The heights above sea level ( \(h\) hundred metres) and the temperatures ( \(t ^ { \circ } \mathrm { C }\) ) at 12 randomly selected places in France, at 7 am on July 31st, were recorded.
The data are summarised as follows
Find the value of \(S _ { t t }\)
Calculate the product moment correlation coefficient for these data.
Interpret the relationship between \(t\) and \(h\).
Find an equation of the regression line of \(t\) on \(h\).
At 7 am on July 31st Yinka is on holiday in South Africa. He uses the regression equation to estimate the temperature when the height above sea level is 500 m .
Find the estimated temperature Yinka calculates.
Comment on the validity of your answer in part (e).
$$\sum h = 112 \quad \sum t = 136 \quad \sum t ^ { 2 } = 1828 \quad S _ { h t } = - 236 \quad S _ { h h } = 297$$