Lines-Of-Best-Fit Wjec-Eduqas Foundation

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Exam code:C300

Line of best fit

What is a line of best fit?

If a scatter graph suggests that there is a positive or negative correlation
- a line of best fit can be drawn on the scatter graph
  - This can then be used to make predictions

How do I draw a line of best fit?

A line of best fit is drawn on by eye
- It is a single-ruled straight line
- It must extend across the full data set
- It does not need to pass through any particular point(s)
- There should roughly be as many points on either side of the line (along its whole length)
If there is one extreme value (outlier) that does not fit the general pattern
- then ignore this point when drawing a line of best fit

How do I use a line of best fit?

Once the line of best fit is drawn, you can use it to predict values
- E.g. to estimate y when x = 5
  - Use the line to read off the y value when x is 5
It is best to use your line to predict values that lie within the region covered by the data points
- This is called interpolation
Be careful: if you extend your line too far away from the data points and try to predict values, those parts of the line are unreliable!
- This is called extrapolation

Examiner Tips and Tricks

Sliding a ruler around a scatter graph can help to find the right position for the line of best fit!

Worked Example

Sophie wants to know if the price of a computer is related to the speed of the computer.
She tests 8 computers by running the same program on each, measuring how many seconds it takes to finish.
Sophie’s results are shown in the table below.

Price (£)	320	300	400	650	250	380	900	700
Time (secs)	3.2	5.4	4.1	2.8	5.1	4.3	2.6	3.7

(a) Draw a scatter diagram, showing the results on the axes below.

Plot each point carefully using crosses

A scatter diagram for time against price

(b) Write down the type of correlation shown and use it to form a suitable conclusion.

The shape formed by the points goes from top left to bottom right (a negative gradient)
This is a negative correlation
As one quantity increases (price), the other decreases (time)

The graph shows a negative correlation
This means that the more a computer costs, the quicker it is at running the program

First draw a line of best fit, by eye
Then draw a horizontal line from 3.4 seconds to the line of best fit
Draw a vertical line down to read off the price

A line of best fit drawn on a scatter diagram

A computer that takes 3.4 seconds to run the program should cost around £620
A range of different answers will be accepted,
depending on the line of best fit

Maths Gcse Wjec-Eduqas Foundation