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

doi:10.13229/j.cnki.jdxbgxb.20231537

摘要/Abstract

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HM-OLS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。

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

Abstract:

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.

Key words: HM-OLS stepwise regression model, network learning space data, student grades, correlation analysis

中图分类号:

TP391.1

刘俊杰,董佳怡,杨勇,刘丹,曲福恒,吕彦昌. 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[J]. 吉林大学学报(工学版), 2024, 54(12): 3755-3762.

Jun-jie LIU,Jia-yi Dong,Yong YANG,Dan LIU,Fu-heng QU,Yan-chang LYU. Analysis of factors associated with online learning performance of students based on HM-OLS stepwise regression model[J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(12): 3755-3762.

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变量	最小值	下四分位数	中位数	上四分位数	最大值	平均值
CRR	0.732	0.914	0.94	0.969	0.99	0.926
APR	0.091	0.286	0.506	0.718	0.965	0.512
PCR	0.308	0.644	0.804	0.909	0.994	0.765
NVR	0.003	0.568	0.708	0.813	0.962	0.684
ITR	2	1756	2 926	10 839	5 184 078	386 021
TS	1	25.25	64	78.0	6 865	195.018
BCR	11	124.75	693.5	3442	4 323 638	156 512
DPR	1	5.25	8	13	57	10.703
TRD	0	0.253	0.446	0.689	1	0.474
TM	0	0.066	0.123	0.388	1	0.297
CAS	0	0.089	0.292	0.559	1	0.355
EER	0	0.362	0.387	0.563	1	0.473
EIR	0	0.005	0.375	0.743	1	0.391
EHR	0	0	0.279	0.804	1	0.425

	coef	p	std err	［0.025	0.975］
APR	35.4399	0.001	7.136	21.076	49.804
PCR	52.3951	0.001	6.158	10.001	64.790
CAS	14.1343	0.048	6.970	0.105	28.164
EER	34.1781	0.001	4.682	24.754	43.602

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