Simple Linear Regression for Learner Support and Course Design

Simple linear regression models the relationship between one predictor and a continuous outcome with a best-fitting straight line. Imagine an instructional design team asking whether Week 2 LMS page views can help identify learners who may need early outreach. Simple linear regression estimates an intercept and slope that summarize this relationship: the slope expresses the expected change in the outcome for a one-unit change in the predictor, and the fitted line supports prediction with uncertainty. Using ordinary least squares (NIST, 2012c), we obtain coefficient estimates and then describe uncertainty with confidence intervals for the mean response and prediction intervals (NIST, 2012a) for individual learners, useful for setting practical thresholds, such as flagging students below a target grade. Because valid conclusions depend on assumptions, we examine residuals to assess linearity, independence, constant variance, and approximate normality (van Aalst et al., 2022; NIST, 2012b) using residual-versus-fitted and Q–Q plots. In educational technology research, where behavioral traces such as clicks, time-on-task, or video minutes are abundant, simple linear regression offers a transparent, interpretable first step that turns messy measurements into actionable signals for course design and learner support, while keeping its limits clear (association rather than causation and the need to check model fit (Wesolowsk, 2022)).