P155 ９..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。
（1）当设定模型为ln Y t = β0 + β1 ln x t + μt时，是否存在序列相关。
（2）若按一介自相关假设μt =ρμt-1 + εt，试用广义最小二乘法估计原模型?（3）采用差分形式x t = x t - x t -1与Y t = Y t - Y t -1作为新数据，估计模型Y t* = a0 + a1 xt* + v t，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: 13:25Sample: 1980 2007Included observations: 28Variable Coefficient Std. Error t-Statistic Prob.C 1.588478 0.134220 11.83492 0.0000R-squared 0.992851 Mean dependent var 9.552256Adjusted R-squared 0.992576 S.D. dependent var 1.303948S.E. of regression 0.112351 Akaike info criterion -1.465625Sum squared resid 0.328192 Schwarz criterion -1.370468Log likelihood 22.51876 F-statistic 3610.878模型为：LNY = 1.588478116 + 0.8544154373*LNX由于ＤＷ值为0.379323，没有通过５％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(-1) lny(-1)Dependent Variable: LNYMethod: Least SquaresDate: 11/22/11 Time: 19:56Sample(adjusted): 1981 2007Variable Coefficient Std. Error t-Statistic Prob.C 0.533857 0.138957 3.841886 0.0008LNX 0.425651 0.078022 5.455545 0.0000LNX(-1) -0.131465 0.114789 -1.145271 0.2639R-squared 0.998961 Mean dependent var 9.624593Adjusted R-squared 0.998826 S.D. dependent var 1.270246S.E. of regression 0.043526 Akaike info criterion -3.294976Sum squared resid 0.043573 Schwarz criterion -3.103000Log likelihood 48.48218 F-statistic 7373.686Durbin-Watson stat 0.695752 Prob(F-statistic) 0.000000得ｐ＝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 after adjusting endpointsC 0.512688 0.085421 6.001885 0.0000X1 0.857642 0.025739 33.32068 0.0000 R-squared 0.977979 Mean dependent var 3.327616 Adjusted R-squared 0.977098 S.D. dependent var 0.434222 S.E. of regression 0.065713 Akaike info criterion -2.535863 Sum squared resid 0.107954 Schwarz criterion -2.439875 Log likelihood 36.23415 F-statistic 1110.267 Durbin-Watson stat 1.053997 Prob(F-statistic) 0.000000得到回归方程：Y1 = 0.5126883387 + 0.8576421851*X1原模型：LNY=1c-ρ+c x1*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 Variable: DYMethod: Least SquaresDate: 11/22/11 Time: 14:45Sample(adjusted): 1981 2007Included observations: 27 after adjusting endpointsC 889.3388 260.8836 3.408949 0.0022R-squared 0.940823 Mean dependent var 3902.619 Adjusted R-squared 0.938456 S.D. dependent var 4453.815 S.E. of regression 1104.907 Akaike info criterion 16.92410 Sum squared resid 30520498 Schwarz criterion 17.02009 Log likelihood -226.4753 F-statistic 397.4604对模型进行LM检验：F-statistic 4.710801 Probability 0.019287Test Equation:Dependent Variable: RESID Method: Least Squares Date: 11/22/11 Time: 16:27C 33.11519 229.3418 0.144392 0.8864 DX -0.010847 0.026516 -0.409097 0.6863 RESID(-1) 0.644436 0.213523 3.018112 0.0061 R-squared0.290596 Mean dependent var -8.42E-14 Adjusted R-squared 0.198066 S.D. dependent var 1083.451 S.E. of regression 970.2386 Akaike info criterion 16.72891 Sum squared resid 21651350 Schwarz criterion 16.92089 Log likelihood -221.8403 F-statistic 3.140534 由于20.057.846104 5.99LM =>χ= ，则模型存在序列相关性。
10.（1）回归模型：Y = 245.5157901 + 0.5684245399*X1 - 0.005832617866*X2Dependent Variable: Y Method: Least Squares Date: 11/22/11 Time: 15:40 Sample: 1 10Included observations: 10C 245.5158 69.52348 3.531408 0.0096X1 0.568425 0.716098 0.793781 0.4534X2 -0.005833 0.070294 -0.082975 0.9362 R-squared 0.962099 Mean dependent var 1110.000 Adjusted R-squared 0.951270 S.D. dependent var 314.2893 S.E. of regression 69.37901 Akaike info criterion 11.56037 Sum squared resid 33694.13 Schwarz criterion 11.65115 Log likelihood -54.80185 F-statistic 88.84545 Durbin-Watson stat 2.708154 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 SquaresDate: 11/23/11 Time: 12:38Sample: 1901 1910C -11.47181 34.08484 -0.336566 0.7451R-squared 0.997156 Mean dependent var 1700.000 Adjusted R-squared 0.996800 S.D. dependent var 605.5301 S.E. of regression 34.25397 Akaike info criterion 10.08234 Sum squared resid 9386.678 Schwarz criterion 10.14286 Log likelihood -48.41169 F-statistic 2804.497说明x1 x2之间存在线性关系。
（3）相关系数检验：在工作文件窗口输入命令：cor x1 x2，得到检验结果：X1 X2X1 1 0.998576763268X2 0.998576763268 1由表可知解释变量之间高度相关。