Describe correlation and avoid a causal conclusion
Describe positive, negative or no clear correlation · Judge a pattern from the scatter rather than one pair · Separate association from evidence of causation
Section Paper 4 · Historical Extended · calculator
Exam scope and assessment notes
Core and Extended foundations. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Scatter diagrams
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Describe positive, negative or no clear correlation
- Judge a pattern from the scatter rather than one pair
- Separate association from evidence of causation
Describe the overall pattern
Positive correlation means larger x values tend to occur with larger y values; negative means larger x tends to occur with smaller y. A cloud with no clear trend can be described as zero or no clear correlation. The illustrated points show positive correlation overall even though the score falls from the third to fourth observation. Correlation does not require every consecutive pair to rise.
A relationship has limits
Points closer to a sensible trend line indicate a stronger linear pattern; a single extreme point can affect the appearance. No clear linear correlation does not rule out a curved relationship. Study-time and score association alone cannot establish that increasing study time caused the score difference; other differences and selection can affect the data.
Sources for this lesson
Pause and explain
Does positive correlation prove that changing x causes the change in y?
Worked example
Describe the illustrated study-time and score pattern.
Show the worked solution
- The overall scores tend to increase with time.
- There is variation around the trend, not an exact rule.
Answer Positive correlation; causation is not established by the diagram alone.
Try a topic test
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
As distance travelled increases, recorded fuel remaining generally decreases. Describe the correlation.
Give me a hint
Use the direction of the paired pattern.
Compare my reasoning
- Larger distance tends to pair with smaller fuel remaining.
- The trend is negative.
Negative correlation.
Look for these in your work
- Name the two variables
- Describe the overall direction
The illustrated data rise overall but score falls between x=3 and x=4. Must the overall correlation be negative?
Give me a hint
Consider all five observations.
Compare my reasoning
- The overall pattern is increasing.
- One local fall is compatible with positive correlation and scatter around a trend.
No; the overall correlation is positive.
Look for these in your work
- Use the whole data pattern
- Allow variation around the trend
A scatter diagram has a clear U-shaped pattern but no useful straight-line trend. Does this prove there is no relationship?
Give me a hint
Distinguish linear correlation from a general association.
Compare my reasoning
- A curved pattern is a relationship.
- A straight-line description can miss it.
No; there can be a nonlinear relationship despite no useful linear correlation.
Look for these in your work
- Inspect the shape
- Limit a linear-correlation claim
Common mistakes
- One local fall does not eliminate an overall positive pattern.
- Zero linear correlation can coexist with a nonlinear relationship.
What can you explain now?
Does positive correlation prove that changing x causes the change in y?
Compare with the explanation
No; association alone does not isolate a cause.
Other variables and the way observations were selected can explain the pattern.
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Make it stick
Does positive correlation prove that changing x causes the change in y?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.