线性回归(异方差的诊断、检验和修补)-SPSS操作

1、 实验五异方差的检验与处理一、实验目的：掌握异方差检验的基本原理和方法掌握异方差的处理方法二、实验要求：利用SPSS实现异方差的检验与处理（一元与多元回归）掌握异方差检验的基本步骤和方法三、实验原理：异方差的检验方法：（1）残差图分析法（3种）；（2）等级相关系数法：主要的步骤（见课本）.异方差的处理方法：（1）加权最小二乘法：主要步骤与原理（2）方差稳定变换法四、实验例子：表4.1序号储蓄y（万元）居民收入x（万元）12648777210592103909954413110508512210979610711912740612747850313499943114269105881552211

2、898167301295017663137791857514819196351512222116316170222880171578241271816542560419140026500201829276702122002830022201727430232105295602416002815025225032100262420325002725703525028172033500291900360003021003620031230038200regression利用SPSS建立y对x普通最小二乘回归，Analyzeregressionlinear，结果如下：VariablesEntered

3、/RemovedModelVariablesEnteredVariablesRemovedMethod1居民收入(万元)a.EnteraAllrequestedvariablesentered.b.DependentVariable储蓄（万元）ANOVAbModelSumofSquaresdfMeanSquareFSig.1Regression18440108118440108.04300.732.000aResidual17782032961317.336Total2021831130a-Predictors:（Constant居民收入（万元）bDependentVariable储蓄（万元）

4、CoefficientsaModelUnstandCoeffiardized一cientsStandardizedCoefficientstSig.BStd.ITrorBeta.1（Constant）居民收入（万元）-648.124.085118.163.005.955-5.48517.342.000.000a.DependentVariable储蓄（万元）2）提取残差，并作出残差图：iruots&kdezuraQnalsuoo0%oiruots&kdezuraQnalsuoo0%o0:J0o400.00000200.000000.00000-200.00000-400.00000100002

5、00003000040000居民收入（万元）从残差图可以看出，发现存在喇叭口形状，暗示着误差项具有明显的异方差性误差随着x的增加呈现出增加的态势。（3）计算等级相关系数，并进行检验（具体步骤见课本），从结果可以看出，通过P值可以看到拒绝原假设，即残差绝对值与变量之间显著相关，存在异方差。序号储蓄y（万元）序号储蓄y（万元）居民收入x（万元）126487772105921039099544131105085122109796107119127406127478503134999431142691058815522118981673012950176631377918575148191963515

6、12222116316170222880171578241271816542560419140026500201829276702122002830022201727430232105295602416002815025225032100262420325002725703525028172033500291900360003021003620031230038200 x等级i残差ei|e.|11169.0169.02-26.626.63-104.6104.64-110.5110.55-159.4159.46-253.4253.47-25.125.18&2&29-129.0129.010-78

7、.078.011129.7129.712102.7102.713-145.5145.514-195.3195.31578.478.416413.0413.017183.4183.418134.4134.419-195.5195.521134.4134.423452.1452.120342.8342.824250.4250.422-135.2135.225180.4180.426316.5316.528233.7233.727-468.2468.229-499.8499.830-316.7316.731-286.1286.1残差|e.|I等级did2i16-152253-117-4168-416

8、15-1010023-172892525174990046361011663614-1119-52551010028-1214418-111174920-111298129-63627-7492224139811786425112174930-3931-2426416247494-1.savSPSSDaiaEditorFile,EditViewT：ansfoi_niArL：ilyce会UtilitiesTfiniQWM|H|團刮创宜創剧圈圉置剑團翌1M1:VRES1absRES1126487771G9018841690221059210-26.6411026643909时4-104.63187

9、104.6341311Q&08-110.5362811054612210979-159.4135015941&10711912-253.4069G253.417406血.仙2425108503134998.230S88.23S43114269-1209G130128.9G1058615622-78.046G378051189E1G730129G7804129681295017&63102.68559102.691377918576-146.62890145S31401915&35-195.27381135.271612222116378.3580678.3E16170522880412.988

10、24-412.991715祠24-127183.41038183.41101G6425604134.36076134.361914002G500-19549909195.5020182927&70134.44286134.4421220028300452.10390452.1022201727430342.76246342.762321052966026042699260.4324160023150-135.19635135.2026226032100180.37687180382624032500316510873165127257035250233.68210233682817203350

11、04G81541446S1529190035000-499B16G64398230210035200-316.7495631G.7631230038200-20G079G7286OSCorrelations居民收入（万元）absRES1Spearmansrho居民收入（万兀）CorrelationCoefficieit1.000.686*Sig.(2tailed).000N3131absRES_1CorrelationCoefficieiit.686*1.000Sig.(2tailed).000N3131*Correlationissignificantatthe0.01level(2tail

12、ed)(4)利用加权最小二乘估计对异方差进行处理，首先计算权数。Analyzeregressionweightestimation,结果如下Sourcevariable.xLog-likelihoodFunction=-224.268830Log-likeliho-odFunctian=-22151500SLog-likelihaodFunctianLog-likelihoodFunction=-224.268830Log-likeliho-odFunctian=-22151500SLog-likelihaodFunctian=-218.832133Log-likelihoodFunction

13、=-21G.252339Log-likelihoodFunction=-213866272Log-likelihoodFunction=-211.773375Log-likelihoodFunction=-210185972Log-likelihoodFimction=-209.316127Log-likelihoodFunction=-209.379714POWERvaluePOWERvaluePOWERvaluePOWERvaluePOWERvaluePOWERvaluePOWERvaluePOWERvalueROWER*日Ili已-2.000-1.5Q0-10Q0-.5000000000

14、00VKo52.000TheValueofPOWERMaximizingLog-likelihoodFunction=1500SourcevariablexPO?ERvslue=100Dependentw日FifihluyListv/iseDeletioncfMissingDataListwiseDeletionofMissingData(MultipleR96744RSquare93696AdjustedRSquare933MStandardError.12632AnalysisofVarianceDFSumofSquaresMeanSquareRegression1G.66489816.6

15、648981Residuals29.45544770167051F=42374136SigmfF-.0000VariablesintheEquationVariableBSEBBetaVariableBSEBBetaTSigT205850000-91820000 x007931.004272205850000-91820000Constant-71912313676.316025Lag-likelihoodFunction=-209.316127根据以上结果可知，m1.5时对数似然函数达到最大，.,（课本99页的一段分析），这说明加权最小二乘估计的效果好于普通最小二乘估计效果。五、练习与作用：（1）课本127页第9题；（2）课本102页例4.4的SPSS实现;（3）课本127页第13题.T4.9（1）由上表可得回归方程：y=-0.831+0.004x由残差