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Read the following description of a data set. $\newline$ Kevin isn't getting enough sleep and suspects it's due to playing too many video games before bed. To find out, he decided to track how much time he spends gaming.Over several days, Kevin recorded how many hours of sleep he had gotten each night, $x$ , as well as how many hours he had spent playing video games before bed, $y$ .The least squares regression line of this data set is: $y = -1.233x + 5.806$ $\newline$ Complete the following sentence: $\newline$ For each additional hour Kevin played video games before bed, the least squares regression line predicts he would sleep $\_\_$ fewer hours that night.

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Interpret regression lines

Full solution

Q. Read the following description of a data set.

\newline

Kevin isn't getting enough sleep and suspects it's due to playing too many video games before bed. To find out, he decided to track how much time he spends gaming.Over several days, Kevin recorded how many hours of sleep he had gotten each night,

x

, as well as how many hours he had spent playing video games before bed,

y

.The least squares regression line of this data set is:

y = -1.233x + 5.806

\newline

Complete the following sentence:

\newline

For each additional hour Kevin played video games before bed, the least squares regression line predicts he would sleep

\_\_

fewer hours that night.

Interpret slope meaning: To answer the question prompt, we need to interpret the slope of the least squares regression line. The slope of the line is the coefficient of $x$ , which represents the change in the dependent variable (hours of sleep) for each unit increase in the independent variable (hours spent playing video games).
Calculate Kevin's slope: The slope of Kevin's least squares regression line is $-1.233$ . This means that for each additional hour spent playing video games, the line predicts that Kevin will sleep $1.233$ hours less.
Complete sentence with slope value: We can now complete the sentence with the value of the slope. For each additional hour Kevin played video games before bed, the least squares regression line predicts he would sleep $1.233$ fewer hours that night.

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