Electric vehicles have greatly increased in popularity recently, but their short battery life (with a few exceptions) continues to be of concern. The article “Design of Robust Battery Capacity Model for Electric Vehicle by Incorporation of Uncertainties” (Int. J. Energy Res. 2017: 1436–1451) includes the following data on temperature (°C), discharge rate, and battery capacity (A-h, ampere-hours) for a certain type of lithiumion battery.

a. Determine the estimated regression equation based on this data (y = capacity).
b. Calculate a point estimate for the expected capacity of a lithium-ion battery of this type when operated at 30 °C with discharge rate 1.00 (meaning the battery should drain in 1 h).
c. Perform a model utility test at the .05 significance level.
d. Calculate a 95% CI for expected capacity at the settings in part (b).
e. Calculate a 95% PI for the capacity of a single such battery at the settings in part (b).
f. Perform variable utility tests on both predictors at a simultaneous .05 significance level. Are both temperature and discharge rate useful predictors of capacity?

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Temp Disch. Capacity Temp rate 0 0 0 25 40 40 20 20 20 25 50 40 50 25 30 50 0 20 25 30 40 50 0.50 1.75 3.00 0.50 1.75 3.00 0.50 1.75 3.00 3.00 3.00 0.50 0.50 1.75 1.75 1.75 1.00 1.00 1.00 1.00 1.00 1.00 0.96001 0 0.85001 20 0.89001 25 1.38001 30 1.05396 0.96337 1.27100 1.24897 20 1.20751 25 1.32001 30 1.39139 40 1.00208 50 1.44001 30 1.30001 0.82697 1.42713 1.08485 1.40556 1.47986 0.91734 1.18187 1.53058 40 50 0 40 50 0 20 25 30 40 50 Disch. Capacity rate 1.25 1.25 1.25 1.25 1.25 1.25 1.50 1.50 1.50 1.50 1.50 1.50 1.25 1.25 1.25 1.50 1.50 1.50 1.50 1.50 1.50 1.06506 1.34459 1.45473 1.32355 1.54713 1.47159 0.85171 1.20890 1.29703 1.16097 1.32047 1.36305 1.32355 1.54713 1.47159 0.85171 1.20890 1.29703 1.16097 1.32047 1.36305