经典线性回归模型诊断和修正

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1、经典线性回归模型的诊断与修正下表为最近20年我国全社会固定资产投资与GDP的统计数据:1年份国内生产总值（亿元）GDP全社会固定资产投资（亿元）PI199671813.622913.519977971524941.1199885195.528406.2199990564.429854.72000100280.132917.72001110863.137213.492002121717.443499.91200313742255566.612004161840.270477.432005187318.988773.612006219438.5109998.162007270232.3137

2、323.942008319515.5172828.42009349081.4224598.772010413030.3251683.772011489300.6311485.132012540367.4374694.742013595244.4446294.091数据来源于国家统计局网站年度数据2014643974512020.652015689052.1561999.831.普通最小二乘法回归结果如下：[=1Equation:EQ01Workfile:04::Untitled-nxIviewjprocObject]PrintNameFreezeEstimateForecastStat

3、sResidsDependentVariable:GDPMethod:LeastSquaresDate:12/06/17Time:14:50Sample:19962015Ineludedobservations.20VariableCoefficientStd.Errort-StatisticProb.C75906548945.063848585800000PI1.1753630.03633132.351180.0000R-squared0.983092Meandependentvar283798.3AdjustedR-squared0.982153S.D.dependentvar208

4、303.1S.E.ofregression27827.84Akaikeinfocriterion23.40010Sumsquaredresid1.39E+10Schwarzcriterion23.49967Loglikelihood-232.0010Hannan-Quinnenter.23.41954F-statistic1046599Durbin-Watsonstat0365276Prob(F-statistic)0000000方程初步估计为:GDP=75906.54+1.1754PI(32.351)R2=0.9822F=1046.599DW=0.36532、异方差的检验与修正首先,用

5、图示检验法,生成残差平方和与解释变量PI的散点图如下：Gjj]Graph:GRAPH01Workfile:04::Untitled-hx[viewProc

6、Object]PrintNameFreeze

7、OptionsUpdate

8、AddTextLine/ShadeRemove80,00060,00040,000Gj20,0000-20,000・40,000100,000300,000500,000PI从上图可以看出，残差平方和与解释变量的散点图主要分布在图形的下半部分，有随PI的变动增大的趋势，因此，模型可能存在异方差。但是否确定存在异方差，还需作进一步的验证。G・Q检验如下：去除序列

9、中间约1/4的部分后,1996-2003年的OLS估计结果如下所示：1=]Equation:UNTITLEDWorkfile:04::Untitled-BX1ViewProcObjectPrintNameFreezeEstimateForecastStatsResidsDependentVariable:GDPMethod:LeastSquaresDate:01/04/18Time:20:59Sample:19962003Includedobservations:8VariableCoefficientStd.Errort-StatisticProb.C29637.515357.566

10、5.5318990.0015PI2.0357580.14935813.630050.0000R-squared0.968714Meandependentvar99696.39AdjustedR-squared0.963500S.D.dependentvar22372.04S上.of「egression4274.201Akaikeinfocriterion19.77090Sumsquaredresid1.10E+08Schwarzcr