Lab 8: How Good Is This Model?

Fit, in percentages and in real units

Instructions

Everything so far has been about estimates — slopes, intercepts, group differences. This lab is about the other half of the output: the numbers that tell you whether the model is worth anything.

You will fit three models to the same outcome, pull apart where the variance went, and report fit in the units a reader actually cares about. The last exercise is a sneak peek at Week 8, and it is the interesting one: a predictor that looks completely useless on its own turns out to matter quite a lot.

Here is what you’ll need:

Save the .csv in your data folder and the .qmd in your project folder. Render to Word and submit both files to myCourses.

Due date — and a heads-up

Tuesday, October 13 at 11:59 pm.

That Monday and Tuesday are Fall Break, so there is no class and no office hours that week before the deadline. The lab is submitted online exactly as usual. If you want help, email me before the break and we can find a time to meet if needed.

Working in JAMOVI?

Go ahead — submit your .omv plus a Word document with your written answers. JAMOVI’s Model Builder with Model Comparisons is genuinely nicer than base R for Exercises 5 and 6.

The study

A researcher recruited 118 undergraduates to study how stress and social support relate to anxiety. Each participant completed measures of:

Variable	Description
`Anxiety`	Current anxiety symptoms (higher = more anxious)
`Stress`	Perceived stress over the past month (higher = more stressed)
`Support`	Perceived social support (higher = more supported)
`Condition`	`"Tx"` or `"Control"` — half the sample completed a brief coping workshop

What you’ll practice

Partitioning variance by hand: \(SS_{total} = SS_{model} + SS_{residual}\)
Reading R², adjusted R², and the residual standard error off the output
Translating fit into the units of the outcome (“how wrong are we, typically?”)
Recognizing that adjusted R² can go negative, and what that means
Comparing nested models with ΔR²
Noticing when a predictor’s story changes once another variable is in the model

Exercises at a glance

Exercise	What you’ll do	Points
1. Describe	Import, describe, correlation matrix	3
2. Model 1	`Anxiety ~ Stress` — and a surprise	4
3. Model 2	`Anxiety ~ Support`	4
4. Partition	Verify \(SS_{total} = SS_{model} + SS_{residual}\) by hand	4
5. Real units	What the residual SE means for a counselor	3
6. Sneak peek 👀	Both predictors at once — and the plot twist	6
7. Judgment	What Model 1 alone would have made you conclude	2
8. Write-up	One paragraph, APA style	2
Bonus	Add `Condition`	+1

Total: 28 points (+1 bonus)

Tip

Exercise 6 is the point of the whole lab. Do not skip to it — the surprise only works if you have already met Model 1 on its own terms.