Question

Warren 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.

Brightness Level (x) 35 57 62 70 77 83 88 91

Hours (y) 6.1 3.7 4.8 1.8 2.9 3.2 2.6 1.6

brightness level

10

20

30

40

50

60

70

80

90

100

110

Hours

1

2

3

4

5

6

7

8

9

Brightness Level

Hours

a) Find the equation for the line of best fit. Keep at least 4 decimals for each parameter in the equation.   

b) Interpret the slope in context.

Warren should expect -0.0687 brightness level per hour.

Warren should expect -0.0687 hours per brightness level.

c) What does the equation predict for the number of hours the phone will last at a brightness level of 62?

Answer 1

_Bright Ness Level (x) - 35 Hours (9) 6.1 3.7 418 I n = Noof obs 209 3.2 2.6 106 sy; = 26.7 3x1= 563 Mean of x;= 70.375- Ÿ = 563 in 563 8 Mean of Yo ý = 26.7 = 3.3375 Standard deviation of x=8x= Exi-nx (n-1) = 18. 6696

Standard deviation of y: sys syir-n.gz : 1.5137 Covariance between x and y a cor (x,y) Cor(x,y) - Exiy, - noxi correlation & - 23.9589 coefficient between x and y = xy cor(x,y) Sx. sy - 23.9589 18.66964 1.5137 & - 0.84 78 - The is Linear given by regression equation between a and y

=> y - 3.3375 = -0. 8448*(- 70.373) => y = - 0.0687 x + 8.1749 - This is the line of best fit. b. In this equation slope is =-0.0687. which indicates for every unit increane of a y will decrease by 0.0687 units. That means, Warren should expect -0.0687 hours per Brightness. 3 c. Given brightness level (x) = 62. from the equation, y = -0.0687x+ 8. 1749 = -0.068.7 x 62+ 8.1749 > y = 3.9155 Predicted number of hours is 3.9155 for Brightness level 62