AQA GCSE Statistics Scatter diagrams and correlation: a complete overview of correlation, causation and lines of best fit

What this module demands

Scatter diagrams and correlation is about relationships between two variables. AQA tests whether you can describe correlation precisely, resist the trap of claiming causation, fit a line and use it to predict safely, and rank data with Spearman's coefficient. Interpretation in context carries most of the marks.

This guide walks through the three topics in specification order, then sets out the exam patterns AQA repeats. Each topic has a matching dot-point page with practice questions; this overview ties them together.

Scatter diagrams

The module opens with scatter diagrams: plotting bivariate data, describing the type of correlation (positive, negative or none) and its strength (strong or weak), and spotting outliers. Always describe both type and strength together.

Correlation and causation

Correlation and causation covers why correlation does not prove cause, spurious correlation, and confounding variables. The classic example is ice cream sales and drowning, both driven by hot weather rather than each other.

Lines of best fit and regression

Lines of best fit and regression covers drawing the line through the mean point, the equation $y = mx + c$, interpolation and extrapolation, and Spearman's rank correlation coefficient, $r_s = 1 - \frac{6 \sum d^2}{n(n^2 - 1)}$.

How this module is examined

A typical AQA profile for this module:

• Scatter diagrams. Describing the type and strength of correlation and spotting outliers.
• Causation. Explaining why correlation does not prove cause and naming a confounding variable.
• Lines of best fit. Predicting by interpolation and judging when extrapolation is unsafe.
• Spearman's rank. Calculating and interpreting the coefficient.

Check your knowledge

A mix of recall and calculation questions covering this module. Attempt them under timed conditions, then check against the solutions.

1. Points slope upwards and lie close to a line. Describe the correlation. (2 marks)
2. Explain why correlation does not prove causation. (2 marks)
3. Name a confounding variable for the link between ice cream sales and drowning. (1 mark)
4. A line of best fit is $y = 2x + 3$. Predict $y$ when $x = 5$. (1 mark)
5. What is extrapolation, and why is it unreliable? (2 marks)
6. For $n = 5$ pairs, $\sum d^2 = 8$. Find Spearman's rank correlation coefficient. (2 marks)
7. What point should a line of best fit pass through? (1 mark)
8. What does a Spearman value near $-1$ mean? (1 mark)