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Why is using a line of best fit useful?

By Kris Boulton on the 11th of June, 2012

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    A line of best fit helps you to estimate values. Without the line of best fit you can't tell which x to take on the graph.
    It also makes seeing the correlation a lot easier by considering the gradient of the line of best fit. 

    Refine By Lee Mansfield on the 14th of June, 2012

Suggested reading…

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.

Correlation explained: 

  • 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.

For example

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).

Follow the links below to see how this topic has appeared in past exam papers

 

AQA Unit 1 November 2012 (H) - Page 4, Question 3

2Simple software

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