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Exam-Style Question on Correlation

A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 12. This question is similar to one that appeared on an IB Studies paper in 2013. The use of a calculator is allowed.

In a survey of insect life near a stream, a student collected data about the number of different insect species \((y)\) that were found at different distances \((x)\) in metres from the stream.

Distance \((x)\) 2 5 8 11 14 17 22 33 39
Insect species \((y)\) 26 25 19 19 14 9 5 3 2

(a) Draw a scatter diagram to show the data.

(b) Using your scatter diagram, describe the correlation between the number of different insect species and the distance from the stream.

(c) Find \(\bar x\), the mean of the distances from the stream;

(d) Find \(\bar y\), the mean number of insect species.

(e) Plot the point \((\bar x,\bar y)\) on your scatter diagram. Label this point M.

(f) Write down the equation of the regression line \(y\) on \(x\) for the above data.

(g) Draw the regression line \(y\) on \(x\) on your scatter diagram.

(h) Estimate the number of insect species to be found 30 metres from the stream.

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