6. A group of climbers collected information about the height above sea level, \(h\) metres, and the air temperature, \(t ^ { \circ } \mathrm { C }\), at the same time at 8 different points on the same mountain.
The data are summarised by
$$\sum h = 6370 \quad \sum t = 61 \quad \sum t h = 31070 \quad \sum t ^ { 2 } = 693$$
- Show that \(\mathrm { S } _ { \text {th } } = - 17501.25\) and \(\mathrm { S } _ { \text {tt } } = 227.875\)
The product moment correlation coefficient for these data is - 0.985
- State, giving a reason, whether or not this value supports the use of a regression equation to predict the air temperature at different heights on this mountain.
- Find the equation of the regression line of \(t\) on \(h\), giving your answer in the form \(t = a + b h\). Give the value of your coefficients to 3 significant figures.
- Give an interpretation of your value of \(a\).
One of the climbers has just stopped for a short break before climbing the next 150 metres.
- Estimate the drop in temperature over this 150 metre climb.