Watch out
Saying correlation proves cause.
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SQA National 5 Mathematics
Scatter graphs
Describing correlation and using a line of best fit.
Formula reference
Check the National 5 rules and formulae linked to this topic.
Which method?
Match exam clues to a suitable method.
Before you start
- Know that each point represents two values.
- Look for overall trend, not one point.
- Use a line of best fit only when there is correlation.
Explanation
A scatter graph shows the relationship between two variables.
Positive correlation means both variables tend to increase together. Negative correlation means one tends to decrease as the other increases.
A line of best fit can be used to estimate values, but estimates outside the data range are less reliable.
Visual support
Scatter graph trend
Key formulae and rules
- positive correlation: upward trend
- negative correlation: downward trend
- no correlation: no clear pattern
Check
Compare your answer with the size you expected from the question.
Exam tip
Use the words positive, negative or no correlation, then add a sentence in context.
Calculator tip
Use brackets for fractions, powers and square roots, then round only at the final line.
Worked examples
Worked example 1
Describe correlation
Points for study time and test score form an upward trend.
- As study time increases, test score tends to increase.
- The points are close to a line.
- This suggests positive correlation.
Answer: There is positive correlation.
Worked example 2
Use a line of best fit
A line of best fit predicts score = 8h + 35, where h is hours studied. Estimate the score for 5 hours.
- Substitute h = 5
- score = 8(5) + 35
- score = 75
So: Estimated score is 75 marks.
Worked example 3
Spot an outlier
Most points follow a rising trend, but one pupil studied 8 hours and scored 30.
- Compare the point with the trend.
- A score of 30 is much lower than nearby points.
- It does not fit the pattern.
Answer: The point is an outlier.
Watch out
- Saying correlation proves cause.
- Joining the dots instead of drawing a line of best fit.
- Using a line of best fit far beyond the data range.