## Exam-Style Question on Correlation## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 98. This question is similar to one that appeared on an IB Studies paper in 2014. The use of a calculator is allowed.

As part of a conservation project, Darren was asked to measure the circumference of trees that were growing at different distances from a beach.

His results are shown in the following table.

Distance, \(x\) (metres) | 6 | 14 | 20 | 25 | 35 | 48 | 46 | 48 | 52 |

Circumference, \(y\) (centimetres) | 52 | 57 | 57 | 68 | 65 | 70 | 75 | 80 | 82 |

(a) State whether distance from the beach is a continuous or discrete variable.

(b) On graph paper, draw a scatter diagram to show Darren’s results. Use a scale of 1 cm to represent 5 m on the x-axis and 1 cm to represent 10 cm on the y-axis.

(c) Calculate the mean distance, \(\bar x\) , of the trees from the beach.

(d) Work out the mean circumference, \(\bar y\) , of the trees.

(e) Plot and label the point M(\(\bar x,\bar y\)) on your graph.

(f) Write down the Pearson’s product–moment correlation coefficient, \(r\) , for Darren's results.

(g) Find the equation of the regression line \(y\) on \(x\), for Darren’s results.

(h) Draw the regression line \(y\) on \(x\) on your graph.

(i) Use the equation of the regression line \(y\) on \(x\) to estimate the circumference of a tree that is 42 m from the beach.

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