Interpret scatter diagrams and lines of fit
Describe correlation, draw a suitable line of best fit and use the Extended GDC regression equation with caution.
Use this pathway for Cambridge IGCSE International Mathematics 0607, 2028–2030. Core and Extended objectives are labelled in each lesson; Extended adds requirements beyond Core. Paper 1 and Paper 2 are non-calculator. Papers 3–6 require a graphic display calculator (GDC). These original lessons use self-checked practice; they are not a Cambridge grade, full timed paper or teacher review.
Before you begin
- Check whether your school has entered you for Core or Extended. Core and Extended share most Number ideas, but some notation and methods are Extended only.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should a line of best fit balance?
What you will learn
- Plot paired data and describe positive, negative or zero correlation
- Draw and use a balanced line of best fit
- Use Extended linear regression output and distinguish interpolation from extrapolation
Describe the pattern, not a cause
Positive correlation means larger x values tend to occur with larger y values; negative means y tends to decrease as x increases; zero means no clear linear trend. Correlation alone does not show that one variable causes the other.
Plot paired measurements with labelled axes and a sensible scale. Identify unusual points and describe the strength or direction only as supported by the pattern.
Fit the trend across the data
A by-eye straight line of best fit should extend across the data, pass through the mean point (x̄, ȳ), and leave a roughly even spread of points above and below. It need not pass through any data point.
Extended candidates can use a GDC to find and use the linear regression equation. Predictions within the observed x range are interpolation; predictions outside it are extrapolation and may be unreliable. The correlation coefficient is not required by this syllabus.
Pause and explain
Does correlation alone show that x causes y?
Worked example
The data points are (1,3), (2,5), (3,7). Describe the correlation and give a line of best fit.
Show the worked solution
- As x increases, y increases, so correlation is positive.
- The points lie exactly on a straight line.
- A suitable line is y = 2x + 1; it passes through the mean point (2,5).
Answer Positive correlation; y = 2x + 1.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
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 weekly practice time increases, measured scores generally increase. State the likely correlation and one conclusion you cannot draw from that alone.
Give me a hint
Describe the direction of the pattern, then separate association from cause.
Compare my reasoning
- The likely correlation is positive.
- The data suggest an association between practice time and score.
- They do not alone prove practice time caused the score change; other factors may matter.
Positive correlation; causation is not established.
Look for these in your work
- Direction identified
- Association stated
- Causal claim limited
For points (1,3), (2,5), (3,7), verify that y = 2x + 1 fits all three and find their mean point.
Give me a hint
Substitute each x and average the coordinates separately.
Compare my reasoning
- At x = 1, 2 and 3 the equation gives y = 3, 5 and 7.
- Mean x = (1+2+3)/3 = 2; mean y = (3+5+7)/3 = 5.
- The mean point is (2,5), on the fitted line.
The line fits all three; mean point (2, 5).
Look for these in your work
- Predictions substituted
- Coordinate means calculated
- Mean-point property checked
A GDC's regression line predicts a study score at 5 hours, while observed study times range from 1 to 4 hours. Classify the prediction and give a caution.
Give me a hint
Compare the prediction input with the observed data range.
Compare my reasoning
- Five hours is outside the observed range 1–4.
- The prediction is extrapolation.
- The association may not continue beyond the data, so interpret it cautiously.
Extrapolation; the trend may not continue outside the observed range.
Look for these in your work
- Range checked
- Prediction type named
- Limitation stated
Common mistakes
- Claiming correlation proves causation
- Drawing a line through every point when the pattern is scattered
- Fitting a line over only part of the x range
- Trusting an extrapolated prediction without qualification
What can you explain now?
What does negative correlation describe?
Compare with the explanation
As x increases, y tends to decrease
This states the direction of the association.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.
Make it stick
What features make a line of best fit balanced, and why should an outside-range prediction be treated cautiously?
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.