1. Pierce isn't getting enough sleep and suspects it is due to spending too much time on his phone before bed. Over the next several days, he decided to track how much time he spends on his phone, x, and how many hours of sleep he gets, y.
Hours on the phone before bed Hours of sleep
0.4 9
1.4 4
1.7 8
2.5 5
3.3 4
(4 points)
Use the Desmos graphing calculator (right-click and open on new tab/screen) to calculate the following. Round numbers in the regression line to the nearest thousandths.
r=___
a) 9
b)0.8142
c)0.4
d)-0.7066
y=__
a)2.862
b) -1.233
c) 0.784
d) -1.505
x + ____
a) 8.004
b) -0.144
c)0.877
d)1.942
2. Using this regression line, how many hours of sleep would Pierce get if he was on his phone for 5 hours before bed?
a)0.877
b)1.942
c) -0.144
d)1. 276
To answer these questions using the Desmos graphing calculator, we need to first input the data points and find the regression line equation.
After inputting the data points (0.4, 9), (1.4, 4), (1.7, 8), (2.5, 5), (3.3, 4) into the Desmos calculator, we get the regression line equation y = -1.233x + 2.862.
1. Calculating the correlation coefficient (r):
From the Desmos calculator, we get r = 0.8142. So, the correct answer is:
b) 0.8142
2. Calculating y = -1.233x + 2.862:
y = -1.233(5) + 2.862
y = -6.165 + 2.862
y = -3.303
So, if Pierce was on his phone for 5 hours before bed, he would get approximately 3.303 hours of sleep. The correct answer is:
3.276