What You'll Learn
- What correlation is and how to recognize three types: positive, negative, and zero
- How to plot and interpret scatter graphs
- Why correlation does NOT mean causation (critical concept)
- How to draw a line of best fit by eye
- How to use lines of best fit to make predictions (interpolation)
- Why extrapolation is unreliable and how far you can safely predict
🎯 What is Correlation?
Correlation describes how two quantities are related to each other — whether they change together or in opposite directions.
Imagine you're watching two dancers on a stage. If they both move forward when the music gets louder, they're moving in sync. If one moves forward while the other moves backward as the music changes, they're moving in opposite directions. Correlation is like describing how synchronized those two dancers are.
The Three Types of Correlation
Positive Correlation
📈
One goes up, the other goes up
Temperature ↑ → Cold drink sales ↑
Negative Correlation
📉
One goes up, the other goes down
Car age ↑ → Car value ↓
Zero / No Correlation
❌
No clear relationship
Snail mass ↔ Exam scores
Strength of Correlation
Not all correlations are equally "tight." Correlation can be strong or weak:
- Strong correlation: The data points lie very close to a straight line. Small change in one variable = predictable change in the other.
- Weak correlation: The data points are scattered loosely around a trend line. One variable increasing tells you little about the other.
⚠️ CRITICAL: Correlation ≠ Causation
If two quantities correlate, it does not mean the first causes the second.
Example: Each day, you measure a sunflower's height and a puppy's weight. As the sunflower grows, the puppy gets heavier. Positive correlation! But you cannot claim: "Make the sunflower taller and your puppy will weigh more!" Both are increasing over time — time is the real cause.
Examiners love testing this misconception. Always ask: could a third variable (like time, age, or season) explain both?
Question 1: A study finds that people who eat more ice cream tend to drown more often. Is this a positive correlation? Should we ban ice cream?
📊 Scatter Graphs
What is a Scatter Graph?
A scatter graph (or scatter diagram) is used to plot pairs of data as individual points.
Key features:
- Points are plotted as crosses (×), not dots
- Points are not joined up with lines
- The horizontal axis (x) and vertical axis (y) represent the two quantities being measured
- The overall shape of the points shows the type of correlation
Reading a Scatter Graph
The pattern of points tells you the correlation:
- Positive correlation: Points go from bottom-left to top-right (positive gradient)
- Negative correlation: Points go from top-left to bottom-right (negative gradient)
- No correlation:
Quick Check: