Line of Best Fit

We often use a 'best-fitting' line to show any relationship

A line of best fit is drawn on the scatter diagram. It is drawn so that the points are evenly distributed on either side of the line.

There are various methods for drawing this 'precisely' but you will 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.

Example

The heights and weights of twenty children in a class are recorded. The results are shown on the scatter diagram below.

Katie is 148 cm tall. Draw a line of best fit and use it to estimate her weight.

Answer

Scatter diagram with correlation between height and weight with a line of best fit

We start by drawing a line of best fit.

Katie is 148 cm 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 are only drawing the line of best fit 'by eye', it is unlikely your answer will be exactly the same as someone else's answer.

Sometimes you are given the equation of the line of best fit. You can use this in estimation.

Example

The equation of the line of best fit for a set of data is w = 1.5h - 170.

Use this equation to obtain an estimate for the weight of Louise, who is 156 cm tall.

Answer

We substitute h = 156 into the equation.

w = 1.5 \times 156 - 170

w = 234 - 170

w = 64

Therefore Louise weighs approximately 64 kg.

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