Scatter graphs: correlation and the line of best fit
Plot scatter graphs, describe correlation, draw a line of best fit and make estimates, and learn why correlation does not mean causation.
KS3GCSEMiddle SchoolHigh SchoolCurriculum fit: GCSE Maths Statistics (Foundation and Higher). US: Grade 8 and High School Statistics and Probability (Interpreting Categorical and Quantitative Data).
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What is it?
A scatter graph plots pairs of values, such as hours of revision and test score, as points on a grid. It helps you see whether there is a relationship between two variables.
The pattern of the points is called correlation. A line of best fit summarises the trend and can be used to make estimates.
Key formulas and ideas
- Positive correlation: as x increases, y tends to increase.
- Negative correlation: as x increases, y tends to decrease.
- No correlation: no clear pattern.
- Line of best fit: a straight line close to as many points as possible, with about equal numbers above and below.
Worked examples
Example 1: Describe correlation
Question: As the temperature rises, ice cream sales rise. What type of correlation is this?
- Both variables increase together.
- So the points slope up from left to right.
Answer: Positive correlation
Example 2: Estimate from a line of best fit
Question: A line of best fit has equation y = 1.5x + 2. Estimate y when x = 6.
- Substitute x = 6: 1.5 × 6 + 2.
- = 9 + 2 = 11.
Answer: 11
Example 3: Reliability
Question: The data covers x from 2 to 10. Is an estimate at x = 40 reliable?
- x = 40 is far outside the data range.
- This is extrapolation, so the trend may not continue.
Answer: No, extrapolation is unreliable
Common mistakes
- Joining the points dot to dot instead of drawing a line of best fit.
- Forcing the line through the origin when it does not fit.
- Saying that correlation proves one thing causes the other.
- Ignoring outliers, or treating them as errors without checking.
Practice questions
Frequently asked questions
What is an outlier?
A point that is much further from the trend than the others. It may be an error or an unusual real value.
Does correlation mean causation?
No. Two variables can be linked because of a third factor, or by coincidence.
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GCSEHigh SchoolSources and review
- DfE: GCSE mathematics subject content and assessment objectives
- Common Core State Standards: Mathematics (high school)
Reviewed by StudyMorrow editorial review on 5 Nov 2026.