Line of best fit
A line of best fit is usually drawn on a scatter diagram.
It's drawn so that the points are evenly distributed on either side of the line.
There are various methods for drawing this 'precisely' but you'll only be expected to draw the line 'by eye'.
When drawing the line of best fit, use a transparent ruler so that you can see how the line fits between all the points before you draw it.
Question
The heights and weights of twenty children in a class are recorded. The results are shown on the scatter diagram below.
Katie is \(148cm\) tall. Draw a line of best fit and use it to estimate her weight
We start by drawing a line of best fit.
Katie is \(148cm\) tall, so we draw a straight line up from \(148cm\) on the horizontal axis until it meets the line of best fit and then along until it meets the vertical axis.
Katie weighs approximately \(52\,kg\).
As you're only drawing the line of best fit 'by eye', it's unlikely your answers will be the same as your friend's.
The equation of the line of best fit
Another way of getting an estimate is to use the equation of the line of best fit.
Try this question:
Question
The equation of the line of best fit is \(w = 1.5h - 170\)
Use this equation to obtain an estimate for the weight of Louise, who is \(156 cm\) tall.
We substitute\(h = 156\) into the equation.
\(w = 1.5 \times 156 - 170\)
\(= 234 - 170\)
\(= 64\)
So, Louise weighs approximately \(64kg\)
Decision making
Sometimes you are asked to comment on a situation presented as a scatter graph.
Try this question:
Question
Class 1C2 sat tests for English and Maths. Here is a scatter diagram of their results.
Cameron says that if you scored well in Maths you are likely to have scored well in English. Is he justified?
Remember that you will have to explain your answers.
Cameron is not justified as the scatter diagram shows that there is no correlation between the Maths scores and the English score.