Regression analysis is the set of tools engineers use to describe and quantify how one variable responds to one or more others. In its simplest form, you fit a straight line through a cloud of data points so that the line summarizes the relationship between an independent (predictor) variable and a dependent (response) variable. Once that line exists, it can be used for two distinct jobs: explaining how much the response changes when a predictor changes, and predicting the response for conditions you have not yet observed.
This topic matters because most engineering decisions involve more than one influence at a time. Yield depends on temperature and pressure; cycle time depends on batch size, operator experience, and machine age. Moving from simple regression (one predictor) to multiple regression (several predictors) lets you separate these effects. Along the way you need a way to judge whether the model is any good, which is where model fit measures such as R-squared, the standard error, and the F-test come in, and whether the model is trustworthy, which is where the underlying assumptions (linearity, independence, constant variance, and approximately normal errors) come in.
As you watch the videos below, keep three questions in mind. First, what exactly is being predicted and what is doing the predicting? Second, what number in the output tells you how well the model fits, and what does that number not tell you? Third, how does the mathematics scale up when you go from one predictor to many? The videos move roughly in that order, from conceptual framing to reading output to the underlying matrix machinery.
A short conceptual overview from IBM that frames linear regression as a method for modeling the relationship between a dependent variable and one or more independent variables, and explains why it is such a common starting point in machine learning and data analysis. Based on its title and description, it is likely to cover the idea of fitting a line to data, the distinction between explanation and prediction, and typical use cases. Expect vocabulary and framing rather than hand calculations.
It is a clean, plain-language entry point to the subtopics What Is Regression Analysis?, Dependent and Independent Variables, and Purpose of Regression in Decision-Making, produced by a well-known technical publisher whose explainer series is aimed at newcomers.
A worked problem that takes a multiple regression scenario with 40 observations and walks through the ANOVA table, filling in degrees of freedom and sums of squares, then computing the F-statistic, R-squared, and the standard error of the estimate. It shows where each quantity in a regression printout comes from and how the pieces of the table relate to one another. The focus is on reading and completing output rather than on deriving the model.
It directly addresses The Concept of Model Fit and the simple-versus-multiple distinction by showing how fit statistics are computed and interpreted when there are several predictors, and Joshua Emmanuel's channel is widely used for concise, step-by-step business-statistics problem solutions.
A longer treatment from LearnChemE that presents multiple linear regression in matrix form, setting up the design matrix and response vector and using the normal equations to obtain the coefficient estimates. The description points to an accompanying spreadsheet, so the presentation is likely to connect the matrix algebra to a practical computational setup. This is the general machinery that simple regression is a special case of.
It shows why multiple regression is a natural extension of simple regression rather than a separate technique, and LearnChemE is a university-produced engineering education channel, so the notation and worked approach fit an engineering audience.
Together these videos build the conceptual base the module outcomes rest on. The IBM overview establishes what regression is and why engineers use it for decision-making, supporting the framing needed for MO1 and MO5. The ANOVA and F-test walkthrough gives direct practice reading the fit statistics named in MO2 and makes clear how output changes as predictors are added, which supports MO3. The matrix-based treatment generalizes the least squares fit from one predictor to many, reinforcing MO1 and MO3. None of the three focuses on residual plots or assumption checking, so MO4 will be addressed primarily through the module readings, lecture material, and your software-based assignments.
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.