Week 8 - Multiple Regression I
Adding Predictors
Up to now every model has had exactly one predictor. That was a teaching convenience, not a research design. Almost nothing you care about has one cause, and almost no variable you measure is unentangled from the rest.
This week we put two predictors in the same model, and the whole week turns on one phrase: holding the other predictor constant. It is not a hedge and it is not boilerplate. It changes what the coefficient is a number about — from “the difference between people who differ in X” to “the difference between people who differ in X and are otherwise matched on everything else in the model.”
A slope is not a property of a variable. It is a property of a variable inside a particular model. Change what else is in the model and the number changes — sometimes a little, sometimes a lot, occasionally all the way to the opposite sign.
We open with a county fire department, 300 fires, and a regression that says sending more fire trucks causes more damage. The output is correct. The conclusion is lethal. Fixing it takes exactly one more variable.
Then we do it with real survey data, where the honest finding is less dramatic: two predictors that barely move each other, which turns out to be the common case and a perfectly reportable result.
Part 6 of the Midterm Project asks for a two-predictor model, each coefficient interpreted with its holding constant clause, and a model-comparison table with ΔR². All of that is today.
If you have been waiting on Part 6, you are no longer waiting. The project is due Tuesday 10/27.
Prepare
Slides
💻 Multiple Regression I - JAMOVI
Both decks use the same data and reach the same numbers. JAMOVI again has the edge on model comparison — Model Builder → Model Comparisons gives you ΔR² and its F test without fitting a second model by hand.
Data
Lecture: County Fire Data (.csv) · Student Stress Survey (.xlsx)
In-class activity: Film Budgets & Box Office (.csv)
The film data is deliberately messy: one of the money columns imports as text because the spreadsheet wrote #N/A into some cells. Part of the activity is noticing that before you try to model it.
In-Class Activity
For Next Time
No lab is due this week. The midterm is the assignment.
📋Midterm Project — due Tuesday 10/27 at 11:59pm
📖Chapter 14.3 - ST — categorical predictors
📖Chapter 8.1 - MSR — interactions
Week 6 gave you groups. Week 8 gave you two predictors. Next week they meet: a model with a group and a continuous predictor in it, and then the question that makes moderation interesting — what if the slope is not the same for every group?
Back to course schedule ⏎