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.
278 exam-style questions on CCEA A Level Maths 2.5 Data presentation and interpretation, covering 2.5.1 Data presentation and interpretation, 2.5.2 Data presentation and interpretation, 2.5.3 Data presentation and interpretation, 2.5.4 Data presentation and interpretation, 2.5.5 Data presentation and interpretation, 2.5.6 Data presentation and interpretation, 2.5.7 Data presentation and interpretation, 2.5.8 Data presentation and interpretation, 2.5.9 Data presentation and interpretation, and 2.5 Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.