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lnY=ln % + B X客运量变化趋势年份（客运量Y）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tYY1

2、978231一1979298671980343451981401581982445441983391-54198455416319857441901986997253198713103131988144213219891283-15919901660377199121785181992288670819933383497截距10149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ttY197812311979229829.0%1980334315.1%1981440116.9%1982544511.0%

3、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 = 187.42e0.176X = 187.42e17 = 8.225(2) Y =373

4、4.43 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000000000 OOOOOOOO 050505054 3 3 2 2 1 150001000015000200002500030000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OOOOOOOOO0 54 3 3 2 2 1 10 5 0 5 0 5量运客(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 - 797.29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）有关系民航客

5、运量与民航航线里程的关系4000020406080100民航航线里程5003500oo oo O oo oo O 5 0 5 0 3 2 2 1 1 量运存航民120（5）受来华旅游入境人数（X5）的影响客运量Y1客运4、建立多元回归方程丫八=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（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,

6、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 F0.05（k, n-k-1）= Fo.o5（5, 16-5-1）= Fo.o5（5, 10）= 3.

7、33F =1140.22 > F0.05（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Coefficients标准误差t StatP-valueIntercept442.9106174.26492.5415930.029283X10.3551660.0845044.2029580.00182X2-0.563310.124402-4.528160.001094X3-0.007150.002018-3.543180.005328X421.57944.0065025.3860960.000307X50

8、.4340210.051088.4969286.92E-06Y = 442.91 + 0.355166X 1 0.56331X20.00715X3 +21.5794X4+0.434021X5(2.54) (4.20)(4.53)(3.54)(5.386)(8.497)结论：通过t检验9、偏相关分析X1X2X3X4X5YX11X20.9989581X30.2512760.2822781X40.9836090.9778040.207221X50.9301670.9422930.4967990.8817981Y0.9894680.985490.2201360.9870920.9242211可见，X3

9、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70.4980316方差分析dfSSMSFSignificance F回归分析4137887023447176693.60053.91E-13残差1154669.74969.9721513843372Coefficients标准误差t StatP-valueLower 95%Upper 95%下限95.0% .Intercept-153.9363.934

10、06-2.407640.03476-294.648-13.2119-294.648X10.5089380.1038254.9019090.000470.2804220.7374550.280422X2-0.75420.160562-4.697260.000653-1.1076-0.40081-1.1076X415.980475.2718913.0312590.0114244.37710827.583834.377108X50.3470770.0641495.4104710.0002130.2058860.4882690.205886RESIDUAL OUTPUT观测值预测Y 残差标准残差125

11、4.7829-23.7829-0.393952297.13480.8652440.0143323324.16818.832040.3119394359.05641.944040.6947725356.695688.304441.4626996418.8283-27.8283-0.460967639.3119-85.3119-1.413138800.9855-56.9855-0.943929968.744728.25530.468028101324.994-14.9945-0.24837111455.114-13.1144-0.21723121364.756-81.756-1.354231316

12、41.81618.184030.301205142050.913127.08672.105098152831.28654.714390.906304163457.413-74.4125-1.23259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:X1X2X4X5YX11X20.9989581X40.9836090.9778041X50.9301670.9422930.8817981Y0.9894680.985490.9870920.9242211偏

13、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Y±2（r = 3502.49±2X70.498 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（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。

14、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 观测值117.021616方差分析dfSSMSFSignificance F回归分析3136790434559681332.96818.16E-12残差12164328.613694.051513843372Coefficientst StatP-valueLower 95%Upper 95%95.0%Intercept

15、-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)(4.90)(4.70)(3.03)(5.41)原有 YA = _ 153.89 + 0.50904X1 0.5436X2 +15

16、.97773X4+0.34712X5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回归分析dfSSMSF Significance F2136684696834235507.96964.57E-13Multiple R0.993663R Square0.987366Adjusted R Square0.985422标准误差115.991516方差分析残差13174902.313454.02总计151

17、3843372Coefficientst StatP-valueLower 95%Upper 95%95.0% .Intercept-410.07457.16828-7.17317.23E-06-533.579-286.569-533.579X431.47132.68842411.706232.81E-0825.6633137.2792825.66331X50.1868020.0510463.6595060.0028840.0765250.297080.076525RESIDUAL OUTPUT观测值预测Y 残差标准残差192.3299138.67011.2841942171.9966126.

18、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)(11.71)(3.6