Scatterplots and the Story of r: Reading Data Honestly
🎯 Today's mission briefing
We are learning to describe, quantify and question the relationship between two numerical variables — so we can use data as evidence without being fooled by it.
You'll know you've got it when:
- I can identify the explanatory and response variables and describe a scatterplot's association by direction, form and strength
- I can interpret the correlation coefficient r — including what r near zero does and does not mean
- I can use a least-squares line to make and interpret predictions, and say when a prediction is interpolation I can trust versus extrapolation I should flag
- I can explain why association is not causation, and suggest a plausible lurking variable
Ice creams and rips
Connects to what your guest already knows and makes them curious. Activating prior knowledge is one of the strongest predictors of new learning.
Here's a true and slightly alarming fact: across Queensland summers, weeks with higher ice-cream sales also record more surf rescues. Plot the data and you get a beautiful upward-sloping cloud of points. So — should Surf Life Saving campaign against ice cream? Obviously not. But notice what your brain just did: it saw a strong association and immediately went hunting for the third thing (hot weather) that drives both. That instinct — respect the pattern, question the cause — is professional-grade statistical thinking, and today we sharpen it into exam-grade technique.