基于HM-OLS逐步回归模型的学生网络学习成绩关联因素分析  

Analysis of factors associated with online learning performance of students based on HM-OLS stepwise regression model

作　　者：刘俊杰[1] 董佳怡 杨勇[1,2] 刘丹 曲福恒[1] 吕彦昌[1] LIU Jun-jie;Dong Jia-yi;YANG Yong;LIU Dan;QU Fu-heng;LYU Yan-chang(College of Computer Science and Technology,Changchun University of Science and Technology,Changchun 130022,China;College of Data Science and Artificial Intelligence,Jilin Engineering Normal University,Changchun 130052,China)

机构地区：[1]长春理工大学计算机科学技术学院,长春130022 [2]吉林工程技术师范学院数据科学与人工智能学院,长春130052

出　　处：《吉林大学学报(工学版)》2024年第12期3755-3762,共8页Journal of Jilin University:Engineering and Technology Edition

基　　金：吉林省教育厅一般项目(JJKH20220777KJ,JJKH20230842KJ)。

摘　　要：针对现有回归分析模型容易估计失真或难以估计准确的问题,本文提出了一种HMOLS逐步回归分析模型。首先,通过主成分分析(PCA)方法对数据进行压缩降维,解决多重共线性问题;其次,利用经过处理的数据构建矩阵,通过最小二乘法估计模型参数,完成模型的拟合,并进行异方差检验与多重共线性检测;最后,以AIC值为参考,采用向前逐步回归法筛选影响因素,重新拟合模型,完成关联性分析。实验结果表明:本文提出的HM-OLS逐步回归分析模型有效消除了量纲的差异,解决了多重共线性问题,其稳定性和拟合效果明显优于传统的OLS、岭回归分析模型,并且能够准确分析出网络学习空间中与学生成绩关联性较强的影响因素。To address the problem of existing regression analysis models being prone to estimation distortion or difficult to estimate accurately,an HM-OLS stepwise regression analysis model was proposed.First,the data was compressed and reduced in dimension using principal component analysis(PCA)to solve the problem of multicollinearity.Second,the processed data was used to construct a matrix,and the model parameters are estimated using least squares method,completing the model fitting,and conducting heteroscedasticity test and multicollinearity detection.Finally,the AIC value was used as a reference,and the forward stepwise regression method is used to select influencing factors,re-fitting the model,and completing the correlation analysis.The experimental results show that the HM-OLS stepwise regression analysis model proposed in this paper effectively eliminates the problems of scale differences and multicollinearity,and its stability and fitting effect are significantly better than those of traditional OLS and ridge regression analysis models.It can also accurately analyze the influencing factors with strong correlation to student academic performance in the network learning space.

关 键 词：HM-OLS逐步回归模型 网络学习空间数据 学生成绩 关联性分析 

分 类 号：TP391.1[自动化与计算机技术—计算机应用技术]