Correlation and line of best fit
What you will learn
Know the rule, then use it
These are the short notes. Read each one, then check you can use it in the worked example below.
Method
Correlation: positive — both increase together
Identify the type of correlation
As revision hours increase, exam scores increase → positive correlation
Assess the strength
If points lie close to a straight line, the correlation is strong
Describe drawing the line of best fit
Draw a straight line with roughly equal numbers of points on each side
Watch out
Students draw the line of best fit from one corner to another rather than balancing points on each side
Correlation describes association, not proof of causation.
Interpolate inside the data range; be careful with extrapolation.
Describe the correlation in a scatter graph where higher revision hours are associated with higher exam scores. Draw a line of best fit and explain how to use it.
Identify the type of correlation: As revision hours increase, exam scores increase → positive correlation.
Assess the strength: If points lie close to a straight line, the correlation is strong.
Describe drawing the line of best fit: Draw a straight line with roughly equal numbers of points on each side.It should pass through or near (mean hours, mean score).
Use the line of best fit for prediction: Interpolation: reading off a value within the data range — reliable.Extrapolation: extending beyond the data — unreliable, as the pattern may not continue.
Strong positive correlation; line of best fit passes through the mean point
Build up to the hardest questions
Do them in order. If you miss a step, read the solution, then redo the question without looking.
WorkedreasoningDescribe the correlation in a scatter graph where higher revision hours are associated with higher exam scores. Draw a line of best fit and explain how to use it.
4 marks4 minsscatter-graphs-workedShow solution
Describe the correlation in a scatter graph where higher revision hours are associated with higher exam scores. Draw a line of best fit and explain how to use it.
- 1.Identify the type of correlation: As revision hours increase, exam scores increase → positive correlation.
- 2.Assess the strength: If points lie close to a straight line, the correlation is strong.
- 3.Describe drawing the line of best fit: Draw a straight line with roughly equal numbers of points on each side.It should pass through or near (mean hours, mean score).
- 4.Use the line of best fit for prediction: Interpolation: reading off a value within the data range — reliable.Extrapolation: extending beyond the data — unreliable, as the pattern may not continue.
Strong positive correlation; line of best fit passes through the mean point
- M1: identify the type of correlation
- M1: assess the strength
- M1: describe drawing the line of best fit
- M1: use the line of best fit for prediction
- A1: Strong positive correlation; line of best fit passes through the mean point
Students draw the line of best fit from one corner to another rather than balancing points on each side.The line must have roughly equal scatter above and below it — it is not a 'connect-the-dots' line.
DiagnosticrecallWhat type of correlation: car age vs value?
1 mark2 minsscatter-graphs-q1Show solution
What type of correlation: car age vs value?
- 1.Spot the skill: Correlation: positive — both increase together.
- 2.Use the identify the type of correlation stage first, then assess the strength.
- 3.Keep the final answer visible: Negative correlation.
Negative correlation
- M1: use the correct correlation: positive — both increase together. negative — as one increases the other decreases.no correlation — no pattern. strength: strong (points close to line), weak (spread out).line of best fit: balanced line through the point (x̄, ȳ).
- A1: Negative correlation
Students draw the line of best fit from one corner to another rather than balancing points on each side.The line must have roughly equal scatter above and below it — it is not a 'connect-the-dots' line.
EasyprocedureA line of best fit passes through (5, 40) and (10, 70). Find the equation.
2 marks3 minsscatter-graphs-q2Show solution
A line of best fit passes through (5, 40) and (10, 70). Find the equation.
- 1.Spot the skill: Correlation: positive — both increase together.
- 2.Use the assess the strength stage first, then describe drawing the line of best fit.
- 3.Keep the final answer visible: Gradient = (70−40)/(10−5) = 6; y = 6x + 10.
Gradient = (70−40)/(10−5) = 6; y = 6x + 10
- M1: use the correct correlation: positive — both increase together. negative — as one increases the other decreases.no correlation — no pattern. strength: strong (points close to line), weak (spread out).line of best fit: balanced line through the point (x̄, ȳ).
- A1: Gradient = (70−40)/(10−5) = 6; y = 6x + 10
Students draw the line of best fit from one corner to another rather than balancing points on each side.The line must have roughly equal scatter above and below it — it is not a 'connect-the-dots' line.
MediumreasoningExplain why extrapolation is unreliable.
3 marks4 minsscatter-graphs-q3Show solution
Explain why extrapolation is unreliable.
- 1.Spot the skill: Correlation: positive — both increase together.
- 2.Use the describe drawing the line of best fit stage first, then use the line of best fit for prediction.
- 3.Keep the final answer visible: The relationship shown by the data may not continue beyond the observed range.
The relationship shown by the data may not continue beyond the observed range
- M1: use the correct correlation: positive — both increase together. negative — as one increases the other decreases.no correlation — no pattern. strength: strong (points close to line), weak (spread out).line of best fit: balanced line through the point (x̄, ȳ).
- A1: The relationship shown by the data may not continue beyond the observed range
Students draw the line of best fit from one corner to another rather than balancing points on each side.The line must have roughly equal scatter above and below it — it is not a 'connect-the-dots' line.
Hardproblem solvingThe mean hours studied = 7, mean score = 62. Must the line of best fit pass through (7, 62)?
3 marks5 minsscatter-graphs-q4Show solution
The mean hours studied = 7, mean score = 62. Must the line of best fit pass through (7, 62)?
- 1.Spot the skill: Correlation: positive — both increase together.
- 2.Use the use the line of best fit for prediction stage first, then identify the type of correlation.
- 3.Keep the final answer visible: Yes — the mean point lies on the line of best fit.
Yes — the mean point lies on the line of best fit
- M1: use the correct correlation: positive — both increase together. negative — as one increases the other decreases.no correlation — no pattern. strength: strong (points close to line), weak (spread out).line of best fit: balanced line through the point (x̄, ȳ).
- A1: Yes — the mean point lies on the line of best fit
Students draw the line of best fit from one corner to another rather than balancing points on each side.The line must have roughly equal scatter above and below it — it is not a 'connect-the-dots' line.
Exam-stylemulti-stepDistinguish between correlation and causation.
4 marks6 minsscatter-graphs-q5Show solution
Distinguish between correlation and causation.
- 1.Spot the skill: Correlation: positive — both increase together.
- 2.Use the identify the type of correlation stage first, then assess the strength.
- 3.Keep the final answer visible: Correlation means two variables change together; causation means one directly causes the change in the other.
Correlation means two variables change together; causation means one directly causes the change in the other
- M1: use the correct correlation: positive — both increase together. negative — as one increases the other decreases.no correlation — no pattern. strength: strong (points close to line), weak (spread out).line of best fit: balanced line through the point (x̄, ȳ).
- A1: Correlation means two variables change together; causation means one directly causes the change in the other
Students draw the line of best fit from one corner to another rather than balancing points on each side.The line must have roughly equal scatter above and below it — it is not a 'connect-the-dots' line.
Grade 9 stretchproblem solvingExplain why using a line of best fit to predict far outside the data range may be unreliable.
4 marks7 minsscatter-g9Show solution
Explain why using a line of best fit to predict far outside the data range may be unreliable.
- 1.Identify that the prediction is an extrapolation.
- 2.Explain that the observed relationship may not continue.
It is an extrapolation, so the pattern may change beyond the observed data.
- C1: identify extrapolation
- C1: explain unreliability
Do not rush straight into arithmetic. Select the relevant method and show a complete chain of working.
Switch between skills
Set a timer and attempt all four questions before opening any answers. This is closer to the way skills appear in a real paper.
1Scatter graphs - 2 marksWhat type of correlation: car age vs value?Mark answer
Negative correlation
2Collecting and sampling data - 2 marksWhy might a questionnaire question be biased?Mark answer
Leading wording, only offering responses that agree, or not including a 'no' option
3Averages and range - 2 marksThe mean of 5 numbers is 12. Four of them are 8, 14, 10, 15. Find the fifth.Mark answer
13
4Grouped data and estimated mean - 3 marksA survey records [10,20): 5 responses and [20,30): 15. Estimate total mean across both groups.Mark answer
Use midpoints 15 and 25: (5×15 + 15×25)/20 = = 22.5
- I can explain the method for scatter graphs.
- I can show clear working without skipping key steps.
- I can avoid this mistake: Students draw the line of best fit from one corner to another rather than balancing points on each side.The line must have roughly equal scatter above and below it — it is not a 'connect-the-dots' line.
This guide follows the Pearson Edexcel GCSE Mathematics 1MA1 specification. Practice questions are original Learnova questions shaped around official content and exam skills.