# 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 $$(x)$$ Insect species $$(y)$$ 2 5 8 11 14 17 22 33 39 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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