回歸分析例題SPSS求解過程

1、回歸分析例題SPSS解過程1、一元線性回歸W4.2.1為研究家庭收入與家庭食品支出的關(guān)系，隨機(jī)抽取了10個(gè)家庭.得到表4.2.1的數(shù)據(jù).試根據(jù)這些數(shù)據(jù)：1）建立家庭食品支出對家庭收入的樣本回歸直線；2）預(yù)測當(dāng)家庭收入為420。元時(shí)，家庭的平均食品支出及其置信度為95%的預(yù)測區(qū)間.表4.2.1惠雇收入與食品支廿般據(jù)單位工百元家蜓12345678g1。家庭收入20303340151326383543食品支出7981154810910SPSS解過程:Uirti-tlod-SPSSDataHdn_i:oitFxleEdL£tVicwDa.t.Traxs£oi-mAxkialyzeG

2、y4KsU1.1Xi±.iesWxxxdLowH工p人|Q|昌1回1J_dI由I*J丁fT口用廠|式限10:食品支出1O家庭收入1食品支出1var|var|var|varI120.00?？诳?300O9OO333.0080D440.0011.OD61500S.OO813OO4OO72SDOaon833.001O.ODy3Sno9.OU104300_1a1112pTZTTri1itied-SPSS口足，總。rEile£ditMiewDataIransf0rm|graphsUtilitiesHiridowHelpUQ呂里|G1=力eeript.iven51ft-tistickT

3、ables卜CompareM.eana4G<nex"LiliearModl加而i些adMiodais10：備品支出p10家庭收入1食品支出1varvarvar120.0030.0033.0040.0015.0013.0026.003B.0D35.0043.007.009.006.00T1.005.004.006.0010.009.00234RuEre：5，ionLift*"-.5LgglLineii-*Rat*Raduetiaxt33-Jffonp-aretricTests.Ti_meSeiries"SuJTVl.v-ll.口fflultipl«R

4、后pon與q歸Nii£3-1nsJ£alu.erfkjialy£i-3.CompieKSamples.QurireEstima.t.1on.6Bin-ajryLoictic.Mult*1JwiEtig.Orjjiri-aJL-Probit.7891010.00KonJ-inaur.ghtl？Etim4itian.：£=SLaEsLuam七Sq.u.4res.1512(007.0323C009.0333:008.0344C.0011.0J51E,005.0JJ1-004,022E008.0J13E0010.0J3E009.03OKHe5elhdepertf

5、erJfs!母冢就入SdectaiVdicUe:Help£«eLab5l5:ResideWLSWeghi:$!cndc(dcevatcns22LinearRegressionLinearRegression:Statistics|Gjnl泣eCaicdRegressionCce;lcenlSPEstmatesvCcttifercBHen，覆-CovaiiartemalriK17ModelfitrRscwiedchangerQesairfvesrPalcndpailialccfrefetnjFCojlrwiMd叨煙6“Cepjrxfenl：Blcckloll2416V115就

6、比JP&愴.|Save.-Dyibin-Watsonr£&附加（1即而什。跳節(jié)c而佗（3+RegressionVariablesEnteredjRernovedbModelVariablesEnteredVariablesRemovedMethod1家庭I攵入iEntera.Allrequestedvariablesentered.b.DependentVariable:便品支出ModelSummaryModelRRSquareAdjustedRSquareStd.ErroroftheEstimate1.951a,904892.73304aPredictors:(Co

7、nstant),家庭收入ANOVAbModelSumofSquaresdfMeanSquareFSig.1Regression40.601140.60175.559.0003Residual4.2998.537Total44.9009a.Predictors:Constant),家庭收入b.DependentVariable：食品支出CoefficienlsBModelMndardlzedCoefficientsStandardizedCoefficientstSig.95%ConfidenceIntervalforBBSid.ErrorBetaLowerBoundupperBound1位喇2

8、.1737203.017.5123.333家跳人.202023-i：i8.692000,149.266a.DependentVariable判別：？=4十?=2173+0.202(,且x與y的線性相關(guān)系數(shù)為R=0.951,回歸方程的F檢驗(yàn)值為75.559,對應(yīng)F值的顯著性概率是0.000<0.05,表示線性回歸方程具有顯著性,當(dāng)對應(yīng)F值的顯著性概率>0.05,表示回歸方程不具有顯著性。每個(gè)系數(shù)的t檢驗(yàn)值分別是3.017與8.692,對應(yīng)的檢驗(yàn)顯著性概率分別為：0.017(<0.05)和0.000(<0.05),即否定H0,也就是線性假設(shè)是顯著的。二、一元非線性回歸例4,

9、3.1出鋼時(shí)所用的盛鋼水的鋼包,由于鋼水對耐火材料的侵蝕,容積不斷增大.希望找出使用次數(shù)X與增大的容積丫之間的關(guān)系,試驗(yàn)數(shù)據(jù)列于表4.3.寰4.3J使用次數(shù)X與增大的容積Y的試驗(yàn)數(shù)據(jù)若234567896,428.209.589.509.7010.009.939.99蒼10tl1213141516y)10.4910.5910.6010.8010.6010.9010.76SPSSt解過程:0Q|W|吧I國I“I年同函垂問3效IS:喜審*IO.TS次數(shù)又容枳VIvar|var126.42233.20349.58459.60569.706710.00789.93e99.9991O104910111O5

10、91112106012131O6Q131410.601415IO90151610.7161、Y與X的二次及三次多項(xiàng)式擬合:謝。昌罔-3c?R卷ROUt£tiveStatisticsk*HttnxLinearModel*odels卜It4司HDescripTabiestrGeneralMixedM15IEK1S次數(shù)X容積¥|UIvar126.42r1.859423B.20L2.10413d9.5545950|Regression置Linear.569.70Loglinear>ClassifxDataReductioil上Scale>genpaarMttrieTts

11、ts>TimeSeries量Swrvivil>MjjltipleRe印onse卜MissinzValueAnalsiz.Cm-veEstimation.6710.00BinaryLogiitia789.93MultiziomialLogistic.Ordinal.,.Frobi匕B99.99g-1010.4910111059Nonlinear.iSightEstirnfttin.r.2-StsgeLeaitSquired.-111210EO121310.80131410EOCompleacSamplesOptimalScaling.14151090IU.UUULJ.3Ir15161

12、0.761600009292.375B171819AnalyzeFileEditViewDataTraitsformGraphsUtilitiesWindowHelp次數(shù)*容積丫126.42238.3034S.5S459.6056970671000739.93899.9991U10.49101110.50111210.601213103013141060141510.9015ie10.7620CurtreEstaationVUV1B管您合DependentMthRsqd.f.容弗只¥容枳丫QUA.859CUB.921Q印enderM就#Ymiatfe:元TjffleCaseLabel

13、s:mModelsLinear*Quadratic一LogarithmicF叁Mg廠lveiseI-PowerF口中國MQVA3*EastsBesetCahcelHelpBIncludeconstantinequatorRPlatrnocfefe廣Coflcoiid廠Growth廣£廠E*ciEntiallLogisticU即rbmnd|Save.FSigfbOb1b2b31236.646092774OB-.02901142.B4411B31.7DEB-.1534.口口4£OYObservedQuadkmtic:Cul.dc2所以，二次式為：Y=6.09270.7408x-

14、0.029x2_3三次式為：Y=4.1181.7068x一0.1534x20.0046x32、把Y與X的關(guān)系用雙曲線擬合:作雙曲線變換：ULv次數(shù)XI容積YVIuvarvarv126.42.5000.1558238.20,3330.1220349.58.2500.1040459.50.2000.1053569.70.1667.10316710.00.1420.1000789.93.1250.1007899.99.1110.100191010.49.1000,0953_101110.59.0900.0944111210.60.0830.0943121310.80.0760.0926131410.

15、60.0714.0943141510.90.0667.0917151610.76.0625.09261920rQ第叟卜ICompute.llnVisualBander.次數(shù)XCount.RankCases.AutomaticRecode.V1U1varvar1_2231.85942.1041_34CreateTimeSeriesReplaceMissingRandomNumberSeed.122SA7_45lues.2.2513_562.2721672.302678Kunre2.2956_899.999.0000.10012.301691010.4910,0000.09532.35041011

16、10.5911,0000,09442.3599111210.6012.0000,09432.3609121310.8013.0000.09262.3795131410.6014.0000.09432.3609141510.9015,0000.09172.3888151610.7616.0000.09292.3758TransformeEditViewRataAnalyzegraphsUtilitiesWincowHelp次數(shù)X容積Y126.42238.20349.58459.5056二9.706710.00789.93899.9991010.491011二10.59111210.6012131

17、0.80131410.60141510.90151610.7616CoaputeVariableTargetVariable:NumericExpres$ionType(Label.XY數(shù)職1次容VUV1U1畛金臉畬1/溶積Y*|<I>IFufKtions:|J總加UUiJd士l生臼QjJjJ回djJdllDeleteABS(numexpr)ANY(te$lvaluezvaluez.)ARSIN(numexpc)ARTAN(numexpr)CDFNORM(zvalue)CDF.BERNOULLI(q,p)OK|Easte|Reset|Caned|Help|171819次數(shù)XJ容積Y

18、CoaputeVariable126.42TargetVariable:NumericExpression238.20M1/次數(shù)x3J49.58950Type&LabeL|679701000或容積YLU+I<I>I7|8|9|Functions:|789109.939.991049<f>V<j>U磅VI，U1土I山13/業(yè)皿ABS(numexpr)aANYJtest,value,value,.)ARSIN(numexpr)ARTAN(numexpr)CDFNORM(zvalue)COF.BERNOULU(q,p)101110.5911J2121310

19、601080H113I4141510.6010.90IOK|Raste|Reset|Cancel|Help|15161D7K一一一一一1次數(shù)X容積YVUI126.425000238203333349.582500459.5020006970166767KE001429789.93.1250_89999111191010.49.1000101110.5909091112106008331213UTK).0769131410600714141510900667151610.76062516171821一LinearRegressionV<U1QcpcndcntBlock1ol1andepen

20、den4s):EnterMethodSfllecbonVariableJPasteResetXCancelHdp4RegressionVariablesEnteredjRemovedbModelVariablesEnteredVariablesRemovedMethod1VaEntera.Allrequestedvariablesentered.b.DependentVariable:UModelSummaryModelRRSquareAdjustedRSquareStd.ErroroftheEstimate1.968.938.933.0042568a.Predictors:(Constant

21、),VANOVAbModelSumofSquaresdfMeanSquareFSig.Regression.0041.004196.227.000aResidual.00013.000Total.00414a.Predictors:(Constant),Vb.DependentVariable:Ucoemuients0ModelunslandardizedCoefficientsstandardizedCoefficientst95%ConfidenceIntervalforBBStd.ErrorEstaLow&rBoundUpperBound1(Conalarrt).082.0024

22、4,514.000.070086V,131,009,96314.DOB.000,111151a.DependsmOanatue'U11判別：U=0.0820.131V,u=-,V=-,V與U的相關(guān)系數(shù)為R=0.968,回歸yx方程系數(shù)的F檢驗(yàn)值為196.227,對應(yīng)F值的顯著性概率是0.000(<0.05),表示線性回歸方程具有顯著性，每個(gè)系數(shù)的t檢驗(yàn)值分別是440514與14.008,對應(yīng)的檢驗(yàn)顯著性概率分別為：0.000(<0.05)和0.000(<0.05),即否定H0,也就是線性假設(shè)是顯著的。Y13、把Y與X的關(guān)系用倒指數(shù)函數(shù)擬合：Y=aex,則lnY=lna

23、+bx令U1=LN(Y),V1=V=1/x,有U1=c+bV1.我數(shù)X容積Y|126.42238.20349&_459.5C_569.705710.0C_799.93_899.999io10.J9WiT10.5S1?1210.6012131Q.8C131410.60U1510.90151610.76MlCoiputeVariable16TargetVaiiable：TypeJ；Label.NumericExpressionABSfnunnexprl酬1悔虬丫目電丫疝/一.)AFISIN上廊即。AFlTANnwmej(prjCDFNORM(zvaluB)CDF.BERNOLJLU(q,p

24、)K/4>-(-1：".次數(shù)X容積Yur1216.42,5000.1558238.20.3333.1220349.5825001044459.5020001053569.701667.10316710.0014291000789.931250,1007899.99.1111.100191010.49.1000.0953101110.590909,09441112106008330943121310.8007690926_131410.6007140943141510.9006670917151610.76062509291718%LinearRegression粉次數(shù)X粉容積Y

25、4>v6VlDependent:EF¥ui-Block1oHncfependW弓VMethod:|EnterLinearRegression:StatisticsRegressionCoefficientsvFstimates3Cof/idenceintervafcCovanancematrixResidualsFDyrbin-V/at$onr-£asewi$edagnosticsGOuUecrjtudeCz三rrrrModdftR$qud(edchangeQescriptivesPartandpartialconeiahon$Colinearitydiagnosti

26、csContinueCancelHelp，RegressionVariablesEnteredjRemovedbModelVariablesEnteredVariablesRemovedMethod1VaEnteraAllrequestedvariablesentered.b.DependentVariable:U1ModelSummaryModelRRSquareAdjustedRSquareStd.ErroroftheEstimate1.979a,959,956.0289852a.Predictors:(Constant),VANOVAbModelSumofSquaresdfMeanSqu

27、areFSig.1RegressionResidualTotal.255,011.26611314.255.001303.190.00(Pa.Predictors:(Constant),VbDe»p©ndntVariable:U1Coefficients1h/lodelnslandardizedCoefficientsStandardizedCiDgfficigm忸tSig.95%Con1idGncIn加rvalfci門日BStd.ErrorBetaLowerBoundUpperBound1(Constsnt)V2.458-1.111,013.064-.9791135.22

28、1-17.412,000,0002J311.2492.185-.973a.DependentVariable:Ui判別：U1=2.4581.111V,U1=lny,V=1/x,V與U1的相關(guān)系數(shù)為R=0.979,回歸方程的F檢驗(yàn)值為303.190,對應(yīng)F值的顯著性概率是0.000(<0.05),表示線性回歸方程具有顯著性，每個(gè)系數(shù)的t檢驗(yàn)值分別是195.221與-17.412,對應(yīng)的檢驗(yàn)顯著性概率分別為：0.000(<0.05)和0.000(<0.05),即否定H。，也就是線性假設(shè)是顯著的。三、多元線性回歸例4.4.1在平爐煉鋼中，由于礦石與爐氣的氧化作用，鐵水的總含碳量在不

29、斷降低，一爐鋼在冶煉初期總的去碳量y與所加的兩種礦石的量天、德及熔化時(shí)間火3(單位,5mi口)有關(guān).經(jīng)實(shí)測某號(hào)平爐的49組數(shù)據(jù)如表4.4.1所示.求Y對工，Xs的線性回歸方程，檢驗(yàn)回歸方程和回歸系數(shù)的顯著性.如有不顯著的變量，清剔除之并求剔除不顯著的變量之后的回歸方程一4C4-4.1集¥鹿盧的仆主且安*1我文加f珀號(hào)*<ffl)(5minJ.<T>中9工1CtW)H*(*W>-Ha,(5mln)vCt)H2OKSO4.33<J2q6392.706627g4CJ27133SI5.631435464.AH3ON片呂13415.81524123435.54G&

30、#171;N9127475JI30之51ZO右鼻午.497n30ClN4tbL5.O63IN403,112531512374.43M73ITG45.118233415494.方54QSW5393.875Q33ONO4手4.521N97舊374u670O34G16424.8d5OIOO23S34.Q5364174S5.356小I131660S.006O361O44S4.609后12flIKay5,衛(wèi)13"7414362.3S1513S4505.377N385133G3.8小鼻G144515.4H493gg8SI4.1915o21514.(>40后135-158B163145】5.

31、丘行4三415KLOO$.©三73177125<5行.<1795425I144M.g石口IS16O483-194H6&34.3y7O194s1-6455,SO7644N554.<162工20Ot5524730«5-457目502-N9O5SL9O4。4.6SO54W454.7113NN4£>323.1Hzi7247IO54.S3ION21<I"7丁之.6104-4S317<S45.3637N4O443,71744913726.07712523.5946X1IX2X3Yvarvar12.00|18.00504.3

32、30027OO9OO403648035OO14OO4644830412OO1OO3OO4355-460520OO6-45.497063.0012.0017.00403.112073.00645.118086.005.00393.875097OO8OO37467001OOO23OO55A9530-13OO16OO605006012OO18OO495.270013e.oo4.00505.3770146.0014.00515.484015OO21OO514.5960163OO14OO515664017ZOO12OO566OZ9Oia1BOO6.00OO48321901916OO455.007020O

33、O15.00524.7300219.00OO404.6800224.006OO323.127023OO17OO47261002-49OOOO44371ZO252.0016OO393.8940269.006.00392.70602712.005.00515.6310286.0012OO13.00415.8150297OO475130030OO24OO6159TOucc1JDaiXaVIewXVariat>leVjLew/Fil<aEditViowDatATr1GrapKsUtilitiosWindowHalp/I。昌I回I_|也|R«ortsDazcrix>tivaS

34、stics:刈1：XITablasX1|X2CompareMoans12.00|18.00Gon。#alLinaorModal27OO9OOMixedModels35.0014.00Correlate，III412.0051003.0020OOL&dixi«r>Qui-vcEstimation.63.0012.00Cl。二二i£?Dini&ryLoiktic.73.0017.00DataReduetionMuitino<ni«0.L.ox；iStic.§9500ova。Ordinal.y/.uubf.UUdcnQavnocyl

35、，liProbit.10.0023.00113nniannMuifinl12OO18.00MissincVlueAnix2一SQa匕。LeastSquaures.138.004.00ComplexSamples146001400C1OptimalScaling.15OO21.005145960163.0014.00515.66401770012.0056607901816OO.OO4832190196.0016.00455.0070200015.005247300219OO.OO4046800224.006.00323.1270230017.00472.6100249OOOO4437T7O25

36、2.0016.00393.8940269.006.00392.70602712OO5OO51&B3TD2B6.0013.00415.81502912.007.00475.1300RegressionVariablesEntered/RemovedbModelVariablesEnteredVariablesRemovedMethod1X3.X1.X2aEnteraAllrequestedvariablesentered,b.DependentVariable:YModelSummaryModelRRSquareAdjustedRSquareStdErroroftheEstimate15

37、82.3392958120246aPredictors:(Constant).X3.X1.X2ANOVAbModelSumofSquaresdfMeanSquareFSig.1RegressionResidualTotal15.23629,67244.908345485.079,6597.702.OOCPaPredictors:(Constant).X3.X1,X2bDependentVariable:YCoeTficienls"hdodeiUnstandardizedCoefficientsstandardizedCoefficients1Sig.95%ConficlencBInl

38、ervalforBBstd.Error日B啟LowerBoundupperBound1(Canslain,695,665.803T,426Wmbt2.437X1,161,060.6172.663.011,039.282X2108.037.6722.876.00BX32,103X3,036,011.4213.401,001,015.0573-DependentVariable：v判別：y=0.695+0.16翻+0.10&2+0.03&3,x1,x2,x3與y的復(fù)相關(guān)系數(shù)為R=0.582,回歸方程的F檢驗(yàn)值為7.702,對應(yīng)F值的顯著Tt概率是0.000(<0.05)，表示線性回歸方程具有顯著性，每個(gè)系數(shù)的t檢驗(yàn)值分別是0.803、2.663、2.876與3.401,對應(yīng)的檢驗(yàn)顯著性概