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Read the following description of a data set. $\newline$ Janice has trouble getting her math homework done on time, and her mother suspects it is due to lack of sleep.For the next few nights, Janice's mother notes the number of hours she sleeps, $x$ , and the number of minutes it takes her to do her math homework the following day, $y$ .The least squares regression line of this data set is: $y = -3.032x + 203.753$ $\newline$ Complete the following sentence: $\newline$ If Janice sleeps for one extra hour at night, the least squares regression line predicts it will take her $\_\_\_\_$ fewer minutes to do her 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

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

x

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

y

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

y = -3.032x + 203.753

\newline

Complete the following sentence:

\newline

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

\_\_\_\_

fewer minutes to do her math homework the next day.

Regression Line Equation: The least squares regression line is given by the equation $y = -3.032x + 203.753$ , where $y$ represents the number of minutes it takes Janice to do her math homework, and $x$ represents the number of hours she sleeps.
Coefficient Analysis: To find out how many fewer minutes it will take Janice to do her math homework if she sleeps for one extra hour, we need to look at the coefficient of $x$ in the regression equation, which is $-3.032$ . This coefficient tells us the change in the number of minutes ( $y$ ) for each additional hour of sleep ( $x$ ).
Effect of Extra Sleep: Since the coefficient is negative, it means that for each extra hour Janice sleeps, the time it takes her to do her math homework decreases. The coefficient $-3.032$ means that for each extra hour of sleep, it will take Janice $3.032$ fewer minutes to do her homework.

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