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 |
| 1 | 85 | 87 | 42 | 2 | 1 |
| 1 | 98 | 96 | 45 | 1 | 1 |
| 1 | 74 | 80 | 35 | 2 | 1 |
| 1 | 87 | 90 | 40 | 2 | 1 |
| 1 | 86 | 88 | 38 | 1 | 2 |
| 1 | 75 | 70 | 35 | 3 | 2 |
| 1 | 65 | 67 | 28 | 3 | 2 |
| 1 | 78 | 72 | 30 | 2 | 2 |
| 1 | | 70 | 30 | 3 | 2 |
| 1 | 82 | 75 | 34 | 1 | 2 |
| 1 | | 86 | 38 | 1 | 2 |
| 2 | 73 | 77 | 38 | 2 | 3 |
| 2 | 72 | 68 | 32 | 2 | 3 |
| 2 | 60 | 65 | 20 | 3 | 3 |
| 2 | 66 | 61 | 30 | 3 | 3 |
| 2 | | 93 | 39 | 2 | 1 |
| 2 | 88 | 88 | 43 | 1 | 1 |
| 2 | 82 | 80 | 41 | 1 | 3 |
| 2 | 80 | 85 | 39 | 2 | 3 |
| 2 | 83 | 85 | 45 | 2 | 3 |
| 2 | 77 | 80 | 40 | 3 | 3 |
| 2 | 97 | 96 | 50 | 1 | 1 |
初步设定回归方程：
| Descriptive Statistics |
| Mean | Std. Deviation | N |
| 期末成绩 | 79.95 | 10.330 | 22 |
| 班级 | 1.50 | .512 | 22 |
| 每周学习时间 | 36.91 | 6.768 | 22 |
| 半期成绩 | 79.55 | 10.294 | 22 |
| 入学等级 | 1.95 | .785 | 22 |
| 教师等级 | 2.05 | .844 | 22 |
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 | -.014 | 1.000 | .151 | -.072 | .059 | .496 |
| 每周学习时间 | .860 | .151 | 1.000 | .863 | -.619 | -.383 |
| 半期成绩 | .921 | -.072 | .863 | 1.000 | -.798 | -.573 |
| 入学等级 | -.681 | .059 | -.619 | -.798 | 1.000 | .362 |
| 教师等级 | -.595 | .496 | -.383 | -.573 | .362 | 1.000 |
| Sig. (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 | 22 | 22 | 22 | 22 | 22 | 22 |
| 班级 | 22 | 22 | 22 | 22 | 22 | 22 |
| 每周学习时间 | 22 | 22 | 22 | 22 | 22 | 22 |
| 半期成绩 | 22 | 22 | 22 | 22 | 22 | 22 |
| 入学等级 | 22 | 22 | 22 | 22 | 22 | 22 |
| 教师等级 | 22 | 22 | 22 | 22 | 22 | 22 |
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/Removedb |
| Model | Variables Entered | Variables Removed | Method |
| 1 | 教师等级, 入学等级, 班级, 每周学习时间, 半期成绩a | . | Enter |
| 2 | . | 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: Probability 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 Summaryf |
| Model | R | R Square | Adjusted R Square | Std. Error of the Estimate | Change Statistics | Durbin-Watson |
| R Square Change | F Change | df1 | df2 | Sig. F Change |
| 1 | .941a | .885 | .849 | 4.014 | .885 | 24.620 | 5 | 16 | .000 | |
| 2 | .940b | .884 | .857 | 3.906 | .000 | .102 | 1 | 16 | .754 | |
| 3 | .938c | .879 | .859 | 3.875 | -.005 | .715 | 1 | 17 | .410 | |
| 4 | .930d | .865 | .850 | 3.996 | -.015 | 2.200 | 1 | 18 | .155 | |
| 5 | .921e | .848 | .840 | 4.126 | -.017 | 2.327 | 1 | 19 | .144 | 2.737 |
| a. 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: (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。
| ANOVAf |
| Model | Sum of Squares | df | Mean Square | F | Sig. |
| 1 | Regression | 1983.187 | 5 | 396.637 | 24.620 | .000a |
| Residual | 257.768 | 16 | 16.110 | | |
| Total | 2240.955 | 21 | | | |
| 2 | Regression | 1981.546 | 4 | 495.387 | 32.465 | .000b |
| Residual | 259.408 | 17 | 15.259 | | |
| Total | 2240.955 | 21 | | | |
| 3 | Regression | 1970.1 | 3 | 656.880 | 43.741 | .000c |
| Residual | 270.313 | 18 | 15.017 | | |
| Total | 2240.955 | 21 | | | |
| 4 | Regression | 1937.605 | 2 | 968.803 | 60.680 | .000d |
| Residual | 303.349 | 19 | 15.966 | | |
| Total | 2240.955 | 21 | | | |
| 5 | Regression | 1900.456 | 1 | 1900.456 | 111.628 | .000e |
| Residual | 340.498 | 20 | 17.025 | | |
| Total | 2240.955 | 21 | | | |
| a. 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: (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。
| Coefficientsa |
| Model | Unstandardized Coefficients | Standardized Coefficients | t | Sig. | 95% Confidence Interval for B | Correlations | Collinearity Statistics |
| B | Std. Error | Beta | Lower Bound | Upper Bound | Zero-order | Partial | Part | Tolerance | VIF |
| 1 | (Constant) | 15.991 | 19.510 | | .820 | .424 | -25.368 | 57.349 | | | | | |
| 班级 | 1.782 | 2.199 | .088 | .810 | .430 | -2.880 | 6.444 | -.014 | .199 | .069 | .606 | 1.651 |
| 每周学习时间 | .386 | .293 | .253 | 1.317 | .206 | -.236 | 1.008 | .860 | .313 | .112 | .195 | 5.139 |
| 半期成绩 | .637 | .270 | .635 | 2.360 | .031 | .065 | 1.210 | .921 | .508 | .200 | .099 | 10.074 |
| 入学等级 | .630 | 1.973 | .048 | .319 | .754 | -3.554 | 4.813 | -.681 | .080 | .027 | .319 | 3.131 |
| 教师等级 | -2.393 | 1.576 | -.195 | -1.518 | .149 | -5.735 | .949 | -.595 | -.355 | -.129 | .433 | 2.307 |
| 2 | (Constant) | 21.161 | 10.576 | | 2.001 | .062 | -1.152 | 43.474 | | | | | |
| 班级 | 1.808 | 2.139 | .090 | .845 | .410 | -2.704 | 6.320 | -.014 | .201 | .070 | .607 | 1.9 |
| 每周学习时间 | .411 | .275 | .270 | 1.495 | .153 | -.169 | .992 | .860 | .341 | .123 | .210 | 4.772 |
| 半期成绩 | .579 | .193 | .577 | 2.994 | .008 | .171 | .987 | .921 | .588 | .247 | .183 | 5.452 |
| 教师等级 | -2.520 | 1.485 | -.206 | -1.697 | .108 | -5.652 | .613 | -.595 | -.381 | -.140 | .463 | 2.161 |
| 3 | (Constant) | 21.362 | 10.4 | | 2.037 | .057 | -.674 | 43.399 | | | | | |
| 每周学习时间 | .491 | .257 | .322 | 1.914 | .072 | -.048 | 1.030 | .860 | .411 | .157 | .237 | 4.214 |
| 半期成绩 | .557 | .190 | .555 | 2.931 | .009 | .158 | .957 | .921 | .568 | .240 | .187 | 5.355 |
| 教师等级 | -1.883 | 1.270 | -.154 | -1.483 | .155 | -4.551 | .784 | -.595 | -.330 | -.121 | .623 | 1.605 |
| 4 | (Constant) | 9.634 | 7.105 | | 1.356 | .191 | -5.238 | 24.505 | | | | | |
| 每周学习时间 | .3 | .255 | .255 | 1.525 | .144 | -.145 | .922 | .860 | .330 | .129 | .256 | 3.909 |
| 半期成绩 | .704 | .167 | .701 | 4.203 | .000 | .353 | 1.054 | .921 | .694 | .355 | .256 | 3.909 |
| 5 | (Constant) | 6.446 | 7.013 | | .919 | .369 | -8.182 | 21.075 | | | | | |
| 半期成绩 | .924 | .087 | .921 | 10.565 | .000 | .742 | 1.107 | .921 | .921 | .921 | 1.000 | 1.000 |
| a. 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，并按相关性由小到大依次剔除。
| Coefficient Correlationsa |
| Model | 教师等级 | 入学等级 | 班级 | 每周学习时间 | 半期成绩 |
| 1 | Correlations | 教师等级 | 1.000 | .252 | -.500 | -.109 | .439 |
| 入学等级 | .252 | 1.000 | -.037 | -.267 | .677 |
| 班级 | -.500 | -.037 | 1.000 | -.319 | .073 |
| 每周学习时间 | -.109 | -.267 | -.319 | 1.000 | -.774 |
| 半期成绩 | .439 | .677 | .073 | -.774 | 1.000 |
| Covariances | 教师等级 | 2.485 | .783 | -1.732 | -.050 | .187 |
| 入学等级 | .783 | 3.4 | -.160 | -.155 | .361 |
| 班级 | -1.732 | -.160 | 4.836 | -.206 | .043 |
| 每周学习时间 | -.050 | -.155 | -.206 | .086 | -.061 |
| 半期成绩 | .187 | .361 | .043 | -.061 | .073 |
| 2 | Correlations | 教师等级 | 1.000 | | -.507 | -.045 | .377 |
| 班级 | -.507 | | 1.000 | -.342 | .133 |
| 每周学习时间 | -.045 | | -.342 | 1.000 | -.837 |
| 半期成绩 | .377 | | .133 | -.837 | 1.000 |
| Covariances | 教师等级 | 2.205 | | -1.610 | -.018 | .108 |
| 班级 | -1.610 | | 4.574 | -.201 | .055 |
| 每周学习时间 | -.018 | | -.201 | .076 | -.045 |
| 半期成绩 | .108 | | .055 | -.045 | .037 |
| 3 | Correlations | 教师等级 | 1.000 | | | -.269 | .520 |
| 每周学习时间 | -.269 | | | 1.000 | -.850 |
| 半期成绩 | .520 | | | -.850 | 1.000 |
| Covariances | 教师等级 | 1.612 | | | -.088 | .125 |
| 每周学习时间 | -.088 | | | .066 | -.041 |
| 半期成绩 | .125 | | | -.041 | .036 |
| 4 | Correlations | 每周学习时间 | | | | 1.000 | -.863 |
| 半期成绩 | | | | -.863 | 1.000 |
| Covariances | 每周学习时间 | | | | .065 | -.037 |
| 半期成绩 | | | | -.037 | .028 |
| 5 | Correlations | 半期成绩 | | | | | 1.000 |
| Covariances | 半期成绩 | | | | | .008 |
| a. 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，标准化与实际之间的差异越来越小。
| Excluded Variablese |
| Model | Beta In | t | Sig. | Partial Correlation | Collinearity Statistics |
| Tolerance | VIF | Minimum Tolerance |
| 2 | 入学等级 | .048a | .319 | .754 | .080 | .319 | 3.131 | .099 |
| 3 | 入学等级 | .052b | .353 | .729 | .085 | .320 | 3.127 | .100 |
| 班级 | .090b | .845 | .410 | .201 | .607 | 1.9 | .183 |
| 4 | 入学等级 | .104c | .716 | .483 | .166 | .345 | 2.900 | .143 |
| 班级 | -.002c | -.017 | .987 | -.004 | .816 | 1.225 | .210 |
| 教师等级 | -.154c | -1.483 | .155 | -.330 | .623 | 1.605 | .187 |
| 5 | 入学等级 | .147d | 1.020 | .320 | .228 | .3 | 2.750 | .3 |
| 班级 | .053d | .601 | .555 | .137 | .995 | 1.005 | .995 |
| 教师等级 | -.100d | -.941 | .358 | -.211 | .672 | 1.4 | .672 |
| 每周学习时间 | .255d | 1.525 | .144 | .330 | .256 | 3.909 | .256 |
| a. 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 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 Statisticsa |
| Minimum | Maximum | Mean | Std. Deviation | N |
| Predicted Value | 61. | 97.01 | 79.95 | 9.513 | 22 |
| Std. Predicted Value | -1.9 | 1.793 | .000 | 1.000 | 22 |
| Standard Error of Predicted Value | .881 | 1.923 | 1.200 | .335 | 22 |
| Adjusted Predicted Value | 61.03 | 97.26 | 79.92 | 9.600 | 22 |
| Residual | -7.223 | 5.170 | .000 | 4.027 | 22 |
| Std. Residual | -1.751 | 1.253 | .000 | .976 | 22 |
| Stud. Residual | -1.794 | 1.292 | .003 | 1.017 | 22 |
| Deleted Residual | -7.588 | 5.496 | .031 | 4.374 | 22 |
| Stud. Deleted Residual | -1.909 | 1.315 | -.011 | 1.043 | 22 |
| Mahal. Distance | .002 | 3.605 | .955 | 1.128 | 22 |
| Cook's Distance | .000 | .205 | .043 | .050 | 22 |
| Centered Leverage Value | .000 | .172 | .045 | .054 | 22 |
| a. 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。下载本文
