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Read the following description of a data set. $\newline$ Leo has trouble getting his math homework done on time, and his mother suspects it is due to lack of sleep.For the next few nights, Leo's mother notes the number of hours he sleeps, $x$ , and the number of minutes it takes him to do his math homework the following day, $y$ .The least squares regression line of this data set is: $y = -48.057x + 483.245$ $\newline$ Complete the following sentence: $\newline$ If Leo sleeps for one extra hour at night, the least squares regression line predicts it will take him $\_\_$ fewer minutes to do his math homework the next day.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

Leo has trouble getting his math homework done on time, and his mother suspects it is due to lack of sleep.For the next few nights, Leo's mother notes the number of hours he sleeps,

x

, and the number of minutes it takes him to do his math homework the following day,

y

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

y = -48.057x + 483.245

\newline

Complete the following sentence:

\newline

If Leo sleeps for one extra hour at night, the least squares regression line predicts it will take him

\_\_

fewer minutes to do his math homework the next day.

Identify Slope: Identify the slope of the least squares regression line. The equation given is $y = -48.057x + 483.245$ . The slope of the least squares regression line is the coefficient of $x$ , which is $-48.057$ .
Interpret Slope: Interpret the slope. $\newline$ In the equation $y = -48.057x + 483.245$ , $x$ represents the number of hours Leo sleeps, and $y$ represents the number of minutes it takes him to do his math homework. The slope of $-48.057$ indicates that for each one hour increase in sleep, the number of minutes it takes to do homework decreases by $48.057$ minutes.
Answer Question: Answer the question based on the slope. $\newline$ Since the slope is $-48.057$ , if Leo sleeps for one extra hour at night, the least squares regression line predicts it will take him $48.057$ fewer minutes to do his math homework the next day.

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