Lines of Best Fit (Cambridge International IGCSE Mathematics)

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

Exam Hint Sliding a ruler around a scatter graph can help to find the right position for the line of best fit! It is best to use a transparent ruler so that you can see all the points.

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.

Answer:

Plot each point carefully using crosses

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

Answer:

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)

Final answer: 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.

Answer:

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

Final answer: A computer that takes 3.4 seconds to run the program should cost around £640