SPSS統(tǒng)計實驗報告多元線性回歸分析

研究期末成績受哪些因素影響？其影響程度的情況?半期成期末成每周學習時入學等教師等班級績績間級級185874221198964511174803521187904021186883812175703532165672832178723022164703032182753412189863812273773823272683223260652033266613033289933921288884311282804113280853923283854523277804033297965011初步設(shè)定回歸方程：y=P0+Plp+P2i+P3t+eDescriptiveStatisticsMeanStd.DeviationN期末成績79.9510.33022班級1.50.51222每周學習時間36.916.76822半期成績79.5510.29422入學等級1.95.78522教師等級2.05.84422表中為各因素的均值，標準差，和樣本量。

Correlations期末成績班級每周學習時間半期成績?nèi)雽W等級教師等級PearsonCorrelation期末成績1.000-.014.860.921-.681-.595班級-.0141.000.151-.072.059.496每周學習時間.860.1511.000.863-.619-.383半期成績.921-.072.8631.000-.798-.573入學等級-.681.059-.619-.7981.000.362教師等級-.595.496-.383-.573.3621.000Sig.(1-tailed)期末成績.476.000.000.000.002班級.476.251.375.397.009每周學習時間.000.251.000.001.039半期成績.000.375.000.000.003入學等級.000.397.001.000.049教師等級.002.009.039.003.049N期末成績222222222222班級222222222222每周學習時間222222222222半期成績222222222222入學等級222222222222教師等級222222222222表中為各因素的相關(guān)系數(shù)和P值，從表中可看出班級的相關(guān)性最低VariablesEntered/RemovedbModelVariablesEnteredVariablesRemovedMethod1教師等級，入學等級，班級，每周學習時間，半期成績aEnter

2入學等級Backward(criterion:ProbabilityofF-to-remove>=.100).3Backward(criterion:班級ProbabilityofF-to-remove>=.100).4Backward(criterion:教師等級ProbabilityofF-to-remove>=.100).5Backward(criterion:每周學習時間ProbabilityofF-to-remove>=.100).Allrequestedvariablesentered.DependentVariable:期末成績采用向后剔除法，即每次剔除一個最不符合進入模型判斷依據(jù)的變量，直到回歸方程中不再含有不符合判斷依據(jù)的自變量為止。ModelSummaryfModelRRSquareAdjustedRSquareStd.ErroroftheEstimateChangeStatisticsDurbin-WatsonRSquareChangeFChangedf1df2Sig.FChange1.941a.885.8494.014.88524.620516.0002.940b.884.8573.906.000.102116.7543.938c.879.8593.875-.005.715117.4104?930d.865.8503.996-.0152.200118.1555.921e.848.8404.126-.0172.327119.1442.737Predictors:(Constant),教師等級，入學等級，班級，每周學習時間，半期成績Predictors:(Constant),教師等級，班級，每周學習時間，半期成績Predictors:(Constant),教師等級，每周學習時間，半期成績Predictors:(Constant),每周學習時間，半期成績Predictors:(Constant),半期成績DependentVariable:期末成績首先剔除了入學等級，然后剔除了班級，再次剔除了教師等級，再后剔除了每周學習時間，最后剔除半期成績，剩下了期末成績，從剔除順序可知各因素對期末成績的影響程度，入學等級最低，半期成績最高。ANOVAfModelSumofSquaresdfMeanSquareFSig.1Regression1983.1875396.63724.620?000aResidual257.7681616.110Total2240.955212Regression1981.5464495.38732.465?000bResidual259.4081715.259Total2240.955213Regression1970.6413656.88043.741.000cResidual270.3131815.017Total2240.955214Regression1937.6052968.80360.680.000dResidual303.3491915.966Total2240.955215Regression1900.45611900.456111.628?000eResidual340.4982017.025Total2240.95521Predictors:(Constant),教師等級，入學等級，班級，每周學習時間，半期成績Predictors:(Constant),教師等級，班級，每周學習時間，半期成績

Predictors:(Constant),教師等級，每周學習時間，半期成績Predictors:(Constant),每周學習時間，半期成績Predictors:(Constant),半期成績DependentVariable:期末成績從表中可看出F統(tǒng)計量的值是遞增的，即可得出每剔除一個最不符合進入模型判斷依據(jù)的變量，F(xiàn)統(tǒng)計量的值都在增加，即模型的整體顯著性在增強。CoeficientsaModelUnstandardizedCoefficientsStandardizedCoefficientstSig.95%ConfidenceIntervalforBCorrelationsCollinearityStatisicsBStd.ErrorBetaLowerBoundUpperBoundZero-orderPartialPartToleranceVIF1(Constan15.9919.51.820.42-25.3657.34t)10489班級.431.7822.199.088.8100-2.8806.444-.014.199.069.6061.651每周學習.20時間.386.293.2531.3176-.2361.008.860.313.112.1955.139半期成績.637.270.6352.360.03.0651.210.921.508.200.09910.0714入學等級.75.6301.973.048.3194-3.5544.813-.681.080.027.3193.131教師等級-2.3931.576-.195-1.51.14-5.735.949-.595-.355-.12.4332.3078992(Constan21.1610.572.001.06-1.15243.47t)1624班級.411.8082.139.090.8450-2.7046.320-.014.201.070.6071.649每周學習.15時間.411.275.2701.4953-.169.992.860.341.123.2104.772半期成績.579.193.5772.994.008.171.987.921.588.247.1835.452

教師等級-2.5201.485-.206-1.697.108-5.652.613-.595-.381-.140.4632.1613(Constan21.3610.482.037.05-.67443.39t)2979每周學習.07時間.491.257.3221.9142-.0481.030.860.411.157.2374.214半期成績.557.190.5552.931.00.158.957.921.568.240.1875.3559教師等級-1.8831.270-.154-1.48.15-4.551.784-.595-.330-.12.6231.6053514(Constan.1924.509.6347.1051.356-5.238t)15每周學習.14時間.389.255.2551.5254-.145.922.860.330.129.2563.909半期成績.704.167.7014.203.00.3531.054.921.694.355.2563.90905(Constan.3621.076.4467.013.919-8.182t)95半期成績.924.087.92110.56.00.7421.107.921.921.9211.0001.00050a.DependentVariable:期末成績從圖中的相關(guān)性可得出半期考試和每周學習時間與期末成績呈高度正相關(guān)，而其他三個因素（入學等級、班級、教師等級）都是呈負相關(guān)的，并按相關(guān)性由小到大依次剔除。CoefficientCorrelationsaModel教師等級入學等級班級每周學習時間半期成績1Correlations教師等級1.000.252-.500-.109.439入學等級.2521.000-.037-.267.677班級-.500-.0371.000-.319.073每周學習時間-.109-.267-.3191.000-.774半期成績.439.677.073-.7741.000Covariances教師等級2.485.783-1.732-.050.187

入學等級.7833.894-.160-.155.361班級-1.732-.1604.836-.206.043每周學習時間-.050-.155-.206.086-.061半期成績.187.361.043-.061.0732Correlations教師等級1.000-.507-.045.377班級-.5071.000-.342.133每周學習時間-.045-.3421.000-.837半期成績.377.133-.8371.000Covariances教師等級2.205-1.610-.018.108班級-1.6104.574-.201.055每周學習時間-.018-.201.076-.045半期成績.108.055-.045.0373Correlations教師等級1.000-.269.520每周學習時間-.2691.000-.850半期成績.520-.8501.000Covariances教師等級1.612-.088.125每周學習時間-.088.066-.041半期成績.125-.041.0364Correlations每周學習時間1.000-.863半期成績-.8631.000Covariances每周學習時間.065-.037半期成績-.037.0285Correlations半期成績1.000Covariances半期成績.008a.DependentVariable:期末成績表中為相關(guān)系數(shù)標準化與非標準間逐個剔除的對比情況。從中可看出，將相關(guān)性較弱的逐個剔除后，標準化與實際之間的差異越來越小。ExcludedVariableseModelBetaIntSig.PartialCorrelationColinearityStatisticsToleranceVIFMinimumTolerance

2入學等級.048a.319.754.080.3193.131.0993入學等級.052b.353.729.085.3203.127.100班級?090b.845.410.201.6071.649.1834入學等級.104c.716.483.166.3452.900.143班級-.002c-.017.987-.004.8161.225.210教師等級-.154c-1.483.155-.330.6231.605.1875入學等級.147d1.020.320.228.3642.750.364班級.053d.601.555.137.9951.005.995教師等級-.100d-.941.358-.211.6721.489.672每周學習時間.255d1.525.144.330.2563.909.256PredictorsintheModel:(Constant),教師等級，班級，每周學習時間，半期成績PredictorsintheModel:(Constant),教師等級，每周學習時間，半期成績PredictorsintheModel:(Constant),每周學習時間，半期成績PredictorsintheModel:(Constant),半期成績DependentVariable:期末成績以入學等級為基準量，然后依次加入影響因素，從中觀察方差膨脹因子VIF的變化。VIF越接近1表示解釋變量之間的多重共線性越弱，即從依次加入的變量可看出班級與入學等級之間的多重共線性最弱。ResdualsStatisticsaMinimumMaximumMeanStd.DeviationNPredictedValue61.8997.0179.959.51322Std.PredictedValue-1.8991.793.0001.00022StandardErrorofPredictedValue.8811.9231.200.33522AdjustedPredictedValue61.0397.2679.929.60022Residual-7.2235.170.0004.02722Std.