An aerospace engineer is testing the performance of a high-altitude surveillance drone. She records the maximum ascent speed, vvv m/s, of the drone while carrying various payload weights, www kg. Data from 6 test flights are recorded in the table below:
w (kg)13581216v (m/s)20181613117\begin{array}{|c|c|c|c|c|c|c|} \hline w \text{ (kg)} & 1 & 3 & 5 & 8 & 12 & 16 \\ \hline v \text{ (m/s)} & 20 & 18 & 16 & 13 & 11 & 7 \\ \hline \end{array}w (kg)v (m/s)1203185168131211167
[You may use: ∑w=45,∑v=85,∑w2=499 and ∑wv=502\sum w = 45, \sum v = 85, \sum w^2 = 499 \text{ and } \sum wv = 502∑w=45,∑v=85,∑w2=499 and ∑wv=502]
Explain why a linear regression model might be suitable for this data.
Calculate the value of SwvS_{wv}Swv and the value of SwwS_{ww}Sww.
Find the equation of the regression line of vvv on www, giving your answer in the form v=a+bwv = a + bwv=a+bw. Give your values to 3 significant figures.
A specific sensor suite requires a payload of 10 kg. Estimate the maximum ascent speed for the drone when equipped with this suite.
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.