The Regressinator: A Simulation Tool for Teaching Regression Assumptions and Diagnostics in R

When students learn linear regression, they must learn to use diagnostics to check and improve their models. Model-building is an expert skill requiring the interpretation of diagnostic plots, an understanding of model assumptions, the selection of appropriate changes to remedy problems, and an intuition for how potential problems may affect results. Simulation offers opportunities to practice these skills, and is already widely used to teach important concepts in sampling, probability, and statistical inference. Visual inference, which uses simulation, has also recently been applied to regression instruction. This article presents the regressinator, an R package designed to facilitate simulation and visual inference in regression settings. Simulated regression problems can be easily defined with minimal programming, using the same modeling and plotting code students may already learn. The simulated data can then be used for model diagnostics, visual inference, and other activities, with the package providing functions to facilitate common tasks with a minimum of programming. Example activities covering model diagnostics, statistical power, and model selection are shown for both advanced undergraduate and Ph.D.-level regression courses.

学生在学习线性回归时，必须掌握模型诊断（diagnostics）方法以检验并优化自身构建的模型。模型构建是一项需要专业素养的技能，要求学习者能够解读诊断绘图、理解模型假设、选择恰当的修正方案以解决建模问题，并建立对潜在问题如何影响分析结果的直觉认知。模拟实践为学习者提供了锻炼上述技能的契机，目前已被广泛用于讲授抽样、概率与统计推断（statistical inference）中的核心概念。近年来，借助模拟实现的视觉推断（visual inference）也被应用于回归教学领域。本文介绍了regressinator——一款专为回归场景下的模拟与视觉推断设计的R软件包。学习者可借助已掌握的建模与绘图代码，仅需极少量编程工作量即可轻松定义模拟回归问题。生成的模拟数据可用于模型诊断、视觉推断及其他教学活动，该软件包还提供了一系列函数，可在最大限度减少编程量的前提下助力完成各类常见任务。本文还展示了面向高年级本科生与博士阶段回归课程的示例教学活动，涵盖模型诊断、统计功效（statistical power）与模型选择等内容。