| Proportion at 77mm (%) | Average Rainfall | Hand Feeding |
| 67 | 100 | 1 |
| 75 | 150 | 0 |
| 80 | 148 | 0 |
| 72 | 70 | 1 |
| 91 | 210 | 0 |
| 69 | 120 | 1 |
| 55 | 50 | 1 |
| 77 | 167 | 0 |
| 84 | 230 | 0 |
| 92 | 189 | 0 |
| 58 | 40 | 1 |
| 69 | 93 | 1 |
| 74 | 133 | 0 |
| 72 | 80 | 1 |
| 66 | 108 | 1 |
A farmer who specialises in the production of carpet wool wherethe sheep are shorn twice per year is seeking a 75-mm-length clipfrom his Tukidale sheep. He believes that the proportion of sheepat each clip meeting this standard varies according to averagerainfall during the six-month growing period and whether additionalhand feeding of high protein sheep nits occurs during the period(because of a shortage of grass cover in the paddocks). Handfeeding is measured as 1 and no hand feeding as 0. Showing ALLformulas and working; a) Predict the proportion at 75mm if therainfall is 180 mm and there is no hand feeding, a construct a 95%confidence interval estimate and 95% prediction interval.
e) Calculate the coefficients of partial determination andinterpret their meaning.
f) Add an interaction term to the model and, at the 0.05 levelof significance, determine whether it makes a significantcontribution to the model.
