统计分析方法案例

1、中国民航客运量变化趋势及其原因1、统计数据的收集与汇总1978-1993年中国民航客运量情况年份客运量（万人）tY197823119792981980343198140119824451983391198455419857441986997198713101988144219891283199016601991217819922886199333832、了解变化趋势（1）绘制散点图（2）配合趋势线一一指数趋势方程Ye3InY=1 n a + p X客运量变化趋势o O o O5 O3 3502002150量运客99990运Y)(量889份年889897T769 o o O 1 o OO 5回归

2、参数0.176表明，客运量的增量每年约按17.6%速度增长1979年至1993年民客运量变动情况年份客运量年增长量tY Y19782311979298671980343451981401581982445441983391-54198455416319857441901986997253198713103131988144213219891283-15919901660377199121785181992288670819933383497截距10_149表明，当年份为0时，客运量达到的水平，无实际意义。应将时 间变量转化一下。1979年至1993年民客运量变动情况年份时间变量客运量年增长率t

3、tY197812311979229829.0%1980334315.1%1981440116.9%1982544511.0%19836391-12.1%1984755441.7%1985874434.3%1986999734.0%198710131031.4%198811144210.1%1989121283-11.0%199013166029.4%199114217831.2%199215288632.5%199316338317.2%合计（310.6%）平均（20.70%）民航客运量变动趋势时间变量截距187.42表明，当年份为0 （1977年）时，客运量达到的水平（对数）， 有实际意义。

4、用该模型可以进行预测:预测 1994 年客运量：(1) Y = 187.42e0.176X = 187.42e= 8.225(2) Y =3734.43 万人。3、寻找影响因素(1)受国民收入(X1)的影响客运量与国民收入的关系量运客OOOOOOOOO OOOOOOOO 050 5 0 5 0 5 4 3 3 2 2 1150001000015000200002500030000国民收入用国民收入也能预测民航客运量，但角度与时间变量不同(2)与消费额(X2)的关系客运量与消费额的关系运 客(3) 受铁路客运量(X3)的影响民航客运量与铁路客运量的关系y = 0.0191X - 797.29R2

5、 = 0.0485结论：可决系数太小，表明铁路客运量（X3）与民航客运量（Y）无显著相 关。（4）与民航航线里程（X4）有关系（5）受来华旅游入境人数（X5）的影响500050002 2 11量运客航民民航客运量与来华旅游人数的关系10002000300040005000来华旅游人数冗00003353050客运4、建立多元回归方程YA = 442.91 + 0.355166X1 0.56331X2 0.00715X3 +21.5794X4+0.434021X5（国民收入）（消费额）（铁路客运量）（民航航线里程数）（境外来华人数）对偏回归系数进行经济关系上的解释。其中，消费额（X2）与民航客运量

6、（Y）的偏回归的关系有问题，方向应一致。铁路客运量（X3）的偏回归系数接近于0,为0.00715,表明二者关系微弱。5、拟合优度检验回归统计Multiple R0.999124R Square0.998249Adjusted R Square0.997374标准误差49.23349观测值16复相关系数R=0.999124可决系数R2= 0.998249修正后的可决系数 R2 = 0.99737结论：整体上通过检验6、方差分析方差分析dfSSMSF回归分析51381913227638261140.222残差1024239.372423.937总计1513843372给定a =0.05,查 Fo.

7、o5（k, n-k-1）= Fo.o5（5, 16-5-1）= Fo.o5（5, 10）= 3.33F =1140.22 > Fo.o5（5, 10）= 3.33方差分析表明，以上回归方程高度显著，说明X1、X2、X3、X4、X5整体上对民航客运量有显著的影响。8 t检验Coefficie nts标准误差t StatP-valueIn tercept442.9106174.26492.5415930.029283X10.3551660.0845044.2029580.00182X2-0.563310.124402-4.528160.001094X3-0.007150.002018-3.5

8、43180.005328X421.57944.0065025.3860960.000307X50.4340210.051088.4969286.92E-06Y = 442.91 + 0.355166X 1 0.56331X2 0.00715X3 +21.5794X4+0.434021X5(2.54)(4.20)(4.53)(3.54)(5.386)(8.497)结论：通过t检验9、偏相关分析X1X2X3X4X5YX11X20.9989581X30.2512760.2822781X40.9836090.9778040.207221X50.9301670.9422930.4967990.88179

9、81Y0.9894680.985490.2201360.9870920.9242211可见，X3对丫的影响不显著，因为其偏相关系数为 0.2201。10、剔除X3，重建回归方程。SUMMARY OUTPUT回归统计Multiple R0.998023R Square0.996051Adjusted R Square0.994615标准误差70.49803观测值16方差分析dfSSMSFSigni fica nee F回归分析4137887023447176693.60053.91E-13残差1154669.74969.972总计1513843372Coeffieie nts标准误差t Stat

10、P-valueLower 95%Upper 95%下限95.0% 上In tereept-153.9363.93406-2.407640.03476-294.648-13.2119-294.648X10.5089380.1038254.9019090.000470.2804220.7374550.280422X2-0.75420.160562-4.697260.000653-1.1076-0.40081-1.1076X415.980475.2718913.0312590.0114244.37710827.583834.377108X50.3470770.0641495.4104710.0002

11、130.2058860.4882690.205886RESIDUAL OUTPUT观测值预测Y残差标准残差1254.7829-23.7829-0.393952297.13480.8652440.0143323324.16818.832040.3119394359.05641.944040.6947725356.695688.304441.4626996418.8283-27.8283-0.460967639.3119-85.3119-1.413138800.9855-56.9855-0.943929968.744728.25530.468028101324.994-14.9945-0.2483

12、7111455.114-13.1144-0.21723121364.756-81.756-1.35423131641.81618.184030.301205142050.913127.08672.105098152831.28654.714390.906304163457.413-74.4125-1.23259所得回归方程为:YA = 153.89 + 0.50904X1 0.5436X2 +15.97773X4+0.34712X5(2.41)(4.90)(4.70)(3.03)(5.41)相关距阵:X1X2X4X5YX11X20.9989581X40.9836090.9778041X50.9

13、301670.9422930.8817981Y0.9894680.985490.9870920.9242211偏相关系数都很高预测：给定 X1=23872 X2 =14987 X4 = 92.09 X5 = 3856.8代入回归方程YA = 153.89 + 0.50904X1 0.5436X2 +15.97773X4+0.34712X5 = 3502.49区间估计：已知标准误差为（T =70.498给出置信水平为95.45%，则有预测区间为 丫 土2 c = 3502.49±2X 70.498 即3361.52, 3643.46 11、消除多重共线性的影响在自变量中，消费额（X2）

14、与国民收入（X1）之间存在高度相关性，使得消 费额与民航客运量之间的偏回归系数为负值，无法解释经济关系。应消除其中 一个自变量。由于国民收入的偏回归系数和t检验值都较高，所以决定剔除消费 额（X2），重新建立回归方程。SUMMARY OUTPUT回归统计0.9940470.9881290.985162Multiple RR SquareAdjusted R Square标准误差117.021616观测值方差分析dfSSMSFSigni fiea nee F回归分析3136790434559681332.96818.16E-12残差12164328.613694.05总计1513843372Co

15、effieie nts标准误差t StatP-valueLower 95%Upper 95%下限95.0%In tereept-369.48173.89545-5.000060.000309-530.486-208.477-530.486X10.0328830.0374220.8787150.39681-0.048650.114418-0.04865X424.677458.1935133.0118280.0108266.82532442.529596.825324X50.1372040.0764081.7956870.097748-0.029270.303682-0.02927(5.00)(4

16、.90)(4.70)(3.03)(5.41)原有 丫八= -153.89 + 0.50904X1 0.5436X2+15.97773X4+0.34712X5新建 丫八= 369.48 + 0.003288X1 +24.677X4+0.1372X5(2.41)(0.88)(3.01)(1.80)可见，X1未通过检验，应剔除。13、建立丫与X4和X5的回归方程，并分析SUMMARY OUTPUT回归统计Multiple R0.993663R Square0.987366Adjusted R Square0.985422标准误差115.9915观测值16方差分析dfSSMSFSigni fica n

17、ee F回归分析2136684696834235507.96964.57E-13残差总计13174902.313454.021513843372Coefficie nts标准误差t StatP-valueLower 95%Upper 95%下限95.0% 上In tercept-410.07457.16828-7.17317.23E-06-533.579-286.569-533.579X431.47132.68842411.706232.81E-0825.6633137.2792825.66331X50.1868020.0510463.6595060.0028840.0765250.29708

18、0.076525RESIDUAL OUTPUT观测值预测Y残差标准残差192.3299138.67011.2841942171.9966126.00341.166893311.084531.915480.2955624421.721-20.721-0.191895470.2909-25.2909-0.234216487.9661-96.9661-0.897987648.8914-94.8914-0.878778795.4352-51.4352-0.4763391036.814-39.8141-0.36871101317.016-7.01577-0.06497111358.3983.610220.774296121532.749-249.749-2.31287131697.888-37.8883-0.35088141972.594205.40611.902222152841.41144.588940.412929163389.423-6.42281-0.05948YA = 410.074 +31.4713X4+0.1868X5(7.17)(11.7