高数成绩与高考成绩的分层回归模型影响分析

The Analysis on Influence Factors of the Transcripts of Mathematics and Advanced Mathematics Based on Hierarchical Linear Models

摘要: 高考数学成绩是学生高中学习状况的体现，高等数学成绩是大学生大学学习状况的体现，本文通过分层线性模型确定大学生高考数学成绩和高等数学成绩的关系及一些对高等数学成绩具有显著影响的因素,并给出了一些提高大学生数学水平的意见。由于学生来自不同省份，各省情况尤其是教育情况迥异，同时学生个体间存在差异，因此所研究的数据具有明显的嵌套结构，传统的线性回归模型无力分析此类分层模型，本文采用的分层线性模型同时考虑了省份间差异及个体间差异进行统计建模，突破了传统的线性模型在分析嵌套结构上的局限性，建立了各省内关系与各省间关系的假设，估计了各个层次上的变化量，故该模型更接近现实生活中的基本现象，模型解释更为合理。

Abstract: Transcript of Mathematics in college entrance examination represents an individual’s learning situation in high school. At the same time, transcript of Advanced Mathematics represents an indi-vidual’s learning situation in college. By using hierarchical linear models, this article identifies the relationship between the transcripts of Mathematics and Advanced Mathematics along with some factors that affects student’s Advanced Mathematics’ level greatly. Some suggestions that aimed at increasing college students’ Mathematics level are also being provided. Students come from dif-ferent provinces and situations, especially educational situations vary in provinces. Taking students’ individual differences in consideration as well, it is obvious that the data has been studied nested structure, which indicates that traditional Hierarchical linear models are not capable of analyzing this category of hierarchical models. The hierarchical models adopted in this article have fully considered both provincial and individual differences in order to establish statistical models properly. The method has overcome the traditional linear models’ limitation on analyzing nested or hierarchical structure. It establishes appropriate hypothetical relationships both inside and among the provinces, and estimate variables from different hierarchy. As a result, this model is more similar to basic phenomenon in reality and its model interpretation is more reasonable.