经典线性回归模型的诊断与修正下表为最近年我国全社会固定资产投资与的统计数据：年份国内生产总值（亿元）全社会固定资产投资（亿元）数据来源于国家统计局网站年度数据、普通最小二乘法回归结果如下：[=\Equation:EQQ1Workfile:04;:Untitled\.-BXVIEW/|Pro匚0可訪PrintNameFreezeEstimateFore匚日呂tStatsResideDependentVanable'GDPMethod.LeastSquaresDate:12/06；17Time:14:50Sample'19962015Includedobseivatiuns.20VariableCoefficiientStd.Errcirt-Stati^ticProb.吕759OE541.1753639945.062a-qasesa0.03633132.35119OOOOO0.0000R-squaredAdjustedR-squaredE；上afr&gressijjnSumsquarednesidLoglikehhoDdF-statisticProb(F-statistic}0.9830&20.98215327027.S41.39E+10-23200101046.599O.OQOOOOMeandependentvarS.D.dependentvarAkaikeinfocriterionSchwarzcriterionHannan-QuinncrrterDurbin-Watsonstat2037983208303.123.4001023.4990723.419540.365276方程初步估计为：R、异方差的检验与修正首先，用图示检验法，生成残差平方和与解释变量的散点图如下：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。检验如下：去除序列中间约的部分后，年的估计结果如下所示：叵IEquation;UNTITLEDWorkfile;04;;Untitled、-nxviewProcobjectPrintNameFreezeEstimateForecaststatsResidiDependentVariable.GDPMethod:LeastSquaresDate:01/04/19Time:20:6&Sample:1996200^IncludEdobservations:8VariableCoefficientStd.Errort-StatisticProb.G2963751&357.5665.531099Q0015PI2.0357580.14935813.030050.0000R-squar&d0.968714Meandependentvar99696.39AdjustedR-squared09fi3600SDdependentvar22372.04S.E.ofregression4274.201Akaikeinfocriteron19.77090Sumsquaredresid1.10E+08Schwarzcriterion19.79076Loglikelihood-77.09360Hannan-Quinncrrter.19.e369SF-statistic185.7782Durbin-Watsonstat1.097903[view|prDCObjectea.oao-40,000-LU20?000--20;000-Prab(F-statistic}DDD0010残差平方和年的估计结果如下：[=]Equation:UNTITLEDWbirkfile:04::Unti1led\-nxView|ProcObjectPrintNameFreezeEstimateForecas-tStatsResideDependentVariable:GDPMethod:LeastSquaresDate:0VD4/18Time2101Sample:20002015Includedobservations:8VariableCoefficientStdErrort-StatisticProbC162872.120^72.687.9&4«320.0002PI095832200535411739S7300000R-squared0.931616Meandependentvar504945.7AdjustedR-&quared0.978552S.D.dependentvar136279.0STofregression1995044Akaikeinfocriterion2285301Sumsquaredresid230E<€»Schwarzcriterion22.87207Loglikelihood-89.^1204Hann目n-Quinncrrter.22.71906F-s1atistic320□urbin-Watsonst^t1.127692PrDb(F-statistic)0.000002残差平方和根据检验，统计量为Rss*F((RSS因此，在的显著性水平下拒绝两组子样本方差相同的假设，即存在异方差。检验结果如下Equation:UNTITLEDWorkfilet}4:::Untitled\-□X|view|PrDCObject|PrintLNamejFreezejEstimateFarecastLStatsRElidsDependsnlVariable:LOG[E2)MethodLeastSquaresDate:01W/1ATime20:40Sample(adjusted):20042011Includedobservations:7afteradjustmenlsVariableCoefficientStdErrort-StatisticProbC-18.814^77.50703^-2.51K[}D5D.0541LOG(PI)2392905063156037SSS8200128R-squared0.711677depernJentvar9.6M314AdjustedR-squared0.690013S.D.dependentvar1.504728SEofregression0837730AkaikeinFocriterion2718834Sumsquaredresid3.509375Schwarzcriterion2.7Q3379Loglikelihood-7.515917Hannan-Quinnenter2.52732F-statistic14.35563Durbin-Watsonslat2.093348Prnb(F-st3tis1ic)0.012773参数的估计值显著地不为，则可以认定模型存在着异方差。异方差的修正：运用加权最小二乘法对异方差进行修正已统计量R因此，可以判断在给[s]Equation:UNTITLEDWorkfile:04!：Untitled\-5XView...
