基于线性回归的学生学业表现分析与研究

Analysis and Research on Students’ Academic Performance Based on Linear Regression

摘要: 本研究旨在通过线性回归模型分析和预测学生学业表现，以弥补传统教育评估方法的不足。选取BI挪威商学院70名学生作为样本，收集包括年龄、入学考试成绩、学习时间等数据，并随机分为模型构建组(A组，n = 35)和验证组(B组，n = 35)。数据预处理包括清洗、缺失值均值填充和异常值保留；特征工程涉及编码、标准化、SelectKBest筛选。采用Ridge回归构建Python和数据库(DB)课程成绩预测模型。结果显示，Python模型R² = 0.823，MSE = 42.36；DB模型R² = 0.796，MSE = 48.72。入学考试成绩和学习时间为主要正向影响因素，年龄呈弱负相关。模型验证通过配对t检验(p > 0.05)，证实泛化能力良好。研究表明，学业表现受多因素综合作用，该模型可为个性化教学和早期干预提供数据支持。局限性包括样本量小和特征维度有限，未来可扩展样本并引入动态数据以提升精度。

Abstract: This study aims to analyze and predict students’ academic performance through linear regression models, thereby addressing the deficiencies inherent in traditional educational assessment methods. A sample comprising 70 students from BI Norwegian Business School was selected, with data collected on variables such as age, entrance examination scores, study time, and others. The sample was randomly partitioned into a model construction group (Group A, n = 35) and a validation group (Group B, n = 35). Data preprocessing encompassed cleaning, mean imputation for missing values, and retention of outliers. Feature engineering involved encoding, standardization, SelectKBest feature selection, Ridge regression was utilized to develop predictive models for grades in Python and Database (DB) courses. The results revealed that the Python model attained an R² of 0.823 and a mean squared error (MSE) of 42.36, while the DB model achieved an R² of 0.796 and an MSE of 48.72. Entrance examination scores and study time were identified as primary positive predictors, with age demonstrating a weak negative correlation. Model validation, performed via paired t-tests (p > 0.05), substantiated the models’ strong generalization capabilities. The findings indicate that academic performance is shaped by a multifaceted interplay of factors, and this modeling approach can furnish data-driven support for personalized instruction and early interventions. Limitations include the modest sample size and constrained feature dimensions; prospective investigations may expand the sample and integrate dynamic data to augment predictive precision.