線性回歸(異方差的診斷、檢驗(yàn)和修補(bǔ))-SPSS操作

1、 實(shí)驗(yàn)五異方差的檢驗(yàn)與處理一、實(shí)驗(yàn)?zāi)康模赫莆债惙讲顧z驗(yàn)的基本原理和方法掌握異方差的處理方法二、實(shí)驗(yàn)要求：利用SPSS實(shí)現(xiàn)異方差的檢驗(yàn)與處理（一元與多元回歸）掌握異方差檢驗(yàn)的基本步驟和方法三、實(shí)驗(yàn)原理：異方差的檢驗(yàn)方法：（1）殘差圖分析法（3種）；（2）等級(jí)相關(guān)系數(shù)法：主要的步驟（見課本）.異方差的處理方法：（1）加權(quán)最小二乘法：主要步驟與原理（2）方差穩(wěn)定變換法四、實(shí)驗(yàn)例子：表4.1序號(hào)儲(chǔ)蓄y（萬(wàn)元）居民收入x（萬(wàn)元）12648777210592103909954413110508512210979610711912740612747850313499943114269105881552211

2、898167301295017663137791857514819196351512222116316170222880171578241271816542560419140026500201829276702122002830022201727430232105295602416002815025225032100262420325002725703525028172033500291900360003021003620031230038200regression利用SPSS建立y對(duì)x普通最小二乘回歸，Analyzeregressionlinear，結(jié)果如下：VariablesEntered

3、/RemovedModelVariablesEnteredVariablesRemovedMethod1居民收入(萬(wàn)元)a.EnteraAllrequestedvariablesentered.b.DependentVariable儲(chǔ)蓄（萬(wàn)元）ANOVAbModelSumofSquaresdfMeanSquareFSig.1Regression18440108118440108.04300.732.000aResidual17782032961317.336Total2021831130a-Predictors:（Constant居民收入（萬(wàn)元）bDependentVariable儲(chǔ)蓄（萬(wàn)元）

4、CoefficientsaModelUnstandCoeffiardized一cientsStandardizedCoefficientstSig.BStd.ITrorBeta.1（Constant）居民收入（萬(wàn)元）-648.124.085118.163.005.955-5.48517.342.000.000a.DependentVariable儲(chǔ)蓄（萬(wàn)元）2）提取殘差，并作出殘差圖：iruots&kdezuraQnalsuoo0%oiruots&kdezuraQnalsuoo0%o0:J0o400.00000200.000000.00000-200.00000-400.00000100002

5、00003000040000居民收入（萬(wàn)元）從殘差圖可以看出，發(fā)現(xiàn)存在喇叭口形狀，暗示著誤差項(xiàng)具有明顯的異方差性誤差隨著x的增加呈現(xiàn)出增加的態(tài)勢(shì)。（3）計(jì)算等級(jí)相關(guān)系數(shù)，并進(jìn)行檢驗(yàn)（具體步驟見課本），從結(jié)果可以看出，通過P值可以看到拒絕原假設(shè)，即殘差絕對(duì)值與變量之間顯著相關(guān)，存在異方差。序號(hào)儲(chǔ)蓄y（萬(wàn)元）序號(hào)儲(chǔ)蓄y（萬(wàn)元）居民收入x（萬(wàn)元）126487772105921039099544131105085122109796107119127406127478503134999431142691058815522118981673012950176631377918575148191963515

6、12222116316170222880171578241271816542560419140026500201829276702122002830022201727430232105295602416002815025225032100262420325002725703525028172033500291900360003021003620031230038200 x等級(jí)i殘差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殘差|e.|I等級(jí)did2i16-152253-117-4168-416

8、15-1010023-172892525174990046361011663614-1119-52551010028-1214418-111174920-111298129-63627-7492224139811786425112174930-3931-2426416247494-1.savSPSSDaiaEditorFile,EditViewT：ansfoi_niArL：ilyce會(huì)UtilitiesTfiniQWM|H|團(tuán)刮創(chuàng)宜創(chuàng)劇圈圉置劍團(tuán)翌1M1:VRES1absRES1126487771G9018841690221059210-26.6411026643909時(shí)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（萬(wàn)元）absRES1Spearmansrho居民收入（萬(wàn)兀）CorrelationCoefficieit1.000.686*Sig.(2tailed).000N3131absRES_1CorrelationCoefficieiit.686*1.000Sig.(2tailed).000N3131*Correlationissignificantatthe0.01level(2tail

12、ed)(4)利用加權(quán)最小二乘估計(jì)對(duì)異方差進(jìn)行處理，首先計(jì)算權(quán)數(shù)。Analyzeregressionweightestimation,結(jié)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根據(jù)以上結(jié)果可知，m1.5時(shí)對(duì)數(shù)似然函數(shù)達(dá)到最大，.,（課本99頁(yè)的一段分析），這說(shuō)明加權(quán)最小二乘估計(jì)的效果好于普通最小二乘估計(jì)效果。五、練習(xí)與作用：（1）課本127頁(yè)第9題；（2）課本102頁(yè)例4.4的SPSS實(shí)現(xiàn);（3）課本127頁(yè)第13題.T4.9（1）由上表可得回歸方程：y=-0.831+0.004x由殘差