高等数学成绩的分层线性回归分析

Hierarchical Linear Regression Analysis of Achievements in Advanced Mathematics

摘要: 在对某211高校学生的高等数学成绩进行分析时，创新思路从学生嵌套于老师这一关系入手，而没有采用学生嵌套于班级这一通常做法，采用两水平的分层线性模型对其进行分析，打破了普通回归模型在分析具有嵌套结构数据的局限性。在个体水平上，学生的高等成绩主要受其高考数学成绩和性别的影响，其中高考数学成绩对高数成绩具有正效应，女同学的高数成绩平均高于男同学；在老师水平上，学生的高等数学成绩主要受老师性别的影响，男老师所教授学生的高数成绩平均高于女老师所教授的学生。

Abstract: In the analysis of the higher mathematics scores of a 211 college students, the innovative ideas start from the relationship of students nesting in the teacher, instead of adopting the usual practice of students nesting in the class, using a two-level hierarchical linear model. Analysis has broken the limitations of ordinary regression models in analyzing data with nested structures. At the individual level, students’ higher mathematics grades are mainly influenced by their math scores and gender in college entrance examinations. Among them, the math scores of college entrance examinations have positive effects on higher mathematics scores, and the average scores of female students are higher than those of male students. At the teacher level, students’ higher mathematics scores are mainly influenced by the gender of the teacher. The average number of students taught by male teachers is higher than that of the female teachers.