3. A biologist is comparing the intervals ( \(m\) seconds) between the mating calls of a certain species of tree frog and the surrounding temperature ( \(t { } ^ { \circ } \mathrm { C }\) ). The following results were obtained.
| \(t { } ^ { \circ } \mathrm { C }\) | 8 | 13 | 14 | 15 | 15 | 20 | 25 | 30 |
| \(m\) secs | 6.5 | 4.5 | 6 | 5 | 4 | 3 | 2 | 1 |
$$\text { (You may use } \sum t m = 469.5 , \quad \mathrm {~S} _ { t t } = 354 , \quad \mathrm {~S} _ { m m } = 25.5 \text { ) }$$
- Show that \(\mathrm { S } _ { t m } = - 90.5\)
- Find the equation of the regression line of \(m\) on \(t\) giving your answer in the form \(m = a + b t\).
- Use your regression line to estimate the time interval between mating calls when the surrounding temperature is \(10 ^ { \circ } \mathrm { C }\).
- Comment on the reliability of this estimate, giving a reason for your answer.