回归分析报告例题SPSS求解过程

标准文档标准文档标准文档标准文档回归分析例题求解过程、一元线性回归例4.2.1为研究家庭收入与家庭食品支出的关系，随机抽取了10个家庭，得到表4.2.1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4200元时，家庭的平均食品支出及其置信度为95%的预测区间.«4.2.1家庭收入与食品支出数据 单位:百元家庭12345678910家庭收入20303340151326383543S解过:隹：981154810910[===]Untitled-SPSSDataEditorFileEditViewDataTransformAnalyzeGraphsUtilitiesWindowHelp曲口|昌I吗c|c|¥T口|用n囱10:食品支出 10家庭收入I食品支出varvarvarvar120.007.00230.009.00333.008.00440.0011.00515.005.00613.004.00

，RegressionVariablesErrtered/RemnvedbModelVariablesEnteredVariablesRemovedMethod1家廖攵久aEntera.Allrequestedvariablesentered.b.□即日nd日ntMariab回食品支出ModelSummaryModelRRSquareAdjustedRSquareStd.ErroroftheEstimate1,951a,904,892,73304a.Predictors:fCcmE日nt),家庭收入ANOVAbModelSumofSquaresdfMeanSquareFSig.1 Regression40,601140.60175,559,000aResidual4.299S.537Total44,9009a.Predictors:(Ccinstant),家庭收入b.□日pend日ntVmrimble：食品支出Coefficients3ModelUnstandardizedCoefficientsStandardizedCuHfricientstSig.95%ConfidenceIntervalfor日BStd.ErrorBetaLowerBoundUpper日口」nd1 (Constant)家国攵丸2.173,202,720.023.9513.0178.692.017,000,512.1493.833,256a.DependentVariable:#品支出八 八判别：y=B0+B1=2473+0.2o2x,且x与y的线性相关系数为，回归方程的检验值为，对应值的显著性概率是 表示线性回归方程具有显著性，当对应值的显著性概率 表示回归方程不具有显著性。每个系数的检验值分别是 与，对应的检验显著性概率分别为： （ ）和（ ），即否定H，也就是线性假设是显0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,容积不断增大.希望找出使用次数X与增大的容积V之间的关系.试验数据列于表表3.L表4.3.1使用次数X与增大的容积y的试验数据23456789y6.428.209.589.509.7010.009.939.99与10111213141516y10.4910.5910.6010.8010.6010.9010.76

求解过程:q牌|吗|g■SB阖■巴曲R]嗣©FileEditViewDataTransformAnalyzeGraphsUtilitiesWindowHelp15：容积丫FileEditViewDataTransformAnalyzeGraphsUtilitiesWindowHelp15：容积丫欷数X容积Yvarvarvarvar126.42238.20349.58459.50569.706710.00789.93899.9991010.49101110.59i与1的二次及二次多项式拟认合:4n■1j■1non10.76FileEditViewDataTr：=irL5furrriArL：±lyze|aphsUtilitiesWindowHelp百u膏吗J号korts. ..力Descriptive2-iaii sties rTables ►Compare也曰mw 卜GerLHi-：dlLine：!!" Model .MixedModele .Correlate 卜15:廿:数北16欷数X容积YU1varvar126.421.8594238.202.1041349.5S?小97459.50Regi-PEEion►Line：!!-...56970L£glirLe：ai- .Classify .DataReduction .bi：ale .NurLp：di-：iiTiHti-ir TestE .T二 C . 心CurveEEtimation...6710.00BiTi^ryLogistic...Milltinomi：alLogistic...Urdin：!!...Frobit...789.93899.9991010.49101110.59111210.60MultipleReEporLse .Missingy：±lueAnalysis...CumplexS：UTipleE .WeightEstimation...2-StageLeastSquares...121310.80131410.60Ujitim：11Seeing...141510.901□.UUIJIJ.U31i'1516107616,0000,09292.375819DependentMthRsqd.f.FSigf容积YQUA.8591236.64.000容积YCUB.9211142.84.0006.0927.7408-.02904.11831.7068-.1534.0046OObservedQuadraticY=6.0927+0.7408x—0Y=4.118+1.7068x—0.1534x2+0.0046x3的关系用双曲线拟合：昌吗| rLHCuilP rViEu：ilB：irLiieK...在数X次数XCmunt.一RankCases...AntomaticRerode..iV1U1varvar121.859423〕2.104134CreateTimeSeriezReplaceMissing：V：±RandomNumberSeed2.259745lues... J2.2513562.272167—)2.302678Kimrendingl^rstlelorme r2.2956899.999.0000,10012.301691010.4910,0000,09532.3504101110.5911,0000,09442.3599111210.6012,0000,09432.3609121310.8013,0000,09262.3795131410.6014,0000,09432.3609141510.9015,0000,09172.3888151610.7616,0000,09292.3758标准文档标准文档标准文档标准文档a.Predictors:(Constant),Va.Predictors:(Constant),Vb.DependentVariable:U12334455667788991010111112121313141416容积Y6.428.209.689.509.7010.009.939.9910.4910.5910.6010.8010.6010.90MCoMputeVariableTargetVaridble:Type8cLabel...次容wUV1U1叔⑨叔叔叔叔,JumericExpression:>l2d2dll(]I

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_d-l_J0zlFunctions:.^BSfriumexpr]1i,N'r'itest..value.,value.....]ARSIN(numexpr],^RT.AN|'nurnexprlCDFNORMlz'v'aluelCDF.BERNLilJLLI(q..p：|OKPasteResetCancelHelp16771819就数X容积YVU■1LinearRegression126.42,5000,1558■- a238.20,3333,1220砂校数*砂容积Y叔n叔⑥LI1dependent:OKPflShA349.58,2500,1044III城u459.50,2000,1053DIUUI\1UI1Reset569.70,1667,1031Previous|Next6710.00,1429,1000independent(s):Cancel789.93,1250,1007a叔nHelp899.99,1111,100191010.49,1000,0953101110.59,0909,0944Method:|Enter 二］111210.60,0833,0943121310.80,0769,0926SelectionVariable:131410.60,0714,0943LI.inearRegressioiStatistics141510.90,0667,0917l:151610.76,0625,0929RegressionCoefficients*Estimates*Confidenceintervals；I-Covariancematrix.ModelfitFlsquaredchangeDescriptivesContinueCancel1Partandpartialcorrelations HelpCollinearitydiaanosticsnesiauaisI Durbin-WatsonCasewisediagnosticsf*OutliersoutsideCAllcasesp standarddeviations7RI I I I I*RegressionVariablesEmteredJRemovedbModelVariablesEnteredVariablesRemovedMethod1VaEnter日.Allrequestedvariablesentered,b.DependentVariable:UModelSummaryModelRRSquareAdjustedRSquareStd.ErroroftheEstimate1,968a,938,933,0042568aPredictors:(Constant),VANOVAbModelSumofSquaresdfMeanSquareFSig.1 Regression,0041.004196,227,000aResidual,00013,000Total,00414

Coefficients3ModelUnstandardizedCoefficientsStandardizedCoefficientstSig.95%ConfidenceIntervalforBBStd.ErrorEietaLovv'er日匚mndUpper日Durid1 (Constant).082.00244,514.OOLi.078.086V.131.009,96814,008.000.111.161a.DependentVariable:U11判别：U=0.082—0.131V,U=-,V=—,V与U的相关系数为.回归

yx方程系数的检验值为.对应值的显著性概率是 （ ）表示线性回归方程具有显著性，每个系数的检验值分别是 与，对应的检验显著性概率分别为：也就是线性假设是显著的。对应的检验显著性概率分别为：也就是线性假设是显著的。）和（ ），即否定H，0b 1、把与 的关系用倒指数函数拟合：Y=aex，则lnY=lna+b-x令（N 有1234次数乂2345容积,Y6.428.2口9.589.501234次数乂2345容积,Y6.428.2口9.589.50HIConputeVariableTarqetVariable:-NumericExpression:LN|容积丫]Type&Label...07ZKT_d_8j_9jLj_d_dIzJ_±QJDeleteFunctions:.^BSfnurnexpr]ANY(testvalue,value,..JARSIN(numexpr)ARTAN(numexpr)CDFNORM(zvalue)CDF.BERNOULLI(q,p)Help♦RegressionVariablesEnteredJRemovedbModelVariablesEnteredVariablesRemovedMethod1VaEnter日.Allrequestedvariablesentered.b.DependentVariable:U1ModelSummaryModelRRSquareAdjustedRSquareStd.ErroroftheEstimate1,979a,959,956,0289852a-Predictors:(Constant),VANOVAbModelSumofSquaresdfMeanSquareFSig.1 Regression,2551.255303,190,000aResidual,01113.001Total,26614标准文档标准文档标准文档标准文档Coefficients3ModelUnstandardizedCoefficientsStandardizedCoefficientstSig.95%ConfidenceIntervalfor0日Std.Error日巳也Lower日口undUpper日口山记1 (Constant)2.458-1.111,013,064-.979195,221-17.412,000,0002.431-1.2482.485-.973a.DependentVariable:UITOC\o"1-5"\h\z判别：U1=2.458-1.111V,U1=Iny,V=1/x,V与U1的相关系数为 .回归方程的检验值为 .对应值的显著性概率是 （ ）表示线性回归方程具有显著性，每个系数的检验值分别是 与.对应的检验显著性概率分别为： （ ）和（ ），即否定H，0也就是线性假设是显著的。三、多元线性回归例4.4.1在平炉炼钢中，由于矿石与炉气的氧化作用，铁水的总含碳量在不断降低，一炉钢在冶炼初期总的去碳量丫与所加的两种矿石的量Xi、X?及熔化时间X3（单位:5min）有关.经实测某号平炉的49组数据如表4.4.1所示,求Y对X-X2，X3的线性回归方程，检验回归方程和回归系数的显著性.如有不显著的变量，请剔除之并求剔除不显著的变表4.4.1某号平炉的49组实澳I数据编号孙（槽）22（槽）(5min)y(t)编号孙（槽）之2（槽）小(5min)y(t)1218504.33022696,392.7066279403.648527125515.63143514464.483028613415.81524123435.546829127475497030024615.39106312403.112531512374.45337317645.118232415494.6569865393.875933020454.5212978374.670034616424.865010023554.953635417485.356611316605.006036104484.609812018495.270137414362.38151384505.377238513363.874614614515.48493998514.591915021514.596040613545.158816314515.664541581005.437317712566.079542511443.996018160483.21944386634.397019616455.807644213554.0622

昌|与c=C?Rejirirts 卜Descriptive3tatistice 卜Tables 卜Cump：ireMeidTLE k坛已neralLin曰arMudel 卜MixedModels .CurrelatH 卜if1:XI 2X1X212.0018.0027.009.0035.0014.00412.003.00Regression►Line：=Lr...51.0020.00Lugline：!!- >Classi 卜DataReduetion ,b-cale .Nunp：ir：dJTietrii：Tests 卜Ti_meseries kSm-viv：il 卜MultipleReEpunEH ♦Mieeingy：ilueAnalyMim...ComplexS：djnpleE 卜CurveEstimatiun...63.0012.00BinaryLogistic...MuitinumialLugieti.OrdirL：±l...Probit...73.0017.0086.005.0097.008.001023.00Nijnlineiif...出eightEstimation...£-StageLeastSqu：ireE...113.0016.0012,0018.00138.004.00OptimalSi：：dling...146.0014.00□I□.4O4U15,0021.00514.5960163.0014.00515.6640177.0012.00566.07901816.00,00483.2190196.0016.00455.807020,0015.00524.7300219.00,00404.6800224.006.00323.127023,0017.00472.6100249.00,00443.7170252.0016.00393.8940269.006.00392.70602712.005.00515.6310286.0013.00415.81502912.007.00475.1300ArL：ilyzeGraphsU+ilitiesWindowHelpX1X2X3X1X2X3Yvarvar12.0018.00504.330027.009.00403.648035.0014.00464.4830412.003.00435.546051.0020.00645.497063.0012.00403.112073.0017.00645.118086.005.00393.875097.008.00374.670010,0023.00554.9530113.0016.00605.006012,0018.00495.2700138.004.00505.3770146.0014.00515.484015.0021.00514.5960163.0014.00515.6640^7Fi07cIF!FileEditViewDataIranzif口rm，RegressionVariablesErrtered)RemnvedbModelVariablesEnteredVariablesRemovedMethod1X3,X1,X2aEntera.Allrequestedvariablesenteredb.DependentVariable:YModelSummaryModelRRSquareAdjustedRSquareStd.ErroroftheEstimate1.582a.339.295.8120246aPredictors:(Constant),X3,X1,X2ANOVAbModelSumofSquaresdtMeanSquareFSig.1 Regression15.23635.0797.702.OLIO3Residual29.67245.659Total44,90848a.Predictors:(Constant),X3,X1,X2b.DependentVariable:Y

Coefficients3ModelUnstandardizedCoefficientsStandardizedCoefficientstSig.95%ConfidenceIntervalfor日BStd.ErrorBetaLower日QuridUpperEiourid1 (Constant),695,865,803,426-1.0482.437XI,161,060,6172.663,011,039,282X2,108,037,6722.876,006,032,183X3,036,011,4243.401,001,015,057aDependentVariable:Yy=0.695+0.161x+0.108x+0.036xxxx-的自如呈玄判别： 1 2 3,x，x，x与y的复相关系123数为 .回归方程的检验值为 ，对应值的显著性概率是( )表示线性回归方程具有显著性，每个系数的检验值分别是 、2.6、623.8与763.4，0对1应的检验显著性概率分别为：0.4(2>60.)0、05.0()o( )和( )，即对于H:P=0,i=1,2,3,0i否定H，也就是关于各自变量的线性假设是显著的，而对于H:P=00 00接受H0书解特点：a=0.01,x关于y的线性关系不显著( )剔除x,结果11是：X1X2>3Y■ETFTtPGT"Rprpfnn512.0018.00504.3300 笆 lr27.009.00403.6480砂刈Dependent:OK35.0014.00464.4830叔X2O1叔Y—412.003.00435.5460耕乂3nBlock1of1paste51.0020.00645.4970Previous|NextJReset63.0012.00403.1120Cancel717.00645.1180.j.IJU砂X2a|86.005.00393.8750BiHelp97.008.00374.6700I___I10.0023.00554.9530Method:|Erter113.0016.00605.006012.0018.00495.2700SelectionVariable:138.004.00505.3770一Rule...1146.0014.00515.484015.0021.00514.5960ZaseLabels:163.0014.00515.6640口।177.0012.00566.0790WLSWeight:1816.00,00483.2190口I196.0016.00455.807020.0015.00524.7300^Statistics...1Plots...Save...Options...219.00,00404.6800224.006.00323.127023.0017.00472.6100249.00,00443.7170252.0016.00393.8940269.006.00392.70602712.005.00515.6310286.0013.00415.81502912.007.00475.130030.0024.00615.3910匚rm■ZiT..i匚二门|\DataVievXVariableView/SPSSr'rocessorisready丁*开始„：.SPSS19IQ£orWi...।■1|i||।口「口口，口・।|==E|八"