S1 June 2011 Q1

1. On a particular day the height above sea level, \(x\) metres, and the mid-day temperature, \(y\)°C, were recorded in 8 north European towns. These data are summarised below

\[\mathrm{S}_{xx} = 3\,535\,237.5 \qquad \sum y = 181 \qquad \sum y^2 = 4305 \qquad \mathrm{S}_{xy} = -23\,726.25\]

A student thought that the calculations would be simpler if the height above sea level, \(h\), was measured in kilometres and used the variable \(h = \dfrac{x}{1000}\) instead of \(x\).