- A biologist is studying the behaviour of bees in a hive. Once a bee has located a source of food, it returns to the hive and performs a dance to indicate to the other bees how far away the source of the food is. The dance consists of a series of wiggles. The biologist records the distance, \(d\) metres, of the food source from the hive and the average number of wiggles, \(w\), in the dance.
| Distance, \(\boldsymbol { d } \mathbf { m }\) | 30 | 50 | 80 | 100 | 150 | 400 | 500 | 650 |
| Average number | | of wiggles, \(\boldsymbol { w }\) |
| 0.725 | 1.210 | 1.775 | 2.250 | 3.518 | 6.382 | 8.185 | 9.555 |
[You may use \(\sum w = 33.6 \sum d w = 13833 \mathrm {~S} _ { d d } = 394600 \mathrm {~S} _ { w w } = 80.481\) (to 3 decimal places)]
- Show that \(\mathrm { S } _ { d w } = 5601\)
- State, giving a reason, which is the response variable.
- Calculate the product moment correlation coefficient for these data.
- Calculate the equation of the regression line of \(w\) on \(d\), giving your answer in the form \(w = a + b d\)
A new source of food is located 350 m from the hive.
- Use your regression equation to estimate the average number of wiggles in the corresponding dance.
- Comment, giving a reason, on the reliability of your estimate.