Jerónimo is investigating how long his phone's battery lasts (in hours) for various brightness levels (on a scale of 0-100). His data is displayed in the table and graph below. Do not round between steps. Round answers to at least 4 decimal places.

Brightness Level (x)1724303136365064
Hours (y)6.35.76.55.55.15.34.43.9

10203040506070809010011012345678910-1Brightness LevelHours

a) Find the equation for the line of best fit. Keep at least 4 decimals for each parameter in the equation. y^\displaystyle \hat{{y}} =  

b) Interpret the slope in context.

c) What does the equation predict for the number of hours the phone will last at a brightness level of 30?

hours

d) What is the residual for the point (30,6.5)?

hours

e) Find the 99% prediction interval for the number of hours the phone will last at a brightness level of 30.

< y <  hours