What is Correlation?
When we collect data, we often want to know whether two variables are related to each other. Do taller people tend to weigh more? Do students who study longer tend to get higher grades? These are questions about correlation.
A statistical relationship between two variables, where a change in one variable is associated with a change in the other variable.
Correlation does not mean that one variable causes the other to change — it simply means there is a pattern or association between them.
Think of correlation like noticing that when you see more people carrying umbrellas, there tend to be more puddles on the ground. The umbrellas don't cause the puddles — rain causes both! But there is still a clear association between the two observations.
There are three main types of correlation:
- Positive correlation — as one variable increases, the other also tends to increase (e.g., height and shoe size)
- Negative correlation — as one variable increases, the other tends to decrease (e.g., temperature outside and number of hot chocolates sold)
- No correlation — there is no clear pattern between the two variables (e.g., your birthday month and your test score)
Scatter Diagrams and Describing Correlation
The most common way to visualise correlation between two quantitative variables is with a scatter diagram (also called a scatter plot).
A graph that plots pairs of numerical data as points on a coordinate plane, with one variable on the -axis and the other on the -axis.
When you look at a scatter diagram, you describe the correlation using three features:
- Direction — Is it positive, negative, or no correlation?
- Strength — Is the association strong (points close to a line) or weak (points spread out)?
- Form — Is the pattern linear (roughly a straight line) or non-linear (curved)?
Example: A student collects data on hours of exercise per week and resting heart rate for 15 people. When plotted:
- The points slope downward from left to right → negative correlation
- The points are fairly close to a straight line → moderately strong
- The pattern is roughly straight → linear
Description: "There is a moderately strong, negative, linear correlation between hours of exercise per week and resting heart rate."
When describing correlation on an assessment, always mention direction (positive/negative/none) and strength (strong/moderate/weak). Adding linear or non-linear shows deeper understanding.
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