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1974-19__年粮食产销量y，常住人口_1，人均收入_2，肉销售量_3，蛋销

建立线性回归模型：y=c+a1_1+a2_2+a3_3+a4_4+a5_5用ols法估计参数：

DependentVariable:YMethod:LeastSquaresDate:10/30/11Time:16:18Sample:197XXXX1987Includedobservations:14

VariableC_1_2_3_4_5

XXX(F-statistic)

Coefficient-3.XXX.XXX.XXX.XXX.453448-4.491117

XXX.006590.XXX.XXX.XXX.XXX.214862

t-Statistic-0.XXX.XXX.XXX.XXX.409082-2.027719

Prob.0.91010.06690.08770.06580.19650.XXX.712926.098056.XXX.XXX.XXX.972755

XXX.719686Akaikeinfocriterion261.7185Schwarzcriterion-40.36262Hannan-Quinncriter.52.53086Durbin-Watsonstat0.000007

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：

由相关系数表可以看出：_2与_3，_4，_5，以及_3与_4，_5之间存在高度相关性。先找出的回归形式，分别作y与各个变量之间的回归：Y=-90.92+0.32_1可决系数=0.92F=147.67-4.7012.15

Y=99.61+0.08_2可决系数=0.83F=57.5615.507.59

Y=74.65+4._3可决系数=0.86F=75.379.018.68

Y=108.86+5.74_4可决系数=0.80F=46.8318.346.83

Y=113.37+3.08_5可决系数=0.75F=36.1618.666.01

可以看出_1对y的影响最为显著。

DependentVariable:YMethod:LeastSquaresDate:10/30/11Time:XXXSample:XXX7Includedobservations:14

VariableC_1

XXX(F-statistic)

Coefficient-90.920740.316925

XXX.329290.026081

t-Statistic-4.703XXXX8112.15161

Prob.0.00050.XXX.712926.098056.XXX.XXX.XXX.536885

XXX.4469Akaikeinfocriterion665.4873Schwarzcriterion-46.537Hannan-Quinncriter.147.6617Durbin-Watsonstat0.000000

逐步回归：

Y=-90.92+0.32_1可决系数=0.92F=147.67DW=1.-4.7012.15引入_2

Y=-40.94+0.23_1+0.03_2可决系数=0.95DW=1.80-1.465.062.23引入_3

Y=-34.78+0.21_1+0.01_2+1.46_3可决系数=0.96DW=1.68-1.2.300.501.23去掉_3，引入_4

Y=-39.96+0.23_1+0.02_2+0.30_4可决系数=0.95DW=1.83-1.344.780.920.17去掉_4，引入_5

Y=-38.56+0.22_1+0.05_2-0.72_5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_2，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_3，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_3，引入_4，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_4，引入_5，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，_1，_2所组成的模型为粮食产销量最优模型

DependentVariable:YMethod:LeastSquaresDate:12/13/11Time:18:56Sample:197XXXX1987Includedobservations:14

VariableC_1_2

XXX(F-statistic)

Coefficient-40.935740.XXX.027440

XXX.995010.XXX.012311

t-Statistic-1.XXX.XXX.228855

Prob.0.17160.00040.XXX.712926.098056.XXX.XXX.XXX.803650

XXX.455760Akaikeinfocriterion458.4453Schwarzcriterion-44.28662Hannan-Quinncriter.100.7269Durbin-Watsonstat0.000000

回归结果如下：

Y=-40.94+0.23_1+0.03_2+u序列相关性检验：

Breusch-GodfreySerialCorrelationLMTest:

F-statisticObsR-squared

TestEquation:

DependentVariable:RESIDMethod:LeastSquares

2.118430Prob.F(2,9)XXX(2)

Coefficient4.171368-0.XXX.XXX.066929-0.576627

XXX.9790.XXX.XXX.XXX.281250

t-Statistic0.160567-0.XXX.XXX.239959-2.050231

0.17620.10Prob.0.87600.86150.80460.81570.0706-1.51E-145.XXX.XXX.XXX.XXX.046276

Date:10/30/11Time:XXXSample:197XXXX1987Includedobservations:14

Presamplemissingvaluelaggedresidualssettozero.

VariableC_1_2RESID(-1)RESID(-2)

XXX(F-statistic)

XXX.885065Akaikeinfocriterion311.7059Schwarzcriterion-41.58616Hannan-Quinncriter.1.059215Durbin-Watsonstat0.430044

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（_）与交通和通讯（y）支出

obs123XXX161XXXX021XXXX4252627XXXX2930

XXX(F-statistic)

Coefficient-280.43510.1109

XXX.600.0511

t-Statistic-1.XXX.138208

Prob.0.23370.XXX.055527.704439.XXX.XXX.XXX.057404

XXX.78090Akaikeinfocriterion50.783Schwarzcriterion-49.36235Hannan-Quinncriter.4.571934Durbin-Watsonstat0.061199

RSS1=50.783

2，对后11个数据进行最小二乘估计

DependentVariable:YMethod:LeastSquaresDate:12/14/11Time:16:45Sample:2030

Includedobservations:11

VariableC_

XXX(F-statistic)

RSS2=61122.36F=RSS2/RSS1=12.0088

F(0.05)(9,9)=3.18小于F，所以存在递增的异方差性。

Coefficient-74.9300.060372

XXX.58250.019024

t-Statistic-0.XXX.173437

Prob.0.58820.XXX.XXX.805211.XXX.XXX.778651.846759

XXX.40979Akaikeinfocriterion61122.36Schwarzcriterion-63.03338Hannan-Quinncriter.10.07070Durbin-Watsonstat0.011303

二，异方差的修正：WLS估计法W=1/_^2

DependentVariable:YMethod:LeastSquaresDate:12/14/11Time:16:55Sample:130

Includedobservations:30Weightingseries:1/_^2

VariableC_

R-squaredAdjustedR-squared

Coefficient-56.609130.058120

XXX.137720.007514

t-Statistic-1.XXX.734658

Prob.0.11840.XXX.638251.05680

WeightedStatistics

XXX

XXX(F-statistic)

XXXessionDurbin-WatsonstatY=-56.60913+0.058120_再进行WHITE检验

32.15303Akaikeinfocriterion246.Schwarzcriterion-145.85Hannan-Quinncriter.59.82494Durbin-Watsonstat0.000000

UnweightedStatistics

9.XXX.XXX.XXX.614XXXX6256.872797.565XXXX1368.94

XXX.486Sumsquaredresid2.008007

HeteroskedasticityTest:WhiteF-statistic

0.949336Prob.F(3,26)

0.43130.3976

ObXXX(3)

nR^2=2.961738小于5.99，所以不存在异方差性。

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