線性回歸(異方差的診斷、檢驗(yàn)和修補(bǔ))—SPSS操作

1、資料收集于網(wǎng)絡(luò)，如有侵權(quán)請(qǐng)聯(lián)系網(wǎng)站刪除只供學(xué)習(xí)與交流線性回歸（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(jiǎn)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）Analyzeregressionlin earDataSet 1 - SPSS Data Editor* Deta Transform牡n alyzeGraphs LHilities Add-onsWindowHelpReportsDescriptive StatisticsgendidTa

2、bles1mCorripar& MeansGftneral Linear ModelGeneralized Linear ModelsMixed ModelsCorrelatejobcatsalary3$57 J161$40h：121$21,-81$21搞 Unear -N Curve Estimalion. 聶 Perlifll Least Squar&s.LolineerNeural Networks只供學(xué)習(xí)與交流Classifv將當(dāng)前工資變量拉入 dependent框，初始工資進(jìn)入independentDependert:矽 Current Salary salary)de idderb

3、datej_evel (year. Category j alary salbe.2 Hire jokrti. serience (m. :sification Block 1 of 1Selection rieble:點(diǎn)擊上圖中的PLOTS，出現(xiàn)以下對(duì)話框:園 Linear Regression: PlotsDEPENDNT ZPRED ZRESID TRESID *ADJPRED *SRESD *SDRESID工:PreviousStandardized Residual Plots-HistogramNormal probability platContinue Cancel| Prod

4、uce all partial plots以標(biāo)準(zhǔn)化殘差作為Y軸，標(biāo)準(zhǔn)化預(yù)測(cè)值作為 X軸，點(diǎn)擊continue,再點(diǎn)擊OKModel Summary1*Mode1RR SauareAdjusted RSquareStd. Error ofthe Estimate1.SEO*77577450.115,350a Predictors: (Constant), Beginning Salary b Dependent Variable: Current SalaryANOVAbModalSum of SduaresdfMean SauateFSid1RegressionResidualTotal1.0

5、6eEH3.109E101.379E1114724731.068E110.5B6E71622.11Soao=a Predictors; (Constant), Beginning Salary b DependertVariable Current SalaryCoefficients JModelUristaridairdized CoefficientsStands rd ized CoefFicienUtSig.eStd. ErrorBeta(Constant) Beginnirg Salary1923.2051.90980.600.047.8802.17040.276.031.000a

6、. DependeritVariable: Current Salary第一個(gè)表格輸出的是模型擬合優(yōu)度R2，為0.775。調(diào)整后的擬合優(yōu)度為 0.774.第二個(gè)是方差分析，可以說(shuō)是模型整體的顯著性檢驗(yàn)。F統(tǒng)計(jì)量為1622.1, P值遠(yuǎn)小于0.05,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)，constant代表常數(shù)項(xiàng)，初始工資前的系數(shù)為1.909, t檢驗(yàn)的統(tǒng)計(jì)量為40.276,通過(guò)P值，發(fā)現(xiàn)拒絕原假設(shè)，認(rèn) 為系數(shù)顯著異于0。ScatterplotDependent variable: Current Salary8 8 4024-Enp-lnwlzPWU.2SIA即oiiii0246

7、Regression Standardized Predicted Value以上是輸出的殘差對(duì)預(yù)測(cè)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(lái)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(lái)做加權(quán)的最小二乘法，首先計(jì)算權(quán)數(shù)。Analyzeregressionweight estimati onformanalyzeSrphs Utilities Add-Qns ndowReportsDfiscrlicrtive StMlstbcsgendeTablesCompare MeansGen

8、eral Linear ModelGnenersliied Linear McdisltsMixed ModelsLinearCurve Estimation.p隹 PsHisdl Last Squares.jobcatsalary153S57.0016140.20I 121218121 ,90LoglinearNeural NetworksClassifyD-ata ReductionScaleonparafiietrlc TestTime SeriesSurvivalM上 Missing Value Analysis.Multiple ResponseComplex SamplesCorr

9、elateRegressionRLQQRHULTR4RBWeight EstimationBinary Loqistic.Multinomial Logistic.Ordinal.Probirt,啟 Nonlinear“也 Weight Estimation.蠱 2-Stage Least Squares.Optimsl Scaling. .10bo909000035100800 Emplcjge CcjcIb |ici 懇省 Date of Birth todate 訂 | Educdional Level (year),. J| Employment CategoryCurrent Sal

10、ary (salary矽 Beginning Salary salbegin少 Months since Hire jotthie少 Previous Experience (mo.Minority ClasEificstion mil,.,WelSht Variable：& Beginning Salary salbeginiependent；夕 Current Salary (salaryndependent(s);Beginning Salary salbeginPower range:q through: 5Q Include constsnt in equstknOK jPasteR

11、esetCancelHelpOptions.再點(diǎn)擊options,Weight Estimation： Options回 應(yīng)鹽已b已st 曲也價(jià)aw new MafiableDisplay ANOVA and Estimates(* ； Fof Qe曲 power(_.： For eeich power valueContinueCancelHelp點(diǎn)擊continue,再點(diǎn)擊OK，輸出如下結(jié)果:131.922.12.223242.52.627282.933.133.6-4831.064-4823 548-4326.353-4824 471-4822.895-4821.51

12、5-4320.024-4619.914-4819 476-4Bl 9.302a-4819.366-4319.720-4320.298-4821 112-4822157-4823 426-4624.914-4820.016-4628.527由于結(jié)果比較長(zhǎng)，只貼出一部分，第二欄的值越大越好。所以挑出來(lái)的權(quán)重變量的次數(shù)為2.7。得出最佳的權(quán)重侯，即可進(jìn)行回歸AnalyzeregressionlinearLinear RegressionDependent:盤(pán) Emplcyee Code id 蠱I Gender gender 金 Date of Birth bdate 呂 Educational L

13、evel (year. .I Eiriploynient Category 爐日證nriing Salary sabe . 爐 Months wince Hire jobti. 護(hù) Previous Experience (m.Minority Classification .護(hù) Current Salsry salaryBlock 1 of 1Selection Variable：SulLabels：OKPasteResetCancelHelp繼續(xù)點(diǎn)擊save,Linear Regression: Save-Predicted ValuesJnstandsrdized| Standardiz

14、ed Adjusied1 S.E. of mean predictionsResiduals叵 UnstandardizedStandardizedStudentized08(8tedStudentized deletedDistances| MahalanotoisI | CootsLeverage veluerPrediction IntervalsInfluence Statistics DfBeta(Stands rd ized DfBet3(sJ DFitStandardized DfFit在上面兩處打勾，點(diǎn)擊 continue,點(diǎn)擊okANOVAModelSum ofSauresd

15、fMean SquareFSix1RegressionResidualTotal.147jea233im473.147.000801681,oooa3. Predictors: (Constant), Beginning Salaryb. Dependent Variable: Current Salaryc. Weighted Least Squares Regression- Weighted by WGT_iCoefficients3,1*ModelUrstandardized CoefficientsStandardized CoefficientstSigSGtd. ErrorBet

16、a1(Constant)Beginning Salary-460.1 OS2.054989.770.072734-.46528.349.642DOO3. Dependent Variable: 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(duì)預(yù)測(cè)值的散點(diǎn)圖，首先通過(guò)transform里的compute計(jì)算考慮權(quán)重后的預(yù)測(cè)值和殘差Compute VariableTsrget Varisble:preType Label.Numeric ExpressiorcPRE/冷qrtiyJGT*Code idGender genderDate of Birth bddeEducational Level (year.Employment Category j.3 Compute VariableTarget vsriable:residType & ILabeJ.夕 Employee Code idGender genderEducational