Positive correlation
Hours of revision and test score for 8 students.
Positive correlation
As revision time goes up, test scores tend to go up too -- the points rise left to right.
Year 8
Scatter graphs, line of best fit and correlation
Plot and interpret scatter graphs, describe the type of correlation, draw a line of best fit, and explain why correlation does not prove causation.
Lesson overview
Statistics and data
A scatter graph plots pairs of values to show whether two things are linked. If the points rise from bottom-left to top-right, that's positive correlation. If they fall from top-left to bottom-right, that's negative correlation. If there's no clear pattern, there's no correlation. A line of best fit is a straight line drawn through the middle of the points, used to estimate values -- but correlation only shows a link, it never proves that one thing causes the other.
Negative correlation
Age of a car and its resale value for 8 cars.
Negative correlation
As the car gets older, its value tends to fall -- the points fall left to right.
No correlation
Shoe size and test score for 8 students.
No correlation
No clear pattern, and no line of best fit makes sense -- shoe size doesn't affect test score.
Worked example
Use the line of best fit to estimate the test score for 4.5 hours of revision.
- Find 4.5 hours on the x-axis.
- Move straight up until you reach the line of best fit, not an individual point.
- Read across to the y-axis from that spot on the line.
- The line passes through about (4.5, 52), so the estimated score is about 52.
- This is an estimate -- real students at 4.5 hours might score a bit above or below this.
Try it
Look at how the points are arranged before deciding on the type of correlation.
Question 1
A scatter graph shows points rising from bottom-left to top-right. What type of correlation is this?
Question 2
A scatter graph shows points falling from top-left to bottom-right. What type of correlation is this?
Question 3
A study finds towns with more ice cream shops also have more sunburn cases. Does this mean ice cream shops cause sunburn?
Question 4
On a scatter graph with a clear positive correlation, where should you draw the line of best fit?
Question 5
A scatter graph of shoe size against test score shows points scattered with no pattern. What should you conclude?
Common mistakes
Watch for these when working through the lesson.
- Joining the scatter points with a zig-zag line instead of leaving them separate.
- Drawing a line of best fit that doesn't have roughly equal points above and below it.
- Assuming correlation proves one thing causes the other.
Related topics
These ideas fit closely with this lesson.
- Draw and interpret pie charts.
- Choose the most appropriate graph for a data set.
- Plot and interpret linear graphs from y = mx + c.