712.321.001行业净资产收益率458.2582229.1296.841.003总资产报酬率250.1012125.0501
21、0.034.000资产负债率1728.6652864.3334.515.019销售增长率9467.26824733.6343.814.033Error净资产收益率1071.7453233.492总资产报酬率398.7903212.462资产负债率6126.59632191.456销售增长率39711.458321240.983Total净资产收益率4814.44835总资产报酬率2483.79735资产负债率85553.31435销售增长率60514.04635Corrected Total净资产收益率1530.00334总资产报酬率648.89134资产负债率7855.26134销售增长率4
22、9178.72634a. R Squared = .300 (Adjusted R Squared = .256)b. R Squared = .385 (Adjusted R Squared = .347)c. R Squared = .220 (Adjusted R Squared = .171)d. R Squared = .193 (Adjusted R Squared = .142)这个表给出了每个财务指标的分析结果，同时给出了每个财务指标的方差来源，包括校正模型，截距，主效应及总的方差来源，还给出了自由度、均方、F统计量及sig值。第三列给出了用TYPE3方法计算的偏差平方和，可以
23、根据方差分析中是否存在交互效应及设计是否平衡等不同情况选用不同的计算方法。此处只有一个因素，即行业。由表看出，四个sig值分别是0.003、0.000、0.019、0.033。说明三个行业在以上四个财务指标上存在显著差别。在0.05水平下，第一行业与第三行业所有财务指标均无明显差别，第二行业与第三行业资产负债率有明显差别，与其他财务指标没有显著差别。Multivariate Test ResultsValueFHypothesis dfError dfSig.Pillais trace.7124.1498.00060.000.001Wilks lambda.3884.387a8.00058.0
24、00.000Hotellings trace1.3174.6118.00056.000.000Roys largest root1.0778.079b4.00030.000.000a. Exact statisticb. The statistic is an upper bound on F that yields a lower bound on the significance level.Univariate Test ResultsSourceDependent VariableSum of SquaresdfMean SquareFSig.Contrast净资产收益率458.2582229.1296.841.003总资产报酬率250.1012125.05010.034.000资产负债率1728.6652864.3334.515.019销售增长率9467.26824733.6343.814.033Error净资产收益率1071.7453233.492总资产报酬率398.7903212.462资产负债率6126.59632191.456销售增长率39711.458321240.983
