Scatter diagrams and types of variable

Explanatory and response variables

The explanatory (independent) variable is the one that is set or controlled, or that you think causes the change. It goes on the x-axis. The response (dependent) variable is measured and goes on the y-axis. Example: amount of fertiliser (explanatory) and crop yield (response).

Describing correlation

• Positive: y tends to increase as x increases.
• Negative: y tends to decrease as x increases.
• No (zero) correlation: no linear pattern.

Also describe the strength: points close to a line show strong correlation; a loose band shows weak correlation.

Cautions

Correlation does not mean causation: two variables may both depend on a third (ice-cream sales and sunburn both depend on sunny weather). A scatter diagram may show a curved relationship, or separate groups, where a single straight line is not a good model.

Worked example

A student records hours of revision and test score for 10 classmates. Which is the explanatory variable, and on which axis should it go?

1. Revision is chosen by the student and is thought to affect the score.
2. Score is the measured outcome.

Answer: Hours of revision: explanatory, on the x-axis.

Check yourself

1. Temperature (set by a scientist) and the time for a chemical reaction are recorded. Which is the explanatory variable?
   • Reaction time
   • Neither, as they are paired
   • Whichever has larger values
   • Temperature
   Show answer

   Temperature. The temperature is controlled, and the time responds to it.

2. On a scatter diagram, where does the response variable go?
   • On the x-axis
   • On the y-axis
   • On either axis
   • It is not plotted
   Show answer

   On the y-axis. Response goes on the vertical axis.

3. As the age of a car increases, its value tends to fall. What type of correlation is this?
   • Positive
   • Zero
   • Causal only
   • Negative
   Show answer

   Negative. One increases while the other decreases.

4. Towns with more doctors have more deaths each year. Which is the best explanation?
   • Each depends on a third variable, the town's population
   • Doctors cause deaths
   • The data must be wrong
   • Deaths cause more doctors to be trained
   Show answer

   Each depends on a third variable, the town's population. Bigger towns have more of both; correlation does not imply causation.

5. A scatter diagram shows points lying close to a curve that rises then falls. What does this suggest about a linear regression model?
   • It is ideal, as the points are close together
   • It is suitable if the correlation is positive
   • It is not suitable, as the relationship is not linear
   • It is suitable for prediction outside the data
   Show answer

   It is not suitable, as the relationship is not linear. Linear regression and the PMCC only describe straight-line relationships.

Practise with instant feedback Print this lesson

Sources

• Pearson Edexcel International Advanced Level in Mathematics specification (issue 3), Unit S1

Last updated 7 November 2026. Spotted a mistake? Tell us.