6. Anna is investigating the relationship between exercise and resting heart rate. She takes a random sample of 19 people in her year at school and records for each person
- their resting heart rate, \(h\) beats per minute
- the number of minutes, \(m\), spent exercising each week
Her results are shown on the scatter diagram.
\includegraphics[max width=\textwidth, alt={}, center]{3a09f809-fa28-4b3d-bb69-ea074433bd8f-16_531_551_653_740}
- Interpret the nature of the relationship between \(h\) and \(m\)
Anna codes the data using the formulae
$$\begin{aligned}
& x = \log _ { 10 } m
& y = \log _ { 10 } h
\end{aligned}$$
The product moment correlation coefficient between \(x\) and \(y\) is - 0.897 - Test whether or not there is significant evidence of a negative correlation between \(x\) and \(y\)
You should
- state your hypotheses clearly
- use a \(5 \%\) level of significance
- state the critical value used
The equation of the line of best fit of \(y\) on \(x\) is
$$y = - 0.05 x + 1.92$$ - Use the equation of the line of best fit of \(y\) on \(x\) to find a model for \(h\) on \(m\) in the form
$$h = a m ^ { k }$$
where \(a\) and \(k\) are constants to be found.