Lines of Best Fit (WJEC GCSE Maths & Numeracy (Double Award)): Revision Note

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 find the coordinates of the mean point?

• The line of best fit must pass through the mean point if it is given to you, plotted for you, or if you are asked to calculate it

• The mean point, is simple to calculate:

  • Calculate the mean of the x values for all data points, this is

  • Calculate the mean of the y values for all data points, this is

How do I draw a line of best fit?

• To draw a line of best fit:

  • If you are asked to, find the coordinates of the mean point,

  • Plot the mean point on the graph with all of the other data values

  • Draw a single-ruled straight line through the mean point

    • It must extend across the full data set

    • Adjust the angle of the line to try and get roughly the same number of data points on either side of the line along its whole length

  • If the mean point is not given and you are not asked to calculate it you should still ensure your line is:

    • Straight

    • Across the full data set

    • Following the general trend of the data

    • At an angle so that roughly the same number of data points are 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