7. A doctor wished to investigate the effects of staying awake for long periods on a person's ability to complete simple tasks. She recorded the number of times, \(n\), that a subject could clinch his or her fist in 30 seconds after being awake for \(h\) hours.
The results for one subject were as follows.
| \(h\) (hours) | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |
| \(n\) | 116 | 114 | 109 | 101 | 94 | 94 | 86 | 81 | 80 |
- Plot a scatter diagram of \(n\) against \(h\) for these results.
You may use
$$\Sigma h = 180 , \quad \Sigma n = 875 , \quad \Sigma h ^ { 2 } = 3660 , \quad \Sigma h n = 17204 .$$
- Obtain the equation of the regression line of \(n\) on \(h\) in the form \(n = a + b h\).
- Give a practical interpretation of the constant b.
- Explain why this regression line would be unlikely to be appropriate for values of \(h\) between 0 and 16 .
(2 marks)
Another subject underwent the same tests giving rise to a regression line of \(n = 213.4 - 5.87\) h - After how many hours of being awake together would you expect these two subjects to be able to clench their fists the same number of times in 30 seconds?