## 多元统计分析在学生成绩评价中的应用

Application of Multivariate Statistical Analysis in The
Evaluation of Student Performance
Abstract : Principal component analysis, factor analysis and cluster analysis of multivariate statistical methods are two very valuable, but in the course easily misused and confused. From the mathematical model, the basic idea, standardization and application data aspects, discussed the similarities and differences between the two. And case analysis were carried out by case analysis I believe we will be more clearly understood, distinguish and apply these two methods. While examples objective analysis is to evaluate student achievement for the purpose of comprehensive scientific evaluation by providing for the arrangement of teaching programs a strong basis, but also has great practical significance.
Key words: Principal Component Analysis; Main Component Analysis; The Examination Results; Evaluation of Student Performance

1.数据准备与检验    3
1.1 数据采集    3
1.2 频率直方图    3
1.3 正态性的检验    5
1.3.1 检验方法    5 源￥自%六^^维*论-文+网=www.lwfree.cn
1.3.2 数学分析（上）的检验    6
1.3.3 数学分析（下）的检验    6
2.因子分析    7
2.1 因子分析的数学模型    7
2.2 因子分析步骤    8
2.2.1因子分析检验，看能否运用因子分析    8
2.2.2对原始数据标准化    8
2.2.3计算样本的相关系数矩阵，因子荷载矩阵，因子得分    8
2.2.4对公因子评价    8
2.3 实例分析    8
2.3.1进行因子相关性的检验    8
2.3.2因子分析的主成分提取    10
2.3.3计算旋转后的因子载荷矩阵    10
2.3.4计算因子得分矩阵    10
2.3.5成分得分协方差矩阵成分得分矩阵如表11所示.    10
2.3.6对公因子作解释    12
2.4 总结    12
3. 主成分分析模型的构造    12
3.1 模型构造的意义    12
3.2 主成分分析模型    12
3.2.1 模型假设与描述    12
3.2.2 模型求解    13
3.3 实例分析    16
3.3.1将原始指标数据标准化    16
3.3.2各成分的方差贡献率    16
3.3.3主成分得分函数及荷载因子分析    17
3.4结论    18

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