4 The table shows the latitude, \(x\) (in degrees correct to 3 significant figures), and the average rainfall \(y\) (in cm correct to 3 significant figures) of five European cities.
| City | \(x\) | \(y\) |
| Berlin | 52.5 | 58.2 |
| Bucharest | 44.4 | 58.7 |
| Moscow | 55.8 | 53.3 |
| St Petersburg | 60.0 | 47.8 |
| Warsaw | 52.3 | 56.6 |
$$\left[ n = 5 , \Sigma x = 265.0 , \Sigma y = 274.6 , \Sigma x ^ { 2 } = 14176.54 , \Sigma y ^ { 2 } = 15162.22 , \Sigma x y = 14464.10 . \right]$$
- Calculate the product moment correlation coefficient.
- The values of \(y\) in the table were in fact obtained from measurements in inches and converted into centimetres by multiplying by 2.54. State what effect it would have had on the value of the product moment correlation coefficient if it had been calculated using inches instead of centimetres.
- It is required to estimate the annual rainfall at Bergen, where \(x = 60.4\). Calculate the equation of an appropriate line of regression, giving your answer in simplified form, and use it to find the required estimate.
\section*{June 2005}