The data below pertains to the number of hours a laptop has been charged for and the number of hours of backup provided by the battery.

(a) Use the first set of expressions on page 330, involving deviations from the mean, to fit a least squares line to the observations.

(b) Use the equation of the least squares line to estimate the mean battery backup time at \(x=3\).

(c) What difficulty might you encounter if you use the least squares line to predict the mean battery backup time for a laptop that has been charged for 5 hours?

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Charged for (hours) Battery backup (hours) 0.5 0.75 1.0 1.75 1.5 2.5 2.0 4.5 2.5 6.0