線性回歸異方差的診斷檢驗(yàn)和修補(bǔ)—SPSS操作

1、線性回歸（異方差的診斷、檢驗(yàn)和修補(bǔ)） 一SPSS操作首先擬合一般的線性回歸模型，繪制殘差散點(diǎn)圖。步驟和結(jié)果如下: 為方便，只做簡單的雙變量回歸模型，以當(dāng)前工資作為因變量，初 始工資作為自變量。（你們自己做的時(shí)候可以考慮加入其他的自變 量，比如受教育程度等等）Analyzregressionlinear將當(dāng)前工資變量拉入dependent框，初始工資進(jìn)入independent點(diǎn)擊上圖中的PLOTS出現(xiàn)以下對話框:園 Ln earRegression: Plots| Produce all pa rtial plotsbEPEDNT 竝 PRED RESID*DRESD *ADJPR *SRESD

2、*SDRESDStandardized Residual PlotsHistagram| Normsl FJrobability plotOontinueGan cellielp以標(biāo)準(zhǔn)化殘差作為丫軸，標(biāo)準(zhǔn)化預(yù)測值作為 X軸，點(diǎn)擊continue.再點(diǎn)擊OKModel SummarybModeLRR SniuareAdjusted RSquareStd. Error of lhe Estimate1.3S(P775774*8,116.356a. Predictors: (Constant, Beginning Salaryb. Dependent Variable: Current Salary

3、ANOVAModelBum of SauaresdfMean SquareFBia1Regresslo nResidual Total1.D6SE1 13.109E101.379E1 114724731 063E116.6B6E71B22.11B.oct?a. Predictors: (Constant), Beginning Salary b Dapanderrt Variable: Current SalaryCoefficients3ModelUnstandardized CoefficientsStandardized CoefficientstSigStd ErrorBeta(Con

4、stant) Beginning Salary1928.2061 90988E.66D.047.8S02.17040.2 7B.031.000a. Dependent variable: Current Salary第一個(gè)表格輸出的是模型擬合優(yōu)度 R2，為。調(diào)整后的擬合優(yōu)度為第二個(gè)是方差分析，可以說是模型整體的顯著性檢驗(yàn)。F統(tǒng)計(jì)量為,P值遠(yuǎn)小于，故拒絕原假設(shè)，認(rèn)為模型是顯著的。第三個(gè)是模型的系數(shù)，co nsta nt代表常數(shù)項(xiàng)，初始工資前的系數(shù)為, t檢驗(yàn)的統(tǒng)計(jì)量為，通過P值，發(fā)現(xiàn)拒絕原假設(shè)，認(rèn)為系數(shù)顯著異于 0。Scatterplot3-epe ndent Vari able: Curren

5、t Salary6 42-0-2 4 - penp-wvo:pdlN-p毎 purslsToT2lowRegression Standardized Predicted Value以上是輸出的殘差對預(yù)測值的散點(diǎn)圖，發(fā)現(xiàn)存在喇叭口形狀，暗示 著異方差的存在，故接下來進(jìn)行診斷，一般需要診斷異方差是由哪個(gè)自變量引起的， 由于這里我們只選用一個(gè)變量作為自變量，故認(rèn)為異方差由唯一的 自變量“初始工資”引起。接下來做加權(quán)的最小二乘法，首先計(jì)算權(quán)數(shù)。Analyzregressionweight estimati onWeight EtimaticnErriplnyee Code idDependent:少

6、Current Salary (salaryDate of Birth bdate口 I Eduuation引 Level Cyeers). d Employmerrtjob .護(hù) Current Salary salary 夕 日eginriing Slry slbein 爐 Months since Hirs jobtime冷 Prftvious Eyperienee (na. d Mirwriy Classification mi.Indepe ritiEntm):Weiglit Function is iy(W&iht Var) Poweryftighrt Variable:妙？ Be

7、riming Salary sltjegin|Power rane： othrough: 5 by: Q.1回 Irclde： constant in equationOptions.OK I aste氐丹引CancelHdp再點(diǎn)擊options,Weight Estimation: Optionsbast VYeiit as new variableDisplay ANOVA nd Estimatesk j For best parFor each power alueContinueCartedHelp點(diǎn)擊continue，再點(diǎn)擊OK,輸出如下結(jié)果:1.0-4831 0641.9-4828

8、.5482-4926.3532J-4324.4712,24822 8952.3-4821.6152.4-4820 6242.5-4819.9142.6-491 9 476174819.302s2.B-491 9.3882.9-48197203-4320.29S3.1-4021 11 2T2-4022.1573.3-4823 4263 J-4S2J.914as-4525.5153止-4828.527由于結(jié)果比較長，只貼出一部分，第二欄的值越大越好。所以挑出來的權(quán)重變量的次數(shù)為。得出最佳的權(quán)重侯，即可進(jìn)行回歸AnalyzregressionlinearEmployee Code iM Gender

9、 gondsrDart已 oi Girth bdaie Educational Leirel (year. Employ ms nt Category j. Beginning Salary |芒商Ihu.” Months since Hre jototi. PreTious Ewpeneric (m. Minority Ctassificatiori .Q已pencfent總 Currert Salary salaryBlock 1 of 1blextpdependent(s)： 9b inning Salary &albegh曲訟 ErterSeleciion Variable:WLS W

10、eight:WOT 1OK j PasteResetCancel繼續(xù)點(diǎn)擊save,-召 Linear Regression; SavePredicted valuesResiuuals回 Unstandarcli!ed _| Ssndarcized|l Studentized0 DeletedQ Studantizd deleted巨 Jnstandardised StandardizedAdliistedr1IWahlnotiis CQQliSLeverage 旳lu 加IllllUtfllkV WdUMIUi DfBda(s)Stpncl對di爭d Df曰et耳宙)期t| stendarc

11、izecl DfFitI Cd iiu-iwir-hi-Bj-i mf i-iiricnjorion iincrvais IIidm；lk在上面兩處打勾，點(diǎn)擊 continue，點(diǎn)擊okANOVA11*ModelSum ofSiu aresdfMean SciuareFSia1RegressionResidual Total.147.0S52331472473U7.OOCB03.6B1000aa. Predictors: (Constant). Beginning Salaryb. Dependent Variable: Current Salaryc. Weighted Least Squa

12、res Regression-Weighted by WGT_iCoefficients3 bModelUnEtandardized CoefficientsStandard ized CoefficientstBStd. ErrorBeta1(Constant)-460.1099S9.770-465MlBeginning Salary2.054,0727942S.349.000a Dependent Vari able: Current Salary這是輸出結(jié)果，和之前同樣的分析方法。接下需要繪制殘差對預(yù)測值的散點(diǎn)圖，首先通過transform里的compute計(jì)算考慮權(quán)重后的預(yù)測值和殘差C

13、ompute VariableTarget VariablespreType A Label .少 Employee Code (id) R Gender (ganderDate of Birth IodateLj-j Edu匚otnnal Level (year. n j Employment Csrtgory i-Numsric ExpressionFunctiorIaiTLrithme料匚ompute VariableTarget Variable:residNumeric Express!erneS_2*SC|rt(WGr_1j|Type & LataeL.農(nóng) Employee Code id 胡I lender gender 總 Date of Birth bdate J| Educational Level (year. -J Emp