Multiple regression extends simple linear regression by allowing several predictor variables to explain variation in a single response variable. In engineering settings you rarely have just one input driving an outcome: material strength may depend on temperature, curing time, and composition all at once. The multiple regression model expresses the response as an intercept plus a weighted sum of predictors, where each coefficient is estimated by ordinary least squares and interpreted as the effect of that predictor while the others are held constant.
Building a usable model is more than running the computation. You need to judge how well the model fits (R-squared versus adjusted R-squared), whether the model as a whole explains a significant share of variance (the overall F-test), whether individual coefficients are significant (t-tests), and whether the residuals behave as the assumptions of linearity, constant variance, independence, and normality require. Models with too many weak predictors can look impressive on R-squared alone while adding little real explanatory value, which is why refinement strategies matter.
The videos below walk through these decisions with worked examples. As you watch, pay attention to the reasoning used to decide whether a variable earns its place in the model, how adjusted R-squared responds when predictors are added or dropped, and how the F-test statistic is formed from the regression and error sums of squares. Keep a note of the vocabulary used for output tables, since that is the form in which you will see most software results.
This video walks through the interactive, judgment-based side of model building: deciding when a predictor should be kept in a multiple regression model and when it should be dropped. Based on its title and description, it focuses on the decision logic behind including or excluding features rather than on mechanical computation alone. Expect discussion of fit measures and coefficient significance as the evidence behind those decisions.
It speaks directly to the refinement subtopic, showing how adjusted R-squared and coefficient results are weighed in practice, and Brandon Foltz's Statistics 101 series is known for slow, example-driven explanations suited to first-time learners.
This video introduces stepwise regression as a systematic model-building procedure, using a worked example to show how predictors enter or leave the model one at a time. It is likely to cover the criteria used at each step and how the model changes as variables are added or removed. It complements the more judgment-based approach by presenting an algorithmic alternative.
Variable selection strategies are a named subtopic here, and this video gives the standard automated approach along with its logic, letting you compare it against manual, reasoning-driven refinement.
A short, focused clip on the F-test for overall significance of a multiple regression model. It explains what the test is asking, namely whether there is a statistically significant linear relationship between the response and the set of predictors taken together, and how to read the result. Expect the hypotheses, the test statistic, and the interpretation of the outcome.
It isolates the overall F-test in a compact format, making it an efficient review of the distinction between testing the whole model and testing individual coefficients.
Together these videos trace the full model-building cycle described in the module outcomes. The stepwise regression and interactive model-building videos support constructing a regression equation with appropriate predictors (MO1), interpreting what each coefficient contributes alongside the others (MO2), distinguishing R-squared from adjusted R-squared when predictors are added (MO3), and justifying inclusion or removal decisions during refinement (MO5). The F-test video targets MO4 directly by showing how to determine whether the model as a whole explains a significant proportion of variance. Use the videos as worked companions to the textbook treatment of assumption checking and software output interpretation.
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.