计量实验报告作业

多重共线性和序列相关性的检验和处理某市1974-1987年粮食产销量y，常住人口x1，人均收入x2，肉销售量x3，蛋销售量x4，鱼虾销售量x5数据如下图所示：197498.45000560.2000153.20006.5300001.2300001.8900001975100.7000603.1100190.00009.1200001.3000002.0300001976102.8000668.0500240.30008.1000001.8000002.7100001977133.9500715.4700301.120010.100002.0900003.0000001978140.1300724.2700361.000010.930002.3900003.2900001979143.1100736.1300420.000011.850003.9000005.2400001980146.1500748.9100491.760012.280005.1300006.8300001981144.6000760.3200501.000013.500005.4700008.3600001982148.9400774.9200529.200015.290006.09000010.070001983158.5500785.3000552.720018.100007.97000012.570001984169.6800795.5000771.160019.6100010.1800015.120001985162.1400804.8000811.800017.2200011.7900018.250001986170.0900814.9400988.430018.6000011.5400020.590001987178.6900828.73001094.65023.5300011.6800023.37000

建立线性回归模型：y=c+a1x1+a2x2+a3x3+a4x4+a5x5用ols法估计参数：DependentVariable:YMethod:LeastSquaresDate:10/30/11Time:16:18Sample:19741987Includedobservations:14VariableCoefficientStd.Errort-StatisticProb.

C-3.49656330.00659-0.1165260.9101X10.1253300.0591392.1192450.0669X20.0736670.0378771.9448970.0877X32.6775891.2572932.1296460.0658X43.4534482.4508501.4090820.1965X5-4.4911172.214862-2.0277190.0771R-squared0.970442

Meandependentvar142.7129AdjustedR-squared0.951968

S.D.dependentvar26.09805S.E.ofregression5.719686

Akaikeinfocriterion6.623232Sumsquaredresid261.7185

Schwarzcriterion6.897114Loglikelihood-40.36262

Hannan-Quinncriter.6.597879F-statistic52.53086

Durbin-Watsonstat1.972755Prob(F-statistic)0.000007因为预期a1，a2应为正值，a3，a4，a5应为负值，而回归结果显示a3，a4的符号与预期相反。可决系数和修正的可决系数都较高，F=52.53086，检验也表明显著。存在严重的多重共线性。相关系数表：X1X2X3X4X5X1

1.000000

0.866552

0.882293

0.852449

0.821305X2

0.866552

1.000000

0.945896

0.964773

0.982532X3

0.882293

0.945896

1.000000

0.940506

0.948361X4

0.852449

0.964773

0.940506

1.000000

0.981979X5

0.821305

0.982532

0.948361

0.981979

1.000000由相关系数表可以看出：x2与x3，x4，x5，以及x3与x4，x5之间存在高度相关性。

先找出最简单的回归形式，分别作y与各个变量之间的回归：Y=-90.92+0.32x1可决系数=0.92F=147.67-4.7012.15Y=99.61+0.08x2可决系数=0.83F=57.5615.507.59Y=74.65+4.89x3可决系数=0.86F=75.379.018.68Y=108.86+5.74x4可决系数=0.80F=46.8318.346.83Y=113.37+3.08x5可决系数=0.75F=36.1618.666.01

可以看出x1对y的影响最为显著。DependentVariable:YMethod:LeastSquaresDate:10/30/11Time:20:59Sample:19741987Includedobservations:14VariableCoefficientStd.Errort-StatisticProb.

C-90.9207419.32929-4.7037810.0005X10.3169250.02608112.151610.0000R-squared0.924841

Meandependentvar142.7129AdjustedR-squared0.918578

S.D.dependentvar26.09805S.E.ofregression7.446964

Akaikeinfocriterion6.985054Sumsquaredresid665.4873

Schwarzcriterion7.076347Loglikelihood-46.89537

Hannan-Quinncriter.6.976603F-statistic147.6617

Durbin-Watsonstat1.536885Prob(F-statistic)0.000000逐步回归：

Y=-90.92+0.32x1可决系数=0.92F=147.67DW=1.54-4.7012.15引入x2Y=-40.94+0.23x1+0.03x2可决系数=0.95DW=1.80-1.465.062.23引入x3Y=-34.78+0.21x1+0.01x2+1.46x3可决系数=0.96DW=1.68-1.254.300.501.23去掉x3，引入x4Y=-39.96+0.23x1+0.02x2+0.30x4可决系数=0.95DW=1.83-1.344.780.920.17去掉x4，引入x5Y=-38.56+0.22x1+0.05x2-0.72x5可决系数=0.95DW=1.75-1.314.461.14-0.50第一步，在初始模型中引入x2，模型拟合优度提高，参数符号合理，变量通过t检验。第二步，引入x3，模型拟合优度再次提高，但t检验和经济意义检验未能通过。第三步，去掉x3，引入x4，拟合优度不变，t检验和经济意义检验未能通过。第四步，去掉x4，引入x5，拟合优度不变，经济符号合理，但未能通过t检验。表明：在所建立的模型中，x1，x2所组成的模型为粮食产销量最优模型DependentVariable:YMethod:LeastSquaresDate:12/13/11Time:18:56Sample:19741987Includedobservations:14VariableCoefficientStd.Errort-StatisticProb.

C-40.9357427.99501-1.4622510.1716X10.2294280.0453025.0644580.0004X20.0274400.0123112.2288550.0476R-squared0.948224

Meandependentvar142.7129AdjustedR-squared0.938810

S.D.dependentvar26.09805S.E.ofregression6.455760

Akaikeinfocriterion6.755232Sumsquaredresid458.4453

Schwarzcriterion6.892173Loglikelihood-44.28662

Hannan-Quinncriter.6.742556F-statistic100.7269

Durbin-Watsonstat1.803650Prob(F-statistic)0.000000

回归结果如下：Y=-40.94+0.23x1+0.03x2+u序列相关性检验：Breusch-GodfreySerialCorrelationLMTest:F-statistic2.118430

Prob.F(2,9)0.1762Obs*R-squared4.481126

Prob.Chi-Square(2)0.1064TestEquation:DependentVariable:RESIDMethod:LeastSquaresDate:10/30/11Time:21:32Sample:19741987Includedobservations:14Presamplemissingvaluelaggedresidualssettozero.VariableCoefficientStd.Errort-StatisticProb.

C4.17136825.978990.1605670.8760X1-0.0075560.042094-0.1794910.8615X20.0029200.0114590.2548160.8046RESID(-1)0.0669290.2789180.2399590.8157RESID(-2)-0.5766270.281250-2.0502310.0706R-squared0.320080

Meandependentvar-1.51E-14AdjustedR-squared0.017894

S.D.dependentvar5.938436S.E.ofregression5.885065

Akaikeinfocriterion6.655166Sumsquaredresid311.7059

Schwarzcriterion6.883400Loglikelihood-41.58616

Hannan-Quinncriter.6.634038F-statistic1.059215

Durbin-Watsonstat2.046276Prob(F-statistic)0.430044因为nR-squared=4.48小于卡方（0.05）=5.99所以模型不存在序列相关。

异方差性的检验和处理我国城镇居民人均可支配收入与人均交通和通讯支出关系分析：我国城镇居民平均每人全年家庭可支配收入（x）与交通和通讯（y）支出obsXY14009.61159.624098.73137.1134112.41231.5144206.64172.6554219.42193.6564220.24191.7674240.13197.0484251.42176.3994268.5185.78104353.02206.91114565.39227.21124617.24201.87134770.47237.16144826.36214.37154852.87265.98165000.79212.3175084.64270.09185127.08212.46195380.08255.53205412.24252.37215434.26255.79225466.57337.83236017.85255.65246042.78266.48256485.63346.75267110.54258.56277836.76388.79288471.98369.54298773.1384.49308839.68640.56用OLS方法估计参数：设模型为y=b0+b1x+uDependentVariable:YMethod:LeastSquaresDate:12/14/11Time:09:42Sample:130Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.

C-56.9179836.20624-1.5720490.1272X0.0580750.0064808.9620090.0000R-squared0.741501

Meandependentvar256.8727AdjustedR-squared0.732269

S.D.dependentvar97.56583S.E.ofregression50.48324

Akaikeinfocriterion10.74550Sumsquaredresid71359.62

Schwarzcriterion10.83891Loglikelihood-159.1825

Hannan-Quinncriter.10.77538F-statistic80.31760

Durbin-Watsonstat2.008179Prob(F-statistic)0.000000估计结果为：y=-56.91798+0.058075x异方差检验：图示法

残差图表明存在异方差一，G-Q检验n=30，c=n/4从中间去掉8个数据,n1=n2=11分别对n1和n2进行最小二乘估计：1，对前11个数据进行最小二乘估计DependentVariable:YMethod:LeastSquaresDate:12/14/11Time:16:44Sample:111Includedobservations:11VariableCoefficientStd.Errort-StatisticProb.

C-280.4351219.6890-1.2765100.2337X0.1109540.0518912.1382080.0612R-squared0.336867

Meandependentvar189.0555AdjustedR-squared0.263185

S.D.dependentvar27.70443S.E.ofregression23.78090

Akaikeinfocriterion9.338609Sumsquaredresid5089.783

Schwarzcriterion9.410953Loglikelihood-49.36235

Hannan-Quinncriter.9.293005F-statistic4.571934

Durbin-Watsonstat3.057404Prob(F-statistic)0.061199

RSS1=5089.7832，对后11个数据进行最小二乘估计DependentVariable:YMethod:LeastSquaresDate:12/14/11Time:16:45Sample:2030Includedobservations:11VariableCoefficientStd.Errort-StatisticProb.

C-74.98930133.5825-0.5613710.5882X0.0603720.0190243.1734370.0113R-squared0.528072

Meandependentvar341.5282AdjustedR-squared0.475635

S.D.dependentvar113.8052S.E.ofregression82.40979

Akaikeinfocriterion11.82425Sumsquaredresid61122.36

Schwarzcriterion11.89660Loglikelihood-63.03338

Hannan-Quinncriter.11.77865F-statistic10.07070

Durbin-Watsonstat1.846759Prob(F-statistic)0.011303

RSS2=61122.36F=RSS2/RSS1=12.0088F(0.05)(9,9)=3.18小于F，所以存在递增的异方差性。二，异方差的修正：WLS估计法W=1/X^2DependentVariable:YMethod:LeastSquaresDate:12/14/11Time:16:55Sample:130Includedobservations:30Weightingseries:1/X^2VariableCoefficientStd.Errort-StatisticProb.

C-56.6091335.13772-1.6110650.1184X0.0581200.0075147