Use a line of best fit to estimate values on a scatter graph and describe the correlation
Scatter graphs, also called scatter plots, are used to compare two quantities.
Let’s say someone’s interested in whether taller people have bigger feet, they can measure the height and shoe size for a whole bunch of people, then plot them on a scattergraph. When they do, the dots will either seem to go upwards from left to right, go downwards, or just be scattered all over with no pattern.
- Positive correlation
If looking at a scatter diagram and the points increase with each other, i.e. the points go upwards from left to right. This means that as one data set increases, the other is also increasing.
- Negative correlation
If looking at a scatter diagram and the points decrease with each other, i.e. the points go downwards from left to right. This means that as one data set increases, the other decreases
- No correlation
If looking at a scatter diagram and there is no visible pattern to the points, i.e. the points look as if they are randomly placed. This means that there is no connection between the two data sets.
- Strong correlation -
If the points on the graph all seem really close to our line of best fit, then we say there is strong correlation between the two things we measured e.g. strong positive correlation between foot size and height would mean that it is *very* likely that you will have bigger feet, if you are a taller person.
- Weak correlation
If many of the points are relatively far from the line of best fit, we call it weak correlation.
Using a line of best fit
To make the pattern more clear, we can draw a line of best fit over the points. We then use this line to estimate values that we don’t have measurements for.
If we want to find out from our graph of height vs shoe size, what is the height of someone with shoe-size of size 10. We only have to find 10 on the axis with shoe-size, then follow that to the line of best fit, then read off what the corresponding height is (roughly 174.8).
Nothing in this section yet. Why not help us get started?
Follow the links below to see how this topic has appeared in past exam papers
Requires a knowledge of…
After this move on to…