回归分析例题SPSS求解过程

回归分析例题SPSS求解过程1、一元线性回归例4.2.1为研究家庭收人与家庭食品支出的关系，随机抽取了 10个家庭，得到表421 的数据试根据这些数据：1）建立家庭食品支出对家庭收入的样本回归直线；2）预测当家庭收入为4 200元时，家庭的平均食品支出及其置信度 为95%的预测区 间.a4.2.1家庭收入与食品支出数撼单位：百元家庭12345678910家庭收人203()3340151326383543食品支出7981154810910SPSS求解过程:wd冋 Untithd SPSS Data EditorEilQ Zdi I 乂 i ow Rag Irar.zformdl（UI少呀|侗:位品支岀fc|D?io凉庭收入I食品支岀120.00 700230.009.00333.00BOO440.00n .0015.005.00613.004.00726.00BOO30.00io 00S35 009 001043.0010.001213.4Ror t xDescriptive StAti sft cs TablesC omp tar ageneral bnear Model Mi ice 6Models CorrelateLxiclin 口C1 ossifyRata ReductionHonpmelric TestsTimo Seri azSurvivilMui tipie ResporvseMi ssincAneLLysi s. Complex SampLaz1var1var1srLixtwurBinary Logistic.Mui 11 nom 1 Loci sti c - Ordinal.Probi t.KonlinaAr.Jtej Estimation.ZSt4icc Lst SaumrcB.Optimal Sc&Jinc.IX-20.0I230.Q333.0I&40.0I515.01S13.017260C83B.09350C1c430C1o1u1r1 Linear Regression,Qepen denrOKPate曲i力cdHetf?egAicriCoelkAnR&duWLSWcAfcr DRin 诫 toonCovaiicrccnixBkd： Idl如八、MethrflEnlei$kfcl 也P|ok：| Sjve.V3rLinear Regression: StatisticsPE痂w庇P Conlidcrccrtcrdg ：6 r&删疣 cfojml 口7 Model fitR equated changePa-i andpaildoxrdalicrADoHncaidagnoAs&讼CaneHcJ2122 Dt2324RegressionVariables ErrteredARemoved bb. Depen dent Variable:負品支出ModelVariabIGG EnteredVariables RemovedMethod1家庭收入。-Entera Ail requGstGd variables Gntered.Modol Summarya. Predictors: (Constant),收入ModelRR squareAdjusted R squareStd. Error of the Estimate1.951 a.904.892.73304ANOVAbModelSum or SquaresdfMean SquareFGig.1RGgressi on RGsidual T0t9l40.6014.29944.90018940.601.53775.559O OCPa. Predictors: (Constant).减庭收入b. Dependent Vari able：食品支岀Coefficients3ModelUnsta ndardiiedCoefficientsStan dardized CoefficientsSig.95% Confidence IntervalBSid. Error9etaLcv/er BoundUpper Sound1(ConsMj2.173?203.017OH.5123.833勰攵入.202.023.9548.692.000.149.256a DependentVariableAnn 支出判别：$ = Po+A=2.173+O.2ON,且x与的线性相关系数为R=0.951，回归方程的F检验值为75.559,对应F值的显著性概率是0.0000.05,示回归方程不具有显 著性。每个系数的t检验值分别是3.017与&692,对应的检验显著性概率分别为：0.017 (0.05)和0.000 (vO.05),即否定也就是线性假设 是显著的。二、一元非线性回归例4.3.1出钢时所用的盛钢水的钢包，由于钢水对耐火材料的侵 蚀，容枳 不断增大希望找出使用次数X与增大的容积Y之间的关系试验数据列于表 4.3.1. 4.3.1使用次数X与增大的容积Y的试验数据23456789X-6.42& 209.589.509.7010.009.939.9910111213141516y10.4910.5910.6010.8010.6010.9010.76SPSS求解过程:Uml:xlcd 9 屮（）0KditzorEi X c： EdLi. *t Ei c： w Bat aoim Artvi念5Independent 介 Ya iobb| I金次数XTrneCo佬 Ldbete n-Mcdeltr LroarQuodraic厂 Loontrrrio v 泡更r Ircrc 厂 Powei Inch connarr n 冲玄ion厂 Como7-nd V Gccvto 厂 S厂 EporcntbalI Loq 毗 cllpwamTwdSvfe.厂 DispleyANOVA tobteDependent Mth Rsq d.f.FSigf bOb1 b2 b3容积丫QUA .859容积丫CUB .9211236.64 0001142.84 0006.0927.7400 -.02904.1183 1.7068 -.1534.0046 cYObserved QuAdrcrtic Cubic所以，二次式为:y6.0927 + 0.7408% 0.029%2三次式为：K = 4.118 + 1.7068% 0.1534%2 + 0.0046x32、把Y与X的关系用双曲线拟合:作双曲线变换：次数X容积V IUvarvarV126.42.5000.1558233.20.3330.1220349.58.2500.1040459.50.2000.1053569.70.1667.10316710.001420.1000789.93.1250.1007899.99.1110.100191010.49.1000.0953101110.59.0900.0944111210.60.0830.0943121310.80.0760.0926131410.60.0714.0943141510.90.0667151610.76.0625.09261617181920TrartsformAnalyze Graphs 0丄IFJ. -LULLUHVJjdVI I dxouqN-SUV r -, e d/ r 3 k s g? I Y N A |押Q rrr ttr:su-oounb El Li 厂F川 W U VYX5 IIII O S Z QD3qsjBA 8ndc)3斗科 令忖 |K|M|E3|F5| = |E|g|co|JCD|cji|Jco0 8OS88X2燮CDK)三三U vY XTypeHabel.Eta&e1*2Jd2dI 厶 Ld H jjj JJ 鬥二 lid心iK8 看 bi(iI客积7-y I5.425CD01556238.20.333312x0349.68.26001044459.50.202010E3-55970.1旳71031710.00.1429I0CO89.9312501007a99.99.1111.100191010.49.1030ras3101110.59.0909OT44111210.60.0833CQ43121310.80.0769CO: 6131410.60.0714.094314行10.90.0657C91715161076.0626C929.xnoau: KcKEeffsionLinear Reeroesion: St atist cc窃VI uiQ次磁PoiteRcjnswzn Costtcisn，A7 E州rei& CaD(xi?ncc v Cozeancc matk18ResdwahBtoek 1 c/1Cl | % I UIJ j| I1Hextrtdepeojertlg)EUvMethod:Enter735slezbonVj ceibal coireiati:m CajirvsaiiP disgnzAbc?匚 omolHeb222242528272DaDyibnAVAUon fdYMPiu disgnzAbccA GuHeu .ukiJs: p广却1 C%恥wd A RegressionVariables EnteredjRernove (ibModelVariables En teredVariablesRemovedM ethod1V*-Entera. All requested variables entered.b. Dependent Variable: UModel Summarya Predictors: (Constant. VModelRR SquareAdjusted R SquareStd. Error of theEstimate1.968-.938.933.0042568ANOVAbModelSum of SquaresdfMean SquareFSig.1RegressionResidualTotal.004.000.00411314.004.000196.227.000aa. Predictors: (Constant), Vb. Dependent Variable: UCoefflcletrtsAModelUnsla rd 合蚀 8 CoefficientsStandardized CoefficientstSia.95% Confidence Interval for D0Std. ErrorBeiaLower BoundUpper Bound(Conslant).082.00244.514.000.078.086V131.00996814.008.000.ir.151a. Depen de nt Variable: U判别:(/ = 0.082-0.131V, L/ = = ,V= 1, V 与(/的相关系数为 R=0.968,回归方程系数的F检验值为196.227,对应F值的显著性概率是0.000 (pr)1J1IANY(te3IYdlue,Yalue,)ARSINhufiiexp) ARTAN(numexpr| CDFNORM(zvalue) CDF.BERNOULU(qzp)I OK | E&te | Reset | Idncel | Help |丄2345次数X23容积丫642V印00.1558Linear Regression10n121314151S792J212324056769101112137J15168.20989 509.7010.0093999104910.5910.6010.8010.60109010.76.3333?2500.2000.1667.1429J250.11111000.0909匚T0769-mu.C667.625.1220J0441053.1031.100010010953.0944.0943?0926砂次数X 妙夸积丫Depen 軌.R1刊uF电J*Viigd畔加附：vMethxi | EnterJLineaxRcELcssiun; Statislius区.0917.0929094TR 妙伽 $ion CoeflicieruP CoDtidence initivdb 厂 Coyaianc m沛仪F D/bnWaUon 厂 fe泄msed方jx&ics OuEiceouUdc:广 catetrMod(?l fitR equatedWc心Fell and portisl coneHbnsCdlrMri；idagnouCarcelHelpMsdciJdc 心 iuruRegressionVariables Elrtered/Removed bModelVariables EnteredVariables RemovedMethod1Entera. All requested variables entered.D. Dependent Variable: U1Model SummaryModelRR SquareAdjusted R SquareStd. Error of theEstimate1 Q73.959.956.0289852Predictors: (Constant,vANOVAbModelSum of SquaresdfMean SquareFSio1Regressi onResidualTotal.255.011.26611314.255.001303.190.000aa. Predictors: (Constant). Vb. Dependent Variable: U1wdCoetticletrts3ModelUn 虫 an dardized CoefficientsStandardized CoefficientsiSifl.95% Confidence IntewalforDBStd. ErrorBetaLower BoundUpper Bound(Con siani)2.458.013195.221.0002.4312 4 85V-1.111北-.979-17.412.000 1.2/y-.973a. Dependent Variable: U1判别；J/l = 2.458-I.IIIVf U = nyy = !xi V 与 t/1 的相关系数为 R二0.979,回归 方程的F检验值为303.190,对应F值的显著性概率是0.000 (0.05),表示线性 回归方程具有显著性，每个系数的t检验值分别是195.221与-17.412,对应的检 验显著性概率分别为：0.000 (vO.05)和0.000 (S min)-y1旳A12IS50A 330 296302.706 6279403.527125515.631 43514464.483 O28613415.815 24123435 540 B29121475.130 25120ZS 4”O30O24Cil5.301 O6312403 112531512374.4S3 373V764S 1 IS 232415494.656 9865393.S75 933O20434.521 2Q78374-670 O34e1CAN4.865 0IOO23554.933 63541748S 336 61 1316ao5 ooeO36IO4484 609 812O18495.270 1374*436N3851384503 377 238513363-S7A614614515 -484 9399514-5V1 915O21514.396 O4061354S.158 812o4O1955 g o5G5.2ZOO5Og4O5343O)g5o o39苕8543gO433Osi9 MuhinomisLogi Stic 0rdinn2:s ob F.Hon=neAr:Jeo chk Estjme.i 03.: yswcc LaazS2marasupbma- sc5g!RegressionVariables Efiteie (VRevn(Jvedba All requested variables entered. b Dependent Variable; Y3- predictors: (Constano.x3.xi.X2ModelVariables EnteredVariablGS RemovedMettiod1X3.X1.X2JEnterModel SummaryModelFR SquareAdjusted R SqusitQStd Error c(f the Estlrnald1.6823.339.295.8120246ANOVAbHod创Sum of squaresorMean SquareF8101RecressionResidual Total15.23629.67244.908345 心5.079.6597.702OOO4孔 Predictors: (Const&nO.X3. X1. X2b. DGPGndGni variable: YwdCoefficients*ModelUn standardized CoofliciQritsStandardized CoeflicientG18iQ95% Confidenco lnteivAlforBDStd. Error3etaLovzer Bou ndUpper Bound1(Constant)695.865803426-1 04820X1.151J 60.6172.663.011.38.282X2.108.037.6722.876.006.032.183X3036.0114： X3 401001.015057Q Dependent Variables判别：y = 0.695 + 0.161 Jr +0.108 甩+0.0363 与)，的复相关系数为20.582,0归方程的F检验值为7.702,对应F值的显著性概率是0.000 (V0.05),表示线性回归方程具有显著性，每个系数的t检验值分别是0.803、2.663、2.876与3.401,对应的检验显著性概率分别为：0.426 (0.05)v 0.011(v0.05)、0.006 (0.05)和 0.001 (0.01) ,glj除小,结果是：幻 I X2IX3200|10.QOGO4 23CO口7.009 00403 6604X15.0014.00464 48cO|X212.001.0D3.0020.0043545 M6054970禺X33.0D12.004031120 511E03.0017.00646.006.003997.008 0C3710.0023.0065ts 773.0016.006011.OD18.004913B.OD4.0050J4600140051TsOD21.0051JG2.0014 QOS1Ti7.0012.00566 07SO16.00.00321S0JJ6.0016.00456 0702D.OD15.00524 73CO219.0Dao4C4E8CO22234 000060017.003247312702 6TCO249.00.00a3 7170-25 -2.0016 00393 89409.006.003fl2 70EO2712.0D5.00515G3102B5.0D13.00415.8 ICO2912.0070047513CO30OD24.00615 3910HP 毗VIVarLabiev/evHn 1y.ICCJQ.,iSTSS 32.0 for Ytalail 窃丫gjr-dependeni|2) 沁2CoxolHolp13yMoihocl EriGfa0EDSection Vah*l40 IEoce Late(6)IV/LSMgtf:I 蔻睡 t03 ; Rolo. Save. Qpicno. IILd _SPSScar i cModel SummaryModelRR SquareAdjusted R SQuareStd. Error of the Estimate1485.235.202 8641283a. Predictors: (Constant).X3, X2ANWAbModelSum of SquaresOfMean SquareFSig1Regressi onResidual Total10.55934.34944.908246485 2 B0.7477.070.0024a. Predictors: (Constant).X3t X2b. Dependent VariablesCoefficients3WodelUnstaridardized CoelficieritsStand ardized CoefficientstSiQ.95% Confidence lnlerAalforBDStd. ErrorBetaLov/er BoundUooerBound1(ConGtentji2 614.5654.4510001.3773.662X2023.021.1461.098.270-.019066X3036.011.4303.239002.014.059a. Dependent Variable: Y由于结果中又出现七关于y的线性关系不显著(Sig=0.2780.01),剔除勺，结果是：Model SummaryModelPR SquareAJJusted R SquareSid. Error o( the Estimate1.464.21 S198.8660188a. Predictors: (Constant). M3ANOVAbModelSum of SquaresMean SauareFSia.Regressio n Residual Totsl9 &5935 24990B147419 65975012.879.001-3. Predictors: (Constant). X3b. Dependent variable： YCoi4TicierrtsaModelUnstandardized CoetncientsStandardized CoeHi dentstSiC.95% ConfkJe(x:e interval for BEStd ErrorB9tQ-ov/er BoundJpper Bound(Constant)2.647653i.786OOQ1.5343 750X3.039011.4643.589mil17IHI3. Dependentvariable: Y显然，心关于y的线性关系显著(Sig=O001 0.01)