- On a particular day the height above sea level, \(x\) metres, and the mid-day temperature, \(y ^ { \circ } \mathrm { C }\), were recorded in 8 north European towns. These data are summarised below
$$\mathrm { S } _ { x x } = 3535237.5 \quad \sum y = 181 \quad \sum y ^ { 2 } = 4305 \quad \mathrm {~S} _ { x y } = - 23726.25$$
- Find \(\mathrm { S } _ { y y }\)
- Calculate, to 3 significant figures, the product moment correlation coefficient for these data.
- Give an interpretation of your coefficient.
A student thought that the calculations would be simpler if the height above sea level, \(h\), was measured in kilometres and used the variable \(h = \frac { x } { 1000 }\) instead of \(x\).
- Write down the value of \(\mathrm { S } _ { h h }\)
- Write down the value of the correlation coefficient between \(h\) and \(y\).