An atmospheric scientist is investigating the relationship between altitude above sea level, hhh km, and the ambient air temperature, TTT ∘^{\circ}∘C. Data is collected using a weather balloon at 10 different altitudes. The data is summarised in the table below.
| hhh | 1.5 | 2.2 | 3.0 | 3.8 | 4.5 | 5.2 | 6.0 | 6.8 | 7.5 | 8.5 |
|---|---|---|---|---|---|---|---|---|---|---|
| TTT | 5.2 | 1.4 | -3.1 | -7.5 | -12.8 | -16.2 | -22.4 | -26.5 | -31.2 | -38.9 |
[You may assume that ∑h=49\sum h = 49∑h=49, ∑T=−152\sum T = -152∑T=−152, ∑h2=288.56\sum h^2 = 288.56∑h2=288.56, ∑T2=4211.8\sum T^2 = 4211.8∑T2=4211.8, ∑hT=−1048.01\sum hT = -1048.01∑hT=−1048.01 and STT=1901.4S_{TT} = 1901.4STT=1901.4]
Calculate ShTS_{hT}ShT and ShhS_{hh}Shh. 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 linear regression equation to predict temperature at different altitudes. Give a reason for your answer.
Find the equation of the regression line of TTT on hhh giving your answer in the form T=a+bhT = a + bhT=a+bh.
Interpret the value of bbb.
Estimate the decrease in ambient temperature as the altitude increases from 2.5 km to 5.5 km.
