- A meteorologist believes that there is a relationship between the height above sea level, \(h \mathrm {~m}\), and the air temperature, \(t ^ { \circ } \mathrm { C }\). Data is collected at the same time from 9 different places on the same mountain. The data is summarised in the table below.
| \(h\) | 1400 | 1100 | 260 | 840 | 900 | 550 | 1230 | 100 | 770 |
| \(t\) | 3 | 10 | 20 | 9 | 10 | 13 | 5 | 24 | 16 |
[You may assume that \(\sum h = 7150 , \sum t = 110 , \sum h ^ { 2 } = 7171500 , \sum t ^ { 2 } = 1716\), \(\sum t h = 64980\) and \(\mathrm { S } _ { t t } = 371.56\) ]
- Calculate \(\mathrm { S } _ { t h }\) and \(\mathrm { S } _ { h h }\). Give your answers to 3 significant figures.
- Calculate the product moment correlation coefficient for this data.
- State whether or not your value supports the use of a regression equation to predict the air temperature at different heights on this mountain. Give a reason for your answer.
- Find the equation of the regression line of \(t\) on \(h\) giving your answer in the form \(t = a + b h\).
- Interpret the value of \(b\).
- Estimate the difference in air temperature between a height of 500 m and a height of 1000 m .