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1、研究期末成绩受哪些因素影响？其影响程度的情况?班级半期成绩期末成绩每周学习时间入学等级教师等级185874221198964511174803521187904021186883812175703532165672832178723022164703032182753412189863812273773823272683223260652033266613033289933921288884311282804113280853923283854523277804033297965011初步设定回归方程：Descriptive StatisticsMeanStd. DeviationN期末成绩7
2、9.9510.33022班级1.50.51222每周学习时间36.916.76822半期成绩79.5510.29422入学等级1.95.78522教师等级2.05.84422表中为各因素的均值，标准差，和样本量。Correlations期末成绩班级每周学习时间半期成绩入学等级教师等级Pearson Correlation期末成绩1.000-.014.860.921-.681-.595班级-.0141.000.151-.072.059.496每周学习时间.860.1511.000.863-.619-.383半期成绩.921-.072.8631.000-.798-.573入学等级-.681.059
3、-.619-.7981.000.362教师等级-.595.496-.383-.573.3621.000Sig. (1-tailed)期末成绩.476.000.000.000.002班级.476.251.375.397.009每周学习时间.000.251.000.001.039半期成绩.000.375.000.000.003入学等级.000.397.001.000.049教师等级.002.009.039.003.049.N期末成绩222222222222班级222222222222每周学习时间222222222222半期成绩222222222222入学等级222222222222教师等级2222
4、22222222表中为各因素的相关系数和P值，从表中可看出班级的相关性最低Variables Entered/RemovedbModelVariables EnteredVariables RemovedMethod1教师等级, 入学等级, 班级, 每周学习时间, 半期成绩a.Enter2.入学等级Backward (criterion: Probability of F-to-remove = .100).3.班级Backward (criterion: Probability of F-to-remove = .100).4.教师等级Backward (criterion: Probabi
5、lity of F-to-remove = .100).5.每周学习时间Backward (criterion: Probability of F-to-remove = .100).a. All requested variables entered.b. Dependent Variable: 期末成绩采用向后剔除法，即每次剔除一个最不符合进入模型判断依据的变量，直到回归方程中不再含有不符合判断依据的自变量为止。Model SummaryfModelRR SquareAdjusted R SquareStd. Error of the EstimateChange StatisticsDu
6、rbin-WatsonR Square ChangeF Changedf1df2Sig. F Change1.941a.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-.0172.327119.1442.737a. Predictors: (Constant), 教师等级, 入学等级, 班级, 每周学习时间, 半期成绩b. Predict
7、ors: (Constant), 教师等级, 班级, 每周学习时间, 半期成绩c. Predictors: (Constant), 教师等级, 每周学习时间, 半期成绩d. Predictors: (Constant), 每周学习时间, 半期成绩e. Predictors: (Constant), 半期成绩f. Dependent Variable: 期末成绩首先剔除了入学等级，然后剔除了班级，再次剔除了教师等级，再后剔除了每周学习时间，最后剔除半期成绩，剩下了期末成绩，从剔除顺序可知各因素对期末成绩的影响程度，入学等级最低，半期成绩最高。ANOVAfModelSum of Squaresdf
8、Mean SquareFSig.1Regression1983.1875396.63724.620.000aResidual257.7681616.110Total2240.955212Regression1981.5464495.38732.465.000bResidual259.4081715.259Total2240.955213Regression1970.6413656.88043.741.000cResidual270.3131815.017Total2240.955214Regression1937.6052968.80360.680.000dResidual303.349191
9、5.966Total2240.955215Regression1900.45611900.456111.628.000eResidual340.4982017.025Total2240.95521a. Predictors: (Constant), 教师等级, 入学等级, 班级, 每周学习时间, 半期成绩b. Predictors: (Constant), 教师等级, 班级, 每周学习时间, 半期成绩c. Predictors: (Constant), 教师等级, 每周学习时间, 半期成绩d. Predictors: (Constant), 每周学习时间, 半期成绩e. Predictors:
10、 (Constant), 半期成绩f. Dependent Variable: 期末成绩从表中可看出F统计量的值是递增的，即可得出每剔除一个最不符合进入模型判断依据的变量，F统计量的值都在增加，即模型的整体显著性在增强。CoefficientsaModelUnstandardized CoefficientsStandardized CoefficientstSig.95% Confidence Interval for BCorrelationsCollinearity StatisticsBStd. ErrorBetaLower BoundUpper BoundZero-orderPart
11、ialPartToleranceVIF1(Constant)15.99119.510.820.424-25.36857.349班级1.7822.199.088.810.430-2.8806.444-.014.199.069.6061.651每周学习时间.386.293.2531.317.206-.2361.008.860.313.112.1955.139半期成绩.637.270.6352.360.031.0651.210.921.508.200.09910.074入学等级.6301.973.048.319.754-3.5544.813-.681.080.027.3193.131教师等级-2.3
12、931.576-.195-1.518.149-5.735.949-.595-.355-.129.4332.3072(Constant)21.16110.5762.001.062-1.15243.474班级1.8082.139.090.845.410-2.7046.320-.014.201.070.6071.649每周学习时间.411.275.2701.495.153-.169.992.860.341.123.2104.772半期成绩.579.193.5772.994.008.171.987.921.588.247.1835.452教师等级-2.5201.485-.206-1.697.108-5
13、.652.613-.595-.381-.140.4632.1613(Constant)21.36210.4892.037.057-.67443.399每周学习时间.491.257.3221.914.072-.0481.030.860.411.157.2374.214半期成绩.557.190.5552.931.009.158.957.921.568.240.1875.355教师等级-1.8831.270-.154-1.483.155-4.551.784-.595-.330-.121.6231.6054(Constant)9.6347.1051.356.191-5.23824.505每周学习时间.
14、389.255.2551.525.144-.145.922.860.330.129.2563.909半期成绩.704.167.7014.203.000.3531.054.921.694.355.2563.9095(Constant)6.4467.013.919.369-8.18221.075半期成绩.924.087.92110.565.000.7421.107.921.921.9211.0001.000a. Dependent Variable: 期末成绩从图中的相关性可得出半期考试和每周学习时间与期末成绩呈高度正相关，而其他三个因素（入学等级、班级、教师等级）都是呈负相关的，并按相关性由小到
15、大依次剔除。Coefficient CorrelationsaModel教师等级入学等级班级每周学习时间半期成绩1Correlations教师等级1.000.252-.500-.109.439入学等级.2521.000-.037-.267.677班级-.500-.0371.000-.319.073每周学习时间-.109-.267-.3191.000-.774半期成绩.439.677.073-.7741.000Covariances教师等级2.485.783-1.732-.050.187入学等级.7833.894-.160-.155.361班级-1.732-.1604.836-.206.043每
16、周学习时间-.050-.155-.206.086-.061半期成绩.187.361.043-.061.0732Correlations教师等级1.000-.507-.045.377班级-.5071.000-.342.133每周学习时间-.045-.3421.000-.837半期成绩.377.133-.8371.000Covariances教师等级2.205-1.610-.018.108班级-1.6104.574-.201.055每周学习时间-.018-.201.076-.045半期成绩.108.055-.045.0373Correlations教师等级1.000-.269.520每周学习时间-
17、.2691.000-.850半期成绩.520-.8501.000Covariances教师等级1.612-.088.125每周学习时间-.088.066-.041半期成绩.125-.041.0364Correlations每周学习时间1.000-.863半期成绩-.8631.000Covariances每周学习时间.065-.037半期成绩-.037.0285Correlations半期成绩1.000Covariances半期成绩.008a. Dependent Variable: 期末成绩表中为相关系数标准化与非标准间逐个剔除的对比情况。从中可看出，将相关性较弱的逐个剔除后，标准化与实际之间
18、的差异越来越小。Excluded VariableseModelBeta IntSig.Partial CorrelationCollinearity StatisticsToleranceVIFMinimum Tolerance2入学等级.048a.319.754.080.3193.131.0993入学等级.052b.353.729.085.3203.127.100班级.090b.845.410.201.6071.649.1834入学等级.104c.716.483.166.3452.900.143班级-.002c-.017.987-.004.8161.225.210教师等级-.154c-1.
19、483.155-.330.6231.605.1875入学等级.147d1.020.320.228.3642.750.364班级.053d.601.555.137.9951.005.995教师等级-.100d-.941.358-.211.6721.489.672每周学习时间.255d1.525.144.330.2563.909.256a. Predictors in the Model: (Constant), 教师等级, 班级, 每周学习时间, 半期成绩b. Predictors in the Model: (Constant), 教师等级, 每周学习时间, 半期成绩c. Predictors
20、 in the Model: (Constant), 每周学习时间, 半期成绩d. Predictors in the Model: (Constant), 半期成绩e. Dependent Variable: 期末成绩以入学等级为基准量，然后依次加入影响因素，从中观察方差膨胀因子VIF的变化。VIF越接近1表示解释变量之间的多重共线性越弱，即从依次加入的变量可看出班级与入学等级之间的多重共线性最弱。Residuals StatisticsaMinimumMaximumMeanStd. DeviationNPredicted Value61.8997.0179.959.51322Std. Pr
21、edicted Value-1.8991.793.0001.00022Standard Error of Predicted Value.8811.9231.200.33522Adjusted Predicted Value61.0397.2679.929.60022Residual-7.2235.170.0004.02722Std. Residual-1.7511.253.000.97622Stud. Residual-1.7941.292.0031.01722Deleted Residual-7.5885.496.0314.37422Stud. Deleted Residual-1.9091.315-.0111.04322Mahal. Distance.0023.605.9551.12822Cooks Distance.000.205.043.05022Centered Leverage Value.000.172.045.05422a. Dependent Variable: 期末成绩此表为残差统计量：依次为最小值、最大值，均值、标准差和样本量。从图中可看出样本与标准化残差图还是有比较大的差异，残差波动情况较大。结论：期末成绩的影响因素的程度依次递减为：半期成绩，每周学习时间，教师等级，班级，入学等级。