2 The head and body length, \(x\) millimetres, and tail length, \(y\) millimetres, of each of a sample of 20 adult dormice were measured. The following statistics are derived from the results.
$$S _ { x x } = 1280.55 \quad S _ { y y } = 281.8 \quad S _ { x y } = 416.3$$
- Calculate the value of the product moment correlation coefficient between \(x\) and \(y\).
- Interpret your value in the context of this question.
- Write down the value of the product moment correlation coefficient if the measurements had been recorded in centimetres.
- Give a reason why it is not generally advisable to calculate the value of the product moment correlation coefficient without first viewing a scatter diagram of the data. Illustrate your answer with a sketch.