Lines of Best Fit (Edexcel GCSE Statistics)

Lines 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 can often be drawn by eye

  • It is a straight line (use a ruler!)

  • It must extend across the full data set

  • There should be roughly as many points on either side of the line (along its whole length)

  • The spaces between the points and the line should roughly be the same on either side

• 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

What is the double mean point?

• A question may talk about the double mean point

  • This is the point

    • is the mean of the data values that are plotted along the x-axis

    • is the mean of the data values that are plotted along the y-axis

  • The question may give you the values of and

    • Or you may need to calculate the means from the data

• If a question mentions the double mean point, then the line of best fit must go through the double mean point

  • It should still follow all the other rules for drawing a line of best fit (roughly same number of points on each side, etc.)

• If a question doesn't mention the double mean point

  • then you don't need to calculate it or worry about drawing the line through it

How do I use a line of best fit?

• The line of best fit can be used to predict the value of one variable from the other variable

  • See the Worked Example

• Predictions should only be made for values that are within the range of the given data

  • Making a prediction within the range of the given data is called interpolation

    • This will normally give a reliable result

  • Making a prediction outside of the range of the given data is called extrapolation 

    • This is much less reliable

What about the gradient and y-intercept of a line of best fit?

• You need to be able to interpret the meaning of the gradient and y-intercept of a line of best fit

• The gradient is the slope or 'steepness' of the line

  • A question may tell you the gradient of the line of best fit

  • If you need to find it you can calculate it using 'rise over run'

    • Pick two points on the line with coordinates and

    • 

    • Be careful – the plotted data points will usually not be points on the line!

• The gradient of the line of best fit tells you the rate of change of the y-axis variable with respect to the x-axis variable

  • This needs to be interpreted in context

    • For example if the x-axis variable is distance travelled in a taxi (in miles) and the y-axis variable is the cost of the taxi ride (in pounds £)

    • then the gradient of the line of best fit (£ per mile) is the cost in pounds for increasing the distance travelled by 1 mile

• The y-intercept is the value of the y-coordinate at the point where the line crosses the y-axis

  • This can be read off the graph

• The y-intercept of the line of best fit tells you the value of the y-axis variable when the x-axis variable is equal to zero

  • This needs to be interpreted in context

    • For example if the x-axis variable is distance travelled in a taxi (in miles) and the y-axis variable is the cost of the taxi ride (in pounds £)

    • then the y-intercept of the line of best fit tells you the 'flat fee' that is added onto every taxi ride