Multiple regression extends the simple linear model by allowing two or more predictor variables to explain variation in a single response. Instead of fitting a line through a scatterplot, you fit a surface described by an equation of the form y = b0 + b1x1 + b2x2 + ... + bkxk, where each slope coefficient describes the effect of one predictor while the other predictors are held constant. That "holding the others constant" idea is the single most important conceptual shift in this module, and it is also the source of most misinterpretation.
For engineers, multiple regression is the everyday tool for modeling outcomes that depend on several inputs at once: strength as a function of mix proportions and curing time, energy use as a function of temperature and occupancy, process yield as a function of several operating settings. Along with building the model, you need tools for judging it: R-squared and adjusted R-squared for overall fit, t-tests and p-values for individual coefficients, the F-test for the model as a whole, and diagnostics such as the variance inflation factor (VIF) when predictors are correlated with each other.
As you watch the videos below, focus on how each piece of software output maps to a decision. Ask yourself: what does this coefficient mean in the units of the problem? Why does adjusted R-squared behave differently from R-squared when a predictor is added? And when two predictors carry overlapping information, how does multicollinearity distort the coefficient estimates and their standard errors? Keep a worked example of your own nearby so you can follow along with the reasoning rather than just the arithmetic.
A compact walkthrough of the coefficient section of a multiple regression software output. Based on its title and description, it covers how to read and interpret each estimated coefficient, how to construct confidence intervals for the coefficients, and how to carry out hypothesis tests on individual predictors using the reported standard errors, t-statistics and p-values.
It targets the interpretation subtopic directly and in a short, focused format, which makes it a good first stop for learning to read regression output the way you will see it in software rather than in formula form.
This Statistics 101 lesson focuses on adjusted R-squared as a model assessment statistic for multiple regression. It is likely to contrast adjusted R-squared with ordinary R-squared, explain why R-squared never decreases when predictors are added, and show how the adjustment penalizes unnecessary predictors when comparing candidate models.
Brandon Foltz's Statistics 101 series is known for slow, example-driven explanations, and this video addresses both the model fit subtopic and the model building and variable selection subtopic, since adjusted R-squared is a common criterion for deciding which predictors to keep.
A university lecture from the IIT Madras B.S. Degree Programme covering multiple linear regression with an emphasis on the variance inflation factor. Expect a treatment of what multicollinearity is, how VIF is computed from regressions of each predictor on the remaining predictors, and how to use VIF values to flag predictors that are redundant or unstable.
It is the most formal and detailed of the three and is the designated resource for the multicollinearity subtopic, giving you a diagnostic tool to use when coefficient estimates look unstable or contradict expectations.
Together these videos carry you from reading output to judging it. The coefficient walkthrough supports MO2 and MO3 by showing how slope estimates, confidence intervals and p-values are interpreted when several predictors are present, which is exactly what distinguishes multiple from simple regression. The adjusted R-squared lesson reinforces MO2 and MO5 by giving you a defensible basis for choosing among competing models and for explaining to a non-technical audience why a bigger model is not automatically a better one. The VIF lecture supports MO4 by adding multicollinearity to your model-checking routine alongside the residual-based assumption checks, so that a model you report is one you have actually validated. MO1 remains the simple-regression foundation on which all of this is built.
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.