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1、计量经济学期中小论文为考察中国城镇居民2010年年总支出与食品（x1），衣着（x2），居住（x3），交通（x4）的关系。本文数据来源于中华人民共和国国家统计网，采用的数据为2010年我国31个省、市和自治区前三个季度城镇居民人均消费支出，建立了四项统计指标，分别为：食品，衣着，居住，交通。地区食品x1衣着x2居住x3交通x4总支出y北 京5561.541571.741286.322293.2316460.26天 津5005.091153.661528.281567.8713422.46河 北3155.41137.221097.411062.319086.72山 西2974.761137.711
2、250.87931.338806.55内蒙古3553.481616.561028.191191.710828.62辽 宁4378.141187.411270.951295.711231.48吉 林3307.141259.621285.28954.969729.06黑龙江3128.11217.04941.25749.058622.96上 海7108.621520.611646.193373.1919397.89江 苏4544.641166.911042.11357.9611977.54浙 江5522.561546.461333.692392.6315158.29安 徽3905.051010.61
3、988.12920.779524.03福 建5078.851105.311300.11777.0612501.13江 西3633.05969.58851.15872.578717.38山 东3699.421394.111247.041410.4511006.6河 南3079.821141.76963.59915.128837.46湖 北3996.271099.16914.26890.129477.51湖 南3970.421090.72960.82971.059945.53广 东5866.91975.061748.162623.0815527.97广 西4082.99772.28891.3313
4、76.039627.41海 南4226.9491.841106.391303.59408.49重 庆4418.341294.31096.821044.3611146.79四 川4255.481042.45819.281121.459679.14贵 州3597.94851.5836.54871.158349.22云 南4272.291026.5739.21216.469076.62西 藏4262.771011.82634.94966.748323.54陕 西3586.131047.611007.68967.529772.06甘 肃3183.791022.62846.26817.178308.62
5、青 海3315.94945.14802.73787.638192.58宁 夏3352.831178.881069.151096.329558.29新 疆3235.771245.02781.91003.898669.361. 建立模型我们建立简单的多元线性方程，经过eviews处理得到的结果见下表：VariableCoefficientStd. Errort-StatisticProb.C-1504.146746.7859-2.0141590.0544X11.2657340.2078226.0904830.0000X22.4974740.3571466.9928640.0000X32.25158
6、10.4458615.0499660.0000X41.3189540.3948073.3407530.0025R-squared0.980827Mean dependent var10657.15Adjusted R-squared0.977878S.D. dependent var2727.013S.E. of regression405.6042Akaike info criterion14.99532Sum squared resid4277385.Schwarz criterion15.22661Log likelihood-227.4275Hannan-Quinn criter.15
7、.07072F-statistic332.5241Durbin-Watson stat1.770723Prob(F-statistic)0.000000所以得到的回归结果为：.从回归估计的结果来看，模型的拟合较好。可决系数 ，表明城镇居民消费支出的变化的98.0827%可由食品（x1），衣着（x2），居住（x3），交通（x4）的变化来解释。在F检验的概率值为0.0000，说明通过了F检验，即模型建立的正确性。在t检验的概率值也在0.000-0.0025，说明各个自变量也通过了t检验。2. 异方差的问题及处理（1） 随机误差项散点图：从图中可以看出：resid2随着y变量的增大明显增大，这是随机
8、项存在异方差的初步判断。（2） 异方差检验-white检验检验见下表：Heteroskedasticity Test: WhiteF-statistic3.902397Prob. F(14,16)0.0055Obs*R-squared23.97784Prob. Chi-Square(14)0.0461Scaled explained SS25.82084Prob. Chi-Square(14)0.0273Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 05/27/14 Time: 15:33Sample: 1
9、 31Included observations: 31VariableCoefficientStd. Errort-StatisticProb.C3188788.3822354.0.8342470.4164X1522.85751567.0180.3336640.7430X12-0.5239650.280536-1.8677290.0802X1*X22.5317300.8453832.9947750.0086X1*X3-2.6292600.600363-4.3794530.0005X1*X43.0604930.9849503.1072570.0068X2-7137.1203289.733-2.
10、1695140.0454X220.9241740.5615601.6457240.1193X2*X3-1.8172121.754486-1.0357520.3157X2*X4-2.0710061.352329-1.5314360.1452X34706.1152460.7361.9124830.0739X320.6651171.1024320.6033180.5548X3*X45.0053331.8269072.7397850.0145X4-4945.7772527.072-1.9571180.0680X42-4.1492871.158645-3.5811530.0025图中检验结果是white
11、统计量w=Obs*R-squared=23.97784，它所达到的显著水平为0.0461小于0.05，应否定,表明原方程的残差有异方差。帕克检验法：（2）异方差的处理我们采用最小二乘法：方程出现了明显的异方差，我们采用white修正，修正结果见下图：White Heteroskedasticity-Consistent Standard Errors & CovarianceVariableCoefficientStd. Errort-StatisticProb.C-1504.146519.2333-2.8968590.0075X11.2657340.1651297.6651100.0000X
12、22.4974740.3130337.9783140.0000X32.2515810.4889824.6046320.0001X41.3189540.2558435.1553190.0000R-squared0.980827Mean dependent var10657.15Adjusted R-squared0.977878S.D. dependent var2727.013S.E. of regression405.6042Akaike info criterion14.99532Sum squared resid4277385.Schwarz criterion15.22661Log l
13、ikelihood-227.4275Hannan-Quinn criter.15.07072F-statistic332.5241Durbin-Watson stat1.770723Prob(F-statistic)0.000000经过white 处理后的方程表达式为：3. 自相关问题及处理（1） 由软件得到因变量的曲线和残差曲线图： 残差图：从散点图图中，我们无法判断出模型的随机误差项是否存在自相关。然后我们也可以看看残差变化图：也无法明确判断出是否存在自相关的趋势。在建立多元回归方程的时候我们得到了Durbin-Watson stat的值为：1.770723，查表得到：。所以有。所以我们可
14、以确定无自相关的性质。4. 多重共线性问题的处理X1 , X2,X3 ,X4的相关系数表： X1X2X3X4Y10.282193792970.646364702600.918966025680.915359298590.2821937929710.374707474500.408422976870.542605649700.646364702600.3747074745010.764687525430.810493608430.918966025680.408422976870.7646875254310.956309674270.915359298590.542605649700.81049
15、3608430.956309674271表中的数据发现x1与x4间存在高度相关性，相关性达到了0.918966.故采用逐步回归法，回归结果见下表：VariableCoefficientStd. Errort-StatisticProb.C-70.46872898.9122-0.0783930.9381X12.6131930.21345012.242660.0000R-squared0.837883Mean dependent var10657.15Adjusted R-squared0.832292S.D. dependent var2727.013S.E. of regression1116
16、.769Akaike info criterion16.93661Sum squared resid36168045Schwarz criterion17.02912Log likelihood-260.5174Hannan-Quinn criter.16.96677F-statistic149.8828Durbin-Watson stat1.070726Prob(F-statistic)0.000000VariableCoefficientStd. Errort-StatisticProb.C3515.7052095.1481.6780220.1041X26.2837671.8063823.
17、4786480.0016R-squared0.294421Mean dependent var10657.15Adjusted R-squared0.270091S.D. dependent var2727.013S.E. of regression2329.816Akaike info criterion18.40731Sum squared resid1.57E+08Schwarz criterion18.49982Log likelihood-283.3133Hannan-Quinn criter.18.43746F-statistic12.10099Durbin-Watson stat
18、1.529124Prob(F-statistic)0.001612VariableCoefficientStd. Errort-StatisticProb.C1682.6961239.2411.3578450.1850X38.3505841.1206727.4514050.0000R-squared0.656900Mean dependent var10657.15Adjusted R-squared0.645069S.D. dependent var2727.013S.E. of regression1624.648Akaike info criterion17.68631Sum squar
19、ed resid76544922Schwarz criterion17.77883Log likelihood-272.1378Hannan-Quinn criter.17.71647F-statistic55.52344Durbin-Watson stat1.477161Prob(F-statistic)0.000000VariableCoefficientStd. Errort-StatisticProb.C5098.396347.553214.669400.0000X44.2948930.24381817.615140.0000R-squared0.914528Mean dependen
20、t var10657.15Adjusted R-squared0.911581S.D. dependent var2727.013S.E. of regression810.8868Akaike info criterion16.29647Sum squared resid19068583Schwarz criterion16.38899Log likelihood-250.5954Hannan-Quinn criter.16.32663F-statistic310.2932Durbin-Watson stat1.481612Prob(F-statistic)0.000000结合经济意义和统计
21、检验结果分析，在四个一元回归模型中可决系数最高的方程为（4），所以选择方程（4）为初始方程。将其余解释变量逐一代入：VariableCoefficientStd. Errort-StatisticProb.C3599.578911.49493.9490930.0005X43.3249970.5967965.5714140.0000X10.6708910.3793601.7684800.0879R-squared0.923116Mean dependent var10657.15Adjusted R-squared0.917624S.D. dependent var2727.013Variabl
22、eCoefficientStd. Errort-StatisticProb.C3130.101610.30655.1287360.0000X43.9602050.22341517.725770.0000X22.1130580.5760963.6678950.0010R-squared0.942268Mean dependent var10657.15Adjusted R-squared0.938144S.D. dependent var2727.013VariableCoefficientStd. Errort-StatisticProb.C2168.567673.39373.2203560.
23、0033X43.4155230.29552611.557440.0000X21.9697910.5296483.7190560.0009X31.7021550.6674742.5501420.0168R-squared0.953474Mean dependent var10657.15Adjusted R-squared0.948304S.D. dependent var2727.013S.E. of regression620.0327Akaike info criterion15.81734Sum squared resid10379894Schwarz criterion16.00237
24、Log likelihood-241.1687Hannan-Quinn criter.15.87765F-statistic184.4395Durbin-Watson stat1.653265Prob(F-statistic)0.000000在引入x1的时候，x1没有通过显著性检验（显著性水平为0.05），所以应该剔除x1。在逐步加入x2，x3，方程的逐步提高，并且方程的参数都通过检验，且D-W值为1.653265，查表得到：。所以有。所以我们可以确定无自相关的性质。所以处理得到的方程为： 结论：在建立多元线性回归方程时，模型存在异方差，不存在自相关性，存在多重共线性，所以对模型进行简单的异方差处理和多重共线性处理，即得到新的多元线性回归方程。
