A regression line gives you a prediction for every observation, but the quality of a model lives in what the line misses. A residual is simply the observed value minus the predicted value — the vertical distance from a data point to the fitted line. Individually, residuals tell you how far off a single prediction was; collectively, their pattern tells you whether the model you chose was the right one at all.
In this course, residual analysis is the main practical tool for checking the assumptions behind least-squares regression. Fitting a line is easy and software will always produce one, even when a straight line is a poor description of the relationship, even when the spread of errors grows with the predictor, and even when one unusual point is dragging the slope around. Residual plots — most commonly residuals against fitted values or against the predictor — make these problems visible, because a well-behaved model should leave behind residuals that look like structureless, evenly scattered noise centered on zero.
As you watch the videos below, keep a short checklist in mind. Is there curvature or any systematic shape in the residual plot (a sign of non-linearity)? Does the vertical spread stay roughly constant across the range of fitted values (homoscedasticity) or does it fan out? Are there a few points with unusually large residuals, and would removing them noticeably change the fit (outliers versus influential points)? And do the residuals look approximately normally distributed when you histogram them or plot them on a normal probability plot? Also pay attention to the mechanics: how residuals are actually computed and how software produces these plots for you.
This lesson introduces residuals as the gap between observed and predicted values and then builds up to residual plots as a tool for judging whether a linear model is appropriate. Based on its title and accompanying handout, it works through computing residuals from a fitted line and reading residual plots for leftover patterns, using a real context involving income and SAT/ACT scores. Expect worked examples with an emphasis on interpretation rather than formulas.
Skew The Script is known for clear, context-driven statistics instruction, and this video directly covers the foundational subtopics — what residuals are, how to compute them, and how to read residuals versus fitted values to detect non-linearity.
Produced by chemical engineering faculty at CU Boulder, this video frames residual analysis as a check on model accuracy for fitted engineering data. Given the title and source, it likely demonstrates plotting residuals, identifying systematic trends that indicate the wrong functional form, and recognizing non-constant spread or unusual points as signs the model needs revision. It is aimed at an engineering audience working with experimental data.
LearnChemE is a well-established engineering education channel, so the framing and examples match this course's audience and connect residual diagnostics to deciding whether a model is adequate or needs adjustment.
A short, hands-on walkthrough of generating residual plots in Excel 2016 to check regression assumptions. It continues from earlier videos on scatterplots and correlation, so it focuses on the software steps for producing residual output and then on reading those plots for violations of linearity and constant variance.
It supplies the practical, tool-based side of the topic — actually producing residuals and residual plots in software you are likely to use — which complements the conceptual videos and supports assessing homoscedasticity and spotting outliers visually.
Together these three videos move from definition to diagnosis to execution. The first establishes what residuals are and how to compute and plot them, supporting MO2 and the linearity portion of MO1. The second applies residual analysis in an engineering modeling context, reinforcing MO1 and MO2 and pointing toward the judgment calls in MO4 and MO5 about whether a model's functional form should change. The third gives you the software workflow to generate residual plots yourself, which is the practical foundation for the systematic diagnostic routines in MO1 and MO4. Note that cross-validation (MO3) is addressed elsewhere in this module; these videos focus on the residual-based half of model validation.
These videos were chosen from YouTube on October 2, 2026. Each has captions; the player turns them on. Videos on YouTube can be changed or removed — if one no longer plays, tell your instructor. If a player does not appear, use its Watch on YouTube link.