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Y =a exlnY=ln a+BX客运量变化趋势35004000量运客O O52O O O2y = 1E-149e0运客O O52O O O2y = 1E-

2、149e0.176x019761978198019821984198619881990 指麴921994年份筝运回归参数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tYY19782311979298671980343451981401581982445441983391-54198455416319857441901986997253198713103131988144213219891283-15919901660377199121785181992288670819933383497截距10T49表明，当年份为0时，客运量

3、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ttY197812311979229829.0%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%）截距

4、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。用该模型可以进行预测:预测 1994 年客运量：（1） Y = 187.42e0.i76x = 187.42e0.i76e = 8.225（2） Y =3734.43 万人。3、寻找影响因素（1）受国民收入（x1）的影响量运客050001000015000200002500030000国民收入4000客运量与国民收入的关系o o o o o o Q o o o o o o O 量运客050001000015000200002500030000国民收入4000客运量与国民收入的关系o o o o o o Q

5、o o o o o o O 5 0 5 0 5 0 5 3 3 2 2 1 1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400035003000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400035003000量 2500 运 2000 客0客运量与消费额的关系0500010000 15000 20000消费额（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y0.0191x - 797.29铁路客运量民航客运量与铁路客运量的关系y0.0191x - 797.29铁路客运量匚关。结论

6、：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）的影响量运客航民民航客运量与来华旅游人数的关系O O O 3O O O 4OO5 2OO5 3o o o o O o o o O 0 5 0 5 0 1 1O O O量运客航民民航客运量与来华旅游人数的关系O O O 3O O O 4OO5 2OO5 3o o o o O o o o O 0 5 0 5 0 1 1O O O2O O O 3O O O 4O O O 5来华旅游人数、建立多元回归方程唇运量丫 指数客运Y人=442.91 + 0.355166X1 -

7、 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（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 SquareO.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

8、= 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5 1381913227638261140.222残差10 24239.372423.937总计15 13843372给定 a =0.05，查 F0.05(k, n-k-1)= F0.05(5, 16-5-1)= F0.05(5, 10)= 3.33F =1140.22 F005(5, 10)= 3.33方差分析表明，以上回归方程高度显著，说明XX2、X3、X4、X5整体上 对民航客运量有显著的影响。8、t检验Coefficients标准误差t StatP-valueIntercept442.9106174.26

9、492.5415930.029283X10.3551660.0845044.2029580.00182X2-0.563310.124402-4.528160.001094X3-0.007150.002018-3.543180.005328X421.57944.0065025.3860960.000307X50.4340210.051088.4969286.92E-06YA = 442.91 + 0.355166X0.56331X20.00715X3+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

10、分析X1X2X3X4X5YX11X20.9989581X30.2512760.2822781X40.9836090.9778040.207221X50.9301670.9422930.4967990.8817981Y0.9894680.985490.2201360.9870920.9242211可见，X3对Y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dfSSMSFSi

11、gnificance F回归分析4137887023447176693.60053.91E-13残差1154669.74969.972总计1513843372Coefficients标准误差t StatP-valueLower 95%Upper 95% 下限 95.0%_Intercept-153.9363.93406-2.407640.03476-294.648-13.2119-294.648X10.5089380.1038254.9019090.000470.2804220.7374550.280422X2-0.75420.160562-4.697260.000653-1.1076-0.4

12、0081-1.1076X415.980475.2718913.0312590.0114244.37710827.583834.377108X50.3470770.0641495.4104710.0002130.2058860.4882690.205886RESIDUAL OUTPUT观测值预测Y残差标准残差1254.7829-23.7829-0.393952297.13480.8652440.0143323324.16818.832040.3119394359.05641.944040.6947725356.695688.304441.4626996418.8283-27.8283-0.460

13、967639.3119-85.3119-1.413138800.9855-56.9855-0.943929968.744728.25530.468028101324.994-14.9945-0.24837111455.114-13.1144-0.21723121364.756-81.756-1.35423131641.81618.184030.301205142050.913127.08672.105098152831.28654.714390.906304163457.413-74.4125-1.23259所得回归方程为:YA = 一 153.89 + 0.50904X1 -0.5436X2

14、 +15.97773X4+0.34712X5(2.41)(4.90)(4.70)(3.03)(5.41)相关距阵：X1X2X4X5YX11X20.9989581X40.9836090.9778041X50.9301670.9422930.8817981Y0.9894680.985490.9870920.9242211偏相关系数都很高。预测：给定 X1=23872 X2=14987 X4= 92.09X5 = 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。=70

15、.498给出置信水平为95.45%，则有预测区间为 丫土2。= 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）与国民收入各）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0.9940470.9881290.9940470.9881290.985162R SquareAdjusted R Square标准误差117.0216观测值1

16、6方差分析dfSSMSFSignificance F回归分析3136790434559681332.96818.16E-12残差12164328.613694.05总计1513843372Coefficients标准误差t StatP-valueLower 95%Upper 95% 下限 95.0%Intercept-369.48173.89545-5.000060.000309-530.486-208.477-530.486X10.0328830.0374220.8787150.39681-0.048650.114418-0.04865X424.677458.1935133.0118280.

17、0108266.82532442.529596.825324X50.1372040.0764081.7956870.097748-0.029270.303682-0.02927原有 Y = 一 153.89 + 0.50904X1-0.5436X2 +15.97773X4+0.34712X5(5.00)(4.90)(4.70)(3.03)(5.41)新建YA = -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Y与X4和X5的回归方程，并分析。SUMMARY OUTPUT回归统

18、计Multiple R0.993663R Square0.987366Adjusted R Square0.985422标准误差115.9915观测值16方差分析dfSSMSF Significance F回归分析2 136684696834235 507.96964.57E-13残差13 174902.3 13454.02总计15 13843372Coefficients标准误差t StatP-valueLower 95%Upper 95% 下限 95.0%_Intercept-410.07457.16828-7.17317.23E-06-533.579-286.569-533.579X43

19、1.47132.68842411.706232.81E-0825.6633137.2792825.66331X50.1868020.0510463.6595060.0028840.0765250.297080.076525RESIDUAL 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