Lines of Best Fit (Cambridge (CIE) IGCSE Maths)
Revision Note
Written by: Mark Curtis
Reviewed by: Dan Finlay
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
(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
(c) Use a line of best fit to estimate the price of a computer that completes the task in 3.4 seconds.
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 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
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