Correlation: Line of Best Fit, Spearman's and Pearson's
Read a scatter diagram, draw a line of best fit, and interpret the two correlation coefficients - without ever calculating Pearson's, which this board never asks you to do.
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Do they move together? 📈
Correlation is about whether two things **move together**. Plot pairs of values on a **scatter diagram** and a pattern may appear: as one goes up, does the other go up, go down, or do nothing? This module covers reading that pattern, drawing a **line of best fit** to make predictions, and **interpreting** the two correlation coefficients - **Spearman's** and **Pearson's**. One rule matters for this course: you may be asked to interpret Pearson's, but you are **never** asked to calculate it.
The language of correlation 📖
Five terms carry the topic. Learn them before the checks lean on them.
Name the correlation 🎯
On a scatter diagram, as the number of hours revised increases, exam marks also increase. What kind of correlation is this?
- Positive correlation
- Negative correlation
- Zero correlation
- Causation, because revising must cause better marks
Match the pattern 🔗
- Positive correlation
- Negative correlation
- Zero correlation
- Strong correlation
- As one variable increases, the other increases
- As one variable increases, the other decreases
- No pattern between the two variables
- The points lie very close to the line of best fit
Drawing the line 📏
A **line of best fit** is a single straight line through the middle of the points, with roughly **as many points above as below** it. Drawn by eye, it should pass close to the **mean point** (the average x, average y). Once drawn, you can use it to predict: read across from a known value to the line, then down to the other axis. But **where** you read matters, as the next step shows.
How far can you trust it? 🔮
You use a line of best fit to make a prediction. Which prediction is more reliable?
- Interpolation - predicting within the range of the data you have
- Extrapolation - predicting far beyond the range of the data
- Both are equally reliable in every case
- Neither can ever be used for prediction
Two coefficients ⚖️
A correlation coefficient puts a number on the strength and direction of correlation. Both of these run from **-1 to +1**: the **sign** gives the direction, and how **close to 1** gives the strength.
Read the coefficient 🔢
A study reports a Spearman's coefficient of rs = 0.9. What does this tell you?
- A strong positive correlation
- A strong negative correlation
- No correlation at all
- That one variable definitely causes the other
Correlation is not proof ⚠️
Here is the trap the examiner loves. A strong correlation shows two things **vary together** - it does **not** prove one **causes** the other. There may be a hidden **third factor** driving both (ice-cream sales and sunburn rise together, but ice cream does not cause sunburn - hot weather causes both), or it may be coincidence. Always call it an **association**, and resist the leap to causation unless a controlled experiment stands behind it.
Match each value to its meaning 🧩
- rs = 0.85
- r = -0.8
- rs = 0.05
- r = -0.3
- A strong positive correlation
- A strong negative correlation
- Almost no correlation
- A weak negative correlation
Correlation on trial 🧭
An interactive activity.
Use a line of best fit 🪜
An interactive activity.
The summary 📝
When both variables increase together, the correlation is _____. A line of best fit is drawn through the _____ of the points. Predicting within the data is called _____, which is more reliable than extrapolation. Both Spearman's and Pearson's coefficients run from _____ to +1. And a correlation never proves _____ on its own.
Your turn ✍️
An interactive activity.