- A random sample of 10 female pigs was taken. The number of piglets, \(x\), born to each female pig and their average weight at birth, \(m \mathrm {~kg}\), was recorded. The results were as follows:
| Number of piglets, \(\boldsymbol { x }\) | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
| Average weight at | | birth, \(\boldsymbol { m } \mathbf { ~ k g }\) |
| 1.50 | 1.20 | 1.40 | 1.40 | 1.23 | 1.30 | 1.20 | 1.15 | 1.25 | 1.15 |
(You may use \(\mathrm { S } _ { x x } = 82.5\) and \(\mathrm { S } _ { m m } = 0.12756\) and \(\mathrm { S } _ { x m } = - 2.29\) )
- Find the equation of the regression line of \(m\) on \(x\) in the form \(m = a + b x\) as a model for these results.
- Show that the residual sum of squares (RSS) is 0.064 to 3 decimal places.
- Calculate the residual values.
- Write down the outlier.
- Comment on the validity of ignoring this outlier.
- Ignoring the outlier, produce another model.
- Use this model to estimate the average weight at birth if \(x = 15\)
- Comment, giving a reason, on the reliability of your estimate.