Understanding what regression does and when to use it
🎯 Learning Objectives
Understand what regression does (prediction vs. correlation)
See when regression is appropriate vs. other statistical tests
Recognize the power of regression for answering research questions
Learn the three main uses: description, prediction, and explanation
What is Regression?
Regression answers the question: "How well can I predict Y from X?"
More specifically:
📈 How does Y change when X increases by 1 unit?
🎯 How accurately can I predict Y if I know X?
🔍 How much variance in Y is explained by X?
Regression vs. Correlation: What's the Difference?
Aspect
Correlation
Regression
Question
"Are X and Y related?"
"How does Y change as X changes?"
Direction
Symmetrical (X↔Y is same as Y↔X)
Asymmetrical (Y from X ≠ X from Y)
Output
One number (r = -1 to +1)
Equation (Y = a + bX)
Use
Describe relationship strength
Make predictions, quantify effects
Units
Standardized (no units)
In original units of Y
🎮 Demo 1: Correlation vs. Regression
Let's see the difference in action. We'll look at study hours (X) predicting exam scores (Y).
🤔 Question 1: What information does regression give you that correlation doesn't?
The Three Uses of Regression
1. 📋 Description: "What is the relationship?"
Example: For every additional hour studied, exam scores increase by 5.2 points on average.
Why it matters: Quantifies the relationship in meaningful units.
2. 🔮 Prediction: "What will happen?"
Example: If a student studies 6 hours, we predict they'll score 78 points.
Why it matters: Make informed decisions based on known information.
3. 🧪 Explanation: "Does X affect Y?"
Example: Study time significantly predicts exam scores (p < .001), explaining 64% of variance.
Why it matters: Test theoretical predictions and understand mechanisms.
🎮 Demo 2: The Power of Prediction
Let's see regression make predictions on new data it has never seen before!
🤔 Question 2: Why is prediction useful even if we're not claiming causation?
🎮 Demo 3: Choosing the Right Test
Practice identifying when to use regression vs. other statistical tests.
🤔 Question 3: Give an example from your field where regression would be useful
Think about:
What would be your outcome variable (Y)?
What would predict it (X)?
What would you want to know?
Regression vs. t-test vs. ANOVA: Quick Guide
Test
Predictor (X)
Outcome (Y)
Question Answered
t-test
Categorical (2 groups)
Continuous
"Do groups differ?"
ANOVA
Categorical (3+ groups)
Continuous
"Do groups differ?"
Regression
Continuous (or categorical)
Continuous
"How does Y change with X?"
Correlation
Continuous
Continuous
"Are X and Y related?"
💡 Pro Tip: Regression is actually more flexible than this table suggests! You CAN use categorical predictors in regression (called "dummy coding"), and ANOVA is actually just a special case of regression.
🎮 Demo 4: Why Regression is Powerful
Let's compare regression to simpler approaches and see why it's so useful.
When Should You Use Regression?
✅ Use regression when:
You have a clear outcome variable (dependent variable Y)
You have one or more predictor variables (independent variables X)
You want to quantify the relationship in original units
You want to make predictions
Your variables are continuous (or can be treated as such)
❌ Don't use regression when:
You just want to know if groups differ (use t-test or ANOVA instead)
Both variables are categorical (use chi-square instead)
You have no clear dependent variable (use correlation instead)
Your outcome is binary (use logistic regression instead)
Key Takeaways
Remember:
✓ Regression gives you an equation (Y = a + bX)
✓ It tells you how much Y changes per unit of X
✓ It lets you make predictions for new observations
✓ It quantifies how well X predicts Y (R²)
✓ It's more flexible than you might think!
📝 Ready to Continue?
Make sure you understand:
What's the difference between correlation and regression?