Week 14/Module 13 - Validating Regression

This reading introduces regression validation as a structured process for assessing whether a regression model is genuinely trustworthy beyond surface-level metrics like R-squared, and learners use it to understand why and how model checking is necessary before drawing conclusions.

This reading explains the core assumptions underlying ordinary least squares linear regression (such as linearity, independence, homoscedasticity, and normality of errors) and how learners and instructors can identify when those assumptions are met or violated.

This reading covers residual analysis as a diagnostic tool for evaluating whether a fitted regression model is correct, teaching learners how to examine patterns in residuals to detect assumption violations and model misspecification.

This reading explains cross-validation techniques—including holdout sets and k-fold cross-validation—and how learners use them to assess a model's ability to generalize to new data rather than just fitting the training sample.

This reading covers three major categories of structural regression model weaknesses—such as multicollinearity, influential observations, and heteroscedasticity—and teaches learners how to identify and diagnose these problems before they corrupt model estimates.

This reading covers the process of iteratively refining a regression model for trustworthiness and generalizability, guiding learners and instructors through balancing statistical fit with practical performance to support sound decision-making.

An introductory reading that frames regression validation as the second half of model building, explaining why engineers must check least-squares assumptions, assess how well a model fits the sample, and judge whether it will generalize to new data — used as the conceptual starting point for the module.

A reading that catalogues the core assumptions underlying least-squares estimation (linearity of the mean response, constant error variance, independence, and normality of errors) and explains how violations undermine standard errors, t-tests, the F-test, and prediction intervals, so learners know what to check before trusting a model.

A lesson defining residuals as observed minus predicted values and showing how to read individual residuals and residual plots to detect curvature, non-constant variance, and other signs that the chosen model form is wrong; learners use it to practice diagnostic plotting and interpretation.

A reading on cross-validation that explains why training-data statistics like R-squared and residual standard error are optimistically biased and introduces holdout and k-fold style resampling methods for estimating out-of-sample prediction accuracy.

A diagnostic-focused lesson on spotting unstable or misleading models, covering unusual observations such as outliers, high-leverage and influential points, and redundant or collinear predictors that can hide behind a high R-squared; used as a systematic checklist for evaluating model trustworthiness.

A capstone reading on what to do after diagnostics reveal a problem, covering remedies such as adding transformations or polynomial terms for curvature, addressing non-constant variance, handling collinear predictors and influential points, and deciding among competing models.

A consolidated, full-module reading that compiles all six topics — validation foundations, assumption checking, residual analysis, cross-validation, model weakness diagnosis, and model refinement — into a single continuous document for review or printing.

A module landing page that links learners to the Module 13 lecture presentation, supporting video lecture, and a Google Colab notebook for hands-on regression validation exercises.

A comprehensive reading that defines and explains residual analysis, key regression model validation concepts, and supporting techniques, used by learners as a primary reference while working through the module.

A graded discussion prompt asking learners to evaluate and comment on methods for detecting dependency between independent and dependent variables, used to encourage reflection on regression validation approaches across different data types.

A multi-part interactive HTML activity in which learners work through scored problems on selecting and justifying a valid regression model, with optional hints (worth a point penalty) and running point totals, used for self-paced practice and immediate feedback on model-fit decisions.