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Scatter diagrams

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# Correlation and lines of best fit

You can also use a line of best fit to predict results.

Question

The heights and weights of 20 children in a class are recorded. The results are shown on the scatter diagram below.

Katie is 148 cm tall. Estimate her weight.

Start by drawing a line of best fit. Remember that the line of best fit is drawn so that the points are evenly distributed on either side of the line.

Katie is 148 cm tall, so we use the line of best fit to find an approximate weight. Find 148 cm on the height axis. Now follow the line up until you hit the line of best fit. Now read across the graph to the weight axis.

Katie weighs approximately 52 kg. As you are only drawing the line of best fit 'by eye', it is unlikely that your answers will be exactly the same as your friend's. The examiners will take this into account.

Looking at the graph of height against weight we need to interpret the gradient of the graph.

We choose two points on the graph and find the gradient (134, 30) and (148, 52).

As the height increases by 14 cm, the weight increases by 12 kg. So the gradient is 12/14, which tells us that for every increase of 1 cm, the weight increases by 12/14 kg (0.857 kg).

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