An engineer is testing the efficiency of a high-performance lithium-polymer battery pack for an industrial drone. During a controlled test flight, the engineer records the flight duration, TTT minutes, and the terminal voltage, VVV volts, of the battery pack. A random sample of 8 readings was taken during the first 40 minutes of flight, as shown in the table below:
| TTT (min) | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 |
|---|---|---|---|---|---|---|---|---|
| VVV (volts) | 12.35 | 12.12 | 11.85 | 11.60 | 11.38 | 11.10 | 10.88 | 10.60 |
You may use the following summary statistics:
∑T=180 \sum T = 180 ∑T=180 ∑V=91.88 \sum V = 91.88 ∑V=91.88 STT=1050 S_{TT} = 1050 STT=1050 SVV=2.6064 S_{VV} = 2.6064 SVV=2.6064 ∑TV=2015.0 \sum TV = 2015.0 ∑TV=2015.0Calculate the value of STVS_{TV}STV.
Find the equation of the regression line of VVV on TTT in the form V=a+bTV = a + bTV=a+bT. Give the values of aaa and bbb correct to 3 significant figures.
Use your equation to estimate the terminal voltage of the battery pack after 18 minutes of flight.
Comment on the reliability of your estimate in (c), giving a mathematical reason for your answer.
A specialized long-range mission requires the drone to fly for 90 minutes.
Give a reason why the equation in (b) should not be used to estimate the battery voltage for this mission.
