# 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: 689. This question is similar to one that appeared on a GCSE Higher paper in 2022. The use of a calculator is allowed.

In the Bubbleless Bandits free-diving club, members practice breath-holding techniques as part of their routine.

In this club, the older members have been practicing these techniques for many years, leading to increased breath-holding capacity through disciplined training and improved technique. The older members tend to be the more experienced free-divers. They have mastered relaxation and breath control, contributing to their ability to hold their breath for longer periods.

The times, $$t$$ seconds, that club members could hold their breath while diving and their ages, $$x$$ years, are recorded. The results are shown in the table.

Age, $$x$$ years Time, $$t$$ seconds
19 37
31 44
55 101
33 63
29 55
61 110
40 78
35 71

(a) Draw a scatter diagram to represent this data.

(b) What type of correlation is shown on the scatter diagram?

(c) Find the equation of the regression line giving your answer in the form $$t = ax + b$$.

(d) Use your regression equation to estimate the time a person aged 45 could hold their breath.

(e) Give a reason why you should not use the regression equation to estimate the time it would take a person aged 14 to do the task.

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If you need more practice try the self-checking interactive exercises called Estimating Correlation.

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