- The table shows the price of a bottle of milk, \(m\) pence, and the price of a loaf of bread, \(b\) pence, for 8 different years.
| \(m\) | 29 | 29 | 35 | 39 | 41 | 43 | 44 | 46 |
| \(b\) | 75 | 83 | 91 | 121 | 120 | 126 | 119 | 126 |
(You may use \(\mathrm { S } _ { b b } = 3083.875\) and \(\mathrm { S } _ { m m } = 305.5\) )
- Find the exact value of \(\sum b m\)
- Find \(\mathrm { S } _ { b m }\)
- Calculate the product moment correlation coefficient between \(b\) and \(m\)
- Interpret the value of the correlation coefficient.
A ninth year is added to the data set. In this year the price of the bottle of milk is 46 pence and the price of a loaf of bread is 175 pence.
- Without further calculation, state whether the value of the product moment correlation coefficient will increase, decrease or stay the same when all nine years are used. Give a reason for your answer.