The data below are the average one-way commute times (in minutes) for selected students and the number ofabsences for those students during the term. Find the equation of the regression line for the given data. Whatwould be the predicted number of absences if the commute time was 95 minutes? Is this a reasonable question?Round the predicted number of absences to the nearest whole number. Round the regression line values to thenearest hundredth. $\begin{array} { | l | c | c | c | c | c | c | c | c | c | }
\text { Commute time } ( \mathrm { min } ) , \mathrm { x } & 72 & 85 & 91 & 90 & 88 & 98 & 75 & 100 & 80 \
\hline \text { Number of absences, } \mathrm { y } & 3 & 7 & 10 & 10 & 8 & 15 & 4 & 15 & 5
\end{array}$
A) $\hat { y } = 0.45 \mathrm { x } - 30.27 ; 12$ absences; $Y e s$, it is reasonable.
B)$\hat { y } = 0.45 \mathrm { x } - 30.27 ; 12$ absences; No, it is not reasonable. 95 minutes is well outside the scope of the model.
C) $\hat { y } = 0.45 \mathrm { x } + 30.27 ; 73$ absences; Yes, it is reasonable.
D) $\hat { y } = 0.45 \mathrm { x } + 30.27 ; 73$ absences; No, it is not reasonable. 95 minutes is well outside the scope of the model.

Question

The data below are the average one-way commute times (in minutes) for selected students and the number ofabsences for those students during the term. Find the equation of the regression line for the given data. Whatwould be the predicted number of absences if the commute time was 95 minutes? Is this a reasonable question?Round the predicted number of absences to the nearest whole number. Round the regression line values to thenearest hundredth. $\begin{array} { | l | c | c | c | c | c | c | c | c | c | } 
\text { Commute time } ( \mathrm { min } ) , \mathrm { x } & 72 & 85 & 91 & 90 & 88 & 98 & 75 & 100 & 80 \
\hline \text { Number of absences, } \mathrm { y } & 3 & 7 & 10 & 10 & 8 & 15 & 4 & 15 & 5
\end{array}$
A) $\hat { y } = 0.45 \mathrm { x } - 30.27 ; 12$ absences; $Y e s$, it is reasonable.
B)$\hat { y }  = 0.45 \mathrm { x } - 30.27 ; 12$ absences; No, it is not reasonable. 95 minutes is well outside the scope of the model.
C) $\hat { y } = 0.45 \mathrm { x } + 30.27 ; 73$ absences; Yes, it is reasonable.
D) $\hat { y }  = 0.45 \mathrm { x } + 30.27 ; 73$ absences; No, it is not reasonable. 95 minutes is well outside the scope of the model.

Quizplus · Accepted Answer

The regression line is $\hat { y } = 0.45 \mathrm { x } - 30.27$. Substituting $x = 95$ into the regression line, we get $\hat { y } = 0.45 ( 95 ) - 30.27 = 12.38$. Rounding to the nearest whole number, the predicted number of absences is 12. Since 95 minutes is within the range of the commute times in the data, it is reasonable to use the regression line to predict the number of absences.

The Data Below Are the Average One-Way Commute Times (In