Week 13/Module 12 - Multiple Regression

This reading explains why simple linear regression is insufficient for real-world engineering and scientific problems and introduces multiple regression as the method for modeling outcomes that depend on more than one predictor variable; learners read it to build conceptual motivation before studying the technique formally.

This reading covers how a multiple regression model is mathematically structured, including how predictors are combined with coefficients and an intercept to form the model equation; learners use it to understand how to correctly specify a multiple regression model before fitting it to data.

This reading explains how to interpret regression coefficients in a multiple regression context, emphasizing that each coefficient represents the effect of one predictor while holding all others constant; learners use it to correctly draw conclusions from estimated model parameters.

This reading covers the metrics and methods used to evaluate how well a multiple regression model fits the data, including R-squared, adjusted R-squared, and overall model significance tests; learners use it to judge whether a fitted model adequately explains variation in the outcome variable.

This reading provides a practical, end-to-end walkthrough of constructing and evaluating multiple regression models, covering predictor selection, assumption checking, and interpretation of results; learners use it as an applied guide for carrying out a full multiple regression analysis.

A reading that motivates the move from single-predictor to multi-predictor models, using engineering examples like fuel consumption and concrete strength to show why one variable rarely explains an outcome on its own, serving as the conceptual entry point to the module.

A lesson on specifying the multiple regression model, extending y = b0 + b1x + e to several predictors and guiding learners through deciding which variables to include and how the model's structure represents their joint effect on the response.

A reading explaining partial regression coefficients — how each estimated slope represents the expected change in the response per one-unit increase in that predictor while the others are held constant — so learners can correctly interpret multi-predictor output.

A lesson on evaluating how well a fitted model describes the data, covering R-squared and related fit measures and how to use them to compare competing models built from different predictor sets.

A summative reading that walks through the full workflow of constructing and assessing a multiple regression model with engineering examples such as material strength depending on temperature, curing time, and composition.

The consolidated module page compiling all Week 13 topics on multiple regression in sequence, from the transition out of simple regression through model specification, coefficient interpretation, and fit assessment, for use as a single-source review.

A landing page for Module 12 that provides links to the PowerPoint slides, lecture recording, and a Google Colab notebook for multiple regression analysis, used by learners to access all core instructional resources in one place.

A comprehensive study reference page explaining multiple regression concepts including model definition, key characteristics, coefficient interpretation, and model evaluation, used by learners to read, review, and reinforce lecture material.

A graded discussion assignment asking learners to propose a real-world example from a field of their choice where multiple linear regression with at least two independent variables would be appropriate, and to comment on a peer's response.