Question

read the following description of a data set. researchers at a sleep clinic want to know how watching television affects a persons ability to fall asleep. in a study, they measure the amount of time it takes subjects to fall asleep at night after watching television. the researchers note the number of minutes the subjects spent watching television in the evening, x, as well as the number of minutes it took them to fall asleep, y. the least - squares regression line of this data set is: y = 0.345x - 33.648 how many minutes does this line predict it will take a subject to fall asleep if they watch 112 minutes of television in the evening? round your answer to the nearest integer.

Explanation:

Step1: Identify the value of x

The subject watches 120 minutes of television, so $x = 120$.

Step2: Substitute x into the regression - line equation

Substitute $x = 120$ into $y=0.345x - 33.648$.
$y=0.345\times120 - 33.648$.
First, calculate $0.345\times120 = 41.4$.
Then, $y = 41.4-33.648=7.752$.

Step3: Round the result

Round $y = 7.752$ to the nearest integer. Since the decimal part $0.752>0.5$, we round up. So $y\approx8$.

Answer:

8