Question 6 • Exam Practice
6 Marks
An atmospheric scientist records temperature T in ^{\circ}\text{C} at different altitudes h in thousands of metres above sea level: \begin{array}{|l|c|c|c|c|c|c|}\hline \text{Altitude } h \text{ (km)} & 1.0 & 2.0 & 3.5 & 5.0 & 6.5 & 8.0 \\ \hline \text{Temperature } T \ (^{\circ}\text{C}) & 18.2 & 11.5 & 2.1 & -7.8 & -17.4 & -27.1 \\ \hline \end{array} (a) Write down Pearson's correlation coefficient r . [1 mark] (b) Write down the equation of the regression line of T on h . [2 marks] (c) Use your equation to estimate the temperature at an altitude of 4.2\text{ km} . [2 marks] (d) State whether your estimate in part (c) is reliable, giving a reason. [1 mark]
Answer: (a) \ r = -1.00, \quad (b) \ T = -6.47h + 24.6, \quad (c) \ -2.57^{\circ}\text{C}, \quad (d) \ \text{Reliable (Interpolation)}