序列相关性_多重共线性

1、P155 . .中国 1980-2007 年全社会固定资产投资总额 X 与工业总产值 Y 的统计资料如下表所示。年份全社会固定资产投资（X）工业增加值（Y）年份全社会固定资产投资（X）工业增加值（Y）1980910.91996.5199417042.119480.719819612048.4199520019.324950.619821230.42162.3199622913.529447.619831430.12375.6199724941.132921.419841832.92789.0199828406.234018.419852543.23448.7199929854.735861.5

2、19863120.63967.0200032917.740033.619873791.74585.8200137213.543580.619884753.85777.2200243499.947431.319894410.46484.0200355566.654945.5199045176858.0200470477.465210.019915594.58087.1200588773.677230.819928080.110284.52006109998.291310.9199313072.314188.02007137323.9107367.2（1）当设定模型为 ln Yt = 0 + 1

3、ln xt + t 时，是否存在序列相关 。（2）若按一介自相关假设 t = t-1 + t ，试用广义最小二乘法估计原模型 ? （3） 采 用 差 分 形 式 Xt* = Xt - Xt -1与Yt* = Yt - Yt -1 作 为 新 数 据 ， 估 计 模 型 Yt* = a0 + a1Xt* + vt ，该模型是否存在序列相关？ (1) 在工作文件窗口输入命令：genr lny=log(y)genr lnx=log(x)ls lny c lnx，得到结果：Dependent Variable: LNYMethod: Least SquaresDate: 11/22/11 Time:

4、13:25Sample: 1980 2007Included observations: 28VariableCoefficientStd. Errort-StatisticProb. C1.5884780.13422011.834920.0000LNX0.8544150.01421960.090580.0000R-squared0.992851 Mean dependent var9.552256Adjusted R-squared0.992576 S.D. dependent var1.303948S.E. of regression0.112351 Akaike info criteri

5、on-1.465625Sum squared resid0.328192 Schwarz criterion-1.370468Log likelihood22.51876 F-statistic3610.878Durbin-Watson stat0.379323 Prob(F-statistic)0.000000模型为：LNY = 1.588478116 + 0.8544154373*LNX由于值为0.379323，没有通过显著水平下的DW检验。即该模型存在序列相关性。（2）在工作文件窗口输入命令：genr lny=log(y)genr lnx=log(x)ls lny c lnx lnx(-

6、1) lny(-1)Dependent Variable: LNYMethod: Least SquaresDate: 11/22/11 Time: 19:56Sample(adjusted): 1981 2007Included observations: 27 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C0.5338570.1389573.8418860.0008LNX0.4256510.0780225.4555450.0000LNX(-1)-0.1314650.114789-1.14527

7、10.2639LNY(-1)0.6644480.0797518.3315000.0000R-squared0.998961 Mean dependent var9.624593Adjusted R-squared0.998826 S.D. dependent var1.270246S.E. of regression0.043526 Akaike info criterion-3.294976Sum squared resid0.043573 Schwarz criterion-3.103000Log likelihood48.48218 F-statistic7373.686Durbin-W

8、atson stat0.695752 Prob(F-statistic)0.000000得0.664448，在工作文件窗口输入命令：genr lny=log(y)genr lnx=log(x)genr y1=lny-0.664448*lny(-1)genr x1=lnx-0.664448*lnx(-1)ls y1 c x1，得到广义最小二乘估计结果：Dependent Variable: Y1Method: Least SquaresDate: 12/04/11 Time: 20:37Sample(adjusted): 1981 2007Included observations: 27 af

9、ter adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C0.5126880.0854216.0018850.0000X10.8576420.02573933.320680.0000R-squared0.977979 Mean dependent var3.327616Adjusted R-squared0.977098 S.D. dependent var0.434222S.E. of regression0.065713 Akaike info criterion-2.535863Sum squared re

10、sid0.107954 Schwarz criterion-2.439875Log likelihood36.23415 F-statistic1110.267Durbin-Watson stat1.053997 Prob(F-statistic)0.000000得到回归方程：Y1 = 0.5126883387 + 0.8576421851*X1原模型：LNY= +cx1*x1即原模型：LNY=1.5278943353042+0.8576421851*LNX（3）在工作文件窗口输入命令：genr dy=d(y)genr dx=d(x)ls dy c dx，得到差分法结果：Dependent V

11、ariable: DYMethod: Least SquaresDate: 11/22/11 Time: 14:45Sample(adjusted): 1981 2007Included observations: 27 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C889.3388260.88363.4089490.0022DX0.5964130.02991619.936410.0000R-squared0.940823 Mean dependent var3902.619Adjusted R-

12、squared0.938456 S.D. dependent var4453.815S.E. of regression1104.907 Akaike info criterion16.92410Sum squared resid30520498 Schwarz criterion17.02009Log likelihood-226.4753 F-statistic397.4604Durbin-Watson stat0.960842 Prob(F-statistic)0.000000对模型进行LM检验：Breusch-Godfrey Serial Correlation LM Test:F-s

13、tatistic4.710801 Probability0.019287Obs*R-squared7.846104 Probability0.019781Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 11/22/11 Time: 16:27VariableCoefficientStd. Errort-StatisticProb. C33.11519229.34180.1443920.8864DX-0.0108470.026516-0.4090970.6863RESID(-1)0.6444360.2135233

14、.0181120.0061RESID(-2)-0.2387930.212786-1.1222210.2733R-squared0.290596 Mean dependent var-8.42E-14Adjusted R-squared0.198066 S.D. dependent var1083.451S.E. of regression970.2386 Akaike info criterion16.72891Sum squared resid21651350 Schwarz criterion16.92089Log likelihood-221.8403 F-statistic3.1405

15、34Durbin-Watson stat1.860676 Prob(F-statistic)0.044781由于 ，则模型存在序列相关性。10. 编号编号170080081006115018001876026501000100907120020002052039001200127308140022002201049501400142509155024002435051100160016930101500260026860（1）回归模型：Y = 245.5157901 + 0.5684245399*X1 - 0.005832617866*X2Dependent Variable: YMethod

16、: Least SquaresDate: 11/22/11 Time: 15:40Sample: 1 10Included observations: 10VariableCoefficientStd. Errort-StatisticProb. C245.515869.523483.5314080.0096X10.5684250.7160980.7937810.4534X2-0.0058330.070294-0.0829750.9362R-squared0.962099 Mean dependent var1110.000Adjusted R-squared0.951270 S.D. dep

17、endent var314.2893S.E. of regression69.37901 Akaike info criterion11.56037Sum squared resid33694.13 Schwarz criterion11.65115Log likelihood-54.80185 F-statistic88.84545Durbin-Watson stat2.708154 Prob(F-statistic)0.000011（2）判定系数检验：在工作文件窗口输入命令： ls x1 c x2，得到检验结果：Dependent Variable: X1Method: Least Squ

18、aresDate: 11/23/11 Time: 12:38Sample: 1901 1910Included observations: 10VariableCoefficientStd. Errort-StatisticProb. C-11.4718134.08484-0.3365660.7451X20.0980220.00185152.957500.0000R-squared0.997156 Mean dependent var1700.000Adjusted R-squared0.996800 S.D. dependent var605.5301S.E. of regression34.25397 Akaike info criterion10.08234Sum squared resid9386.678 Schwarz criterion10.14286Log likelih