Fitting a regression line is only the first half of the job. Regression validation is the set of practices engineers use to ask whether a fitted model is actually trustworthy: Do the assumptions behind the least-squares machinery hold for this data? Does the model describe the sample well, and will it still perform acceptably on data it has never seen? These two questions — reliability on the data you have and generalizability to data you don't — are distinct, and a model can succeed at one while failing badly at the other.
In this course, validation matters because engineering decisions get made from model predictions: sizing a component, forecasting a load, setting a process tolerance. A model with an impressive R-squared can still produce systematically wrong predictions if the residuals show curvature, if variance grows with the fitted values, or if the model has simply memorized noise in a small sample. Residual analysis is the main diagnostic tool for the first family of problems; resampling methods such as cross-validation address the second. Together they feed a cycle: fit, diagnose, refine, re-check.
As you watch the videos below, keep three questions in mind. First, what specific quantity is being used to judge the model, and what does it actually measure? Second, which plot or procedure would reveal each core assumption violation — linearity, constant variance, independence, normality? Third, how does a validation finding translate into a concrete next step, such as transforming a variable or changing the functional form?
This video walks through common ways of evaluating how well a regression model performs, including R-squared and its interpretation as the proportion of variance in the outcome explained by the model. It is likely to discuss what such summary measures do and do not tell you about model quality, and how prediction error is assessed. Expect attention to the gap between fitting the data at hand and predicting new observations.
It directly supports the "What Is Regression Validation?" and "Reliability vs. Generalizability" subtopics by making clear that a goodness-of-fit number is not by itself evidence that a model is valid.
The opening lecture of Stanford's cross-validation unit, taught in the Hastie and Tibshirani statistical learning sequence, introduces resampling as a way to estimate how a model will perform on data it was not trained on. It is likely to cover the train/test split idea, why training error understates true error, and the motivation for systematic cross-validation procedures. This sets up the distinction between holdout, k-fold, and leave-one-out approaches.
It comes from the authors of the standard statistical learning text and gives an authoritative, carefully motivated treatment of generalizability — the half of validation that residual plots alone cannot address.
A tutor from the University of Liverpool's statistics support service demonstrates, step by step, how to check the assumptions behind a linear regression model using SPSS. The walkthrough is likely to cover the standard diagnostic outputs — residual plots, normality checks of residuals, and indications of non-constant variance or problematic observations — and how to read them. The emphasis is practical: which output to request and what a violation looks like on screen.
It grounds the "Core Assumptions" and "Role of Residual Analysis" subtopics in an actual diagnostic workflow, so you see what assumption checking looks like in practice rather than only in the abstract.
The Liverpool SPSS demonstration maps most directly onto MO1 and MO2, showing how residual diagnostic plots are produced and read to detect violations of linearity, homoscedasticity, independence, and normality, and it also touches the outlier and influence concerns in MO4. The Stanford cross-validation lecture establishes the conceptual basis for MO3 by explaining why out-of-sample estimation is necessary before the specific holdout, k-fold, and leave-one-out procedures are compared. The evaluation-metrics video ties the two strands together, clarifying what R-squared and error measures actually report, which is the judgment students need in order to decide — per MO5 — whether a model should be refined through variable removal, transformation, or a change in functional form. Taken as a set, they frame validation as the repeating diagnose-and-refine cycle this module is built around.
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.