序列相關(guān)性 多重共線性

1、P155 . .中國 1980-2007 年全社會(huì)固定資產(chǎn)投資總額 X 與工業(yè)總產(chǎn)值 Y 的統(tǒng)計(jì)資料如下表所示。年份全社會(huì)固定資產(chǎn)投資（X）工業(yè)增加值（Y）年份全社會(huì)固定資產(chǎn)投資（X）工業(yè)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、19863120.63967.0200032917.740033.619873791.74585.8200137213.543580.619884753.85777.2200243499.947431.319894410.46484.0200355566.654945.5199045176858.0200470477.465210.019915594.58087.1200588773.677230.819928080.110284.52006.291310.9199313072.314188.02007.9.2（1）當(dāng)設(shè)定模型為 ln Yt = 0 + 1 ln xt + t 時(shí)，是否存在序列

3、相關(guān) 。（2）若按一介自相關(guān)假設(shè) t = t-1 + t ，試用廣義最小二乘法估計(jì)原模型 ? （3） 采 用 差 分 形 式 xt = x t - xt -1與Yt = Yt - Yt -1 作 為 新 數(shù) 據(jù) ， 估 計(jì) 模 型 Yt* = a0 + a1 xt* + vt ，該模型是否存在序列相關(guān)？ (1) 在工作文件窗口輸入命令：genr lny=log(y)genr lnx=log(x)ls lny c lnx，得到結(jié)果：Dependent Variable: LNYMethod: Least SquaresDate: 11/22/11 Time: 13:25Sample: 1980

4、2007Included observations: 28VariableCoefficientStd. Errort-StatisticProb. C1.0.11.834920.0000LNX0.0.60.090580.0000R-squared0. Mean dependent var9.Adjusted R-squared0. S.D. dependent var1.S.E. of regression0. Akaike info criterion-1.Sum squared resid0. Schwarz criterion-1.Log likelihood22.51876 F-st

5、atistic3610.878Durbin-Watson stat0. Prob(F-statistic)0.模型為：LNY = 1. + 0.*LNX由于值為0.，沒有通過顯著水平下的DW檢驗(yàn)。即該模型存在序列相關(guān)性。（2）在工作文件窗口輸入命令：genr lny=log(y)genr lnx=log(x)ls lny c lnx lnx(-1) lny(-1)Dependent Variable: LNYMethod: Least SquaresDate: 11/22/11 Time: 19:56Sample(adjusted): 1981 2007Included observation

6、s: 27 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C0.0.3.0.0008LNX0.0.5.0.0000LNX(-1)-0.0.-1.0.2639LNY(-1)0.0.8.0.0000R-squared0. Mean dependent var9.Adjusted R-squared0. S.D. dependent var1.S.E. of regression0. Akaike info criterion-3.Sum squared resid0. Schwarz criterion

7、-3.Log likelihood48.48218 F-statistic7373.686Durbin-Watson stat0. Prob(F-statistic)0.得0.，在工作文件窗口輸入命令：genr lny=log(y)genr lnx=log(x)genr y1=lny-0.*lny(-1)genr x1=lnx-0.*lnx(-1)ls y1 c x1，得到廣義最小二乘估計(jì)結(jié)果：Dependent Variable: Y1Method: Least SquaresDate: 12/04/11 Time: 20:37Sample(adjusted): 1981 2007Inclu

8、ded observations: 27 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C0.0.6.0.0000X10.0.33.320680.0000R-squared0. Mean dependent var3.Adjusted R-squared0. S.D. dependent var0.S.E. of regression0. Akaike info criterion-2.Sum squared resid0. Schwarz criterion-2.Log likelihood36.

9、23415 F-statistic1110.267Durbin-Watson stat1. Prob(F-statistic)0.得到回歸方程：Y1 = 0. + 0.*X1原模型：LNY= +cx1*x1即原模型：LNY=1.42+0.*LNX（3）在工作文件窗口輸入命令：genr dy=d(y)genr dx=d(x)ls dy c dx，得到差分法結(jié)果：Dependent Variable: DYMethod: Least SquaresDate: 11/22/11 Time: 14:45Sample(adjusted): 1981 2007Included observations:

10、27 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C889.3388260.88363.0.0022DX0.0.19.936410.0000R-squared0. Mean dependent var3902.619Adjusted R-squared0. S.D. dependent var4453.815S.E. of regression1104.907 Akaike info criterion16.92410Sum squared resid Schwarz criterion17.02

11、009Log likelihood-226.4753 F-statistic397.4604Durbin-Watson stat0. Prob(F-statistic)0.對(duì)模型進(jìn)行LM檢驗(yàn)：Breusch-Godfrey Serial Correlation LM Test:F-statistic4. Probability0.Obs*R-squared7. Probability0.Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 11/22/11 Time: 16:27VariableCoefficient

12、Std. Errort-StatisticProb. C33.11519229.34180.0.8864DX-0.0.-0.0.6863RESID(-1)0.0.3.0.0061RESID(-2)-0.0.-1.0.2733R-squared0. Mean dependent var-8.42E-14Adjusted R-squared0. S.D. dependent var1083.451S.E. of regression970.2386 Akaike info criterion16.72891Sum squared resid Schwarz criterion16.92089Log

13、 likelihood-221.8403 F-statistic3.Durbin-Watson stat1. Prob(F-statistic)0.由于 ，則模型存在序列相關(guān)性。10. 編號(hào)編號(hào)170080081006115018001876026501000100907120020002052039001200127308140022002201049501400142509155024002435051100160016930101500260026860（1）回歸模型：Y = 245. + 0.*X1 - 0.6*X2Dependent Variable: YMethod: Least

14、SquaresDate: 11/22/11 Time: 15:40Sample: 1 10Included observations: 10VariableCoefficientStd. Errort-StatisticProb. C245.515869.523483.0.0096X10.0.0.0.4534X2-0.0.-0.0.9362R-squared0. Mean dependent var1110.000Adjusted R-squared0. S.D. dependent var314.2893S.E. of regression69.37901 Akaike info crite

15、rion11.56037Sum squared resid33694.13 Schwarz criterion11.65115Log likelihood-54.80185 F-statistic88.84545Durbin-Watson stat2. Prob(F-statistic)0.（2）判定系數(shù)檢驗(yàn)：在工作文件窗口輸入命令： ls x1 c x2，得到檢驗(yàn)結(jié)果：Dependent Variable: X1Method: Least SquaresDate: 11/23/11 Time: 12:38Sample: 1901 1910Included observations: 10Va

16、riableCoefficientStd. Errort-StatisticProb. C-11.4718134.08484-0.0.7451X20.0.52.957500.0000R-squared0. Mean dependent var1700.000Adjusted R-squared0. S.D. dependent var605.5301S.E. of regression34.25397 Akaike info criterion10.08234Sum squared resid9386.678 Schwarz criterion10.14286Log likelihood-48.41169 F-statistic2804.497Durbin-Watson stat1. Prob(F-statistic)0. 說明x1 x2之間存在線性關(guān)系。（3）相關(guān)系數(shù)檢驗(yàn)：在工作文件窗口輸入命令：cor x1 x2，得到檢驗(yàn)結(jié)果：X1X2X110.8X20.81由表可知解釋變量之間高度相關(guān)。（4）方差膨