- A teacher took a random sample of 8 children from a class. For each child the teacher recorded the length of their left foot, \(f \mathrm {~cm}\), and their height, \(h \mathrm {~cm}\). The results are given in the table below.
| \(f\) | 23 | 26 | 23 | 22 | 27 | 24 | 20 | 21 |
| \(h\) | 135 | 144 | 134 | 136 | 140 | 134 | 130 | 132 |
(You may use \(\sum f = 186 \quad \sum h = 1085 \quad \mathrm {~S} _ { f f } = 39.5 \quad \mathrm {~S} _ { h h } = 139.875 \quad \sum f h = 25291\) )
- Calculate \(\mathrm { S } _ { f h }\)
- Find the equation of the regression line of \(h\) on \(f\) in the form \(h = a + b f\). Give the value of \(a\) and the value of \(b\) correct to 3 significant figures.
- Use your equation to estimate the height of a child with a left foot length of 25 cm .
- Comment on the reliability of your estimate in (c), giving a reason for your answer.
The left foot length of the teacher is 25 cm .
- Give a reason why the equation in (b) should not be used to estimate the teacher's height.