A scatter graph plots pairs of data as points, one variable across and one up, to show whether they are related. Each point is one person, day or object, for example one student’s hours of revision and their test score.
Types of correlation
- Positive correlation: as one variable increases, the other tends to increase. The points slope upwards, like revision time and test scores.
- Negative correlation: as one variable increases, the other tends to decrease. The points slope downwards, like a car’s age and its value.
- No correlation: there is no clear pattern. Knowing one variable tells you nothing about the other, like shoe size and test score.
Strong or weak?
The closer the points are to a straight line, the stronger the correlation. When the points form a wide, loose band, the correlation is weak.
The correlation coefficient, written r, puts a number on this. It always lies between −1 and 1:
| r | Description |
|---|---|
| 0.9 to 1 | very strong positive |
| 0.7 to 0.9 | strong positive |
| 0.4 to 0.7 | moderate positive |
| 0.2 to 0.4 | weak positive |
| −0.2 to 0.2 | little or no correlation |
| −0.4 to −0.2 | weak negative |
| −0.7 to −0.4 | moderate negative |
| −0.9 to −0.7 | strong negative |
| −1 to −0.9 | very strong negative |
These bands are a common guide; textbooks draw the lines in slightly different places. The revision data above has r = 0.991, the car data r = −0.996, and the shoe size data r = −0.035.
See r for the revision data in the Line of Best Fit calculator →
Outliers
An outlier is a point that doesn’t fit the pattern of the others, such as a student who revised for 9 hours but scored only 20. Outliers can be mistakes in the data, or genuinely unusual cases. One outlier can change r a lot, so look at the graph as well as the number.
Correlation is not causation
Two things can rise and fall together without one causing the other. Ice cream sales and sunburn cases are positively correlated, but ice cream doesn’t cause sunburn: both increase in hot, sunny weather. The weather is a hidden variable behind both.
So a scatter graph can show that two things are linked, but not why. Deciding whether one causes the other needs more evidence, such as an experiment.
When the correlation is strong, a line of best fit can summarise the pattern and make predictions.