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Read the following description of a data set.Researchers at a sleep clinic want to know how watching television affects a person's 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=0.111x+4.364How many minutes does this line predict it will take a subject to fall asleep if they watch 175 minutes of television in the evening?Round your answer to the nearest integer. minutes

Question

Read the following description of a data set.Researchers at a sleep clinic want to know how watching television affects a person's 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=0.111x+4.364How many minutes does this line predict it will take a subject to fall asleep if they watch 175 minutes of television in the evening?Round your answer to the nearest integer. minutes

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Solution

To find out how many minutes it will take a subject to fall asleep if they watch 175 minutes of television in the evening, we need to substitute x = 175 into the equation of the least squares regression line.

The equation is y = 0.111x + 4.364.

Substituting x = 175, we get:

y = 0.111(175) + 4.364 y = 19.425 + 4.364 y = 23.789

Rounding to the nearest integer, we get 24 minutes. So, it is predicted that it will take a subject 24 minutes to fall asleep if they watch 175 minutes of television in the evening.

This problem has been solved

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