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: ∑\sum∑ w = 45, ∑\sum∑ v = 85, ∑\sum∑ w^2 = 499 and \text{ and } and ∑\sum∑ 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.
