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 40 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. $\begin{array}{l|c|c|c|c|c|c|c|c|c|}
\text { Commute time (min), } \mathrm{x} & 72 & 85 & 91 & 90 & 88 & 98 & 75 & 100 & 80 \
\hline \text { Number of absences. } \mathrm{y} & 3 & 7 & 10 & 10 & 8 & 15 & 4 & 15 & 5
\end{array}$
A) $hat {y }= 0.45 x - 30.27 ; - 12$ absences; No, it is not reasonable. 40 minutes is well outside the scope of the model.
B) $\hat { y } = 0.45 \mathrm { x } - 30.27 ; - 12$ absences; $\mathrm { Yes }$, it is reasonable.
C) $\hat { y } = 0.45 \mathrm { x } + 30.27 ; 48$ absences; Yes, it is reasonable.
D) $\hat { y } = 0.45 \mathrm { x } + 30.27 ; 48$ absences; No, it is not reasonable. 40 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 40 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. $\begin{array}{l|c|c|c|c|c|c|c|c|c|}
\text { Commute time (min), } \mathrm{x} & 72 & 85 & 91 & 90 & 88 & 98 & 75 & 100 & 80 \
\hline \text { Number of absences. } \mathrm{y} & 3 & 7 & 10 & 10 & 8 & 15 & 4 & 15 & 5
\end{array}$
A) $hat {y }= 0.45 x - 30.27 ; - 12$ absences; No, it is not reasonable. 40 minutes is well outside the scope of the model.
B) $\hat  { y } = 0.45 \mathrm { x } - 30.27 ; - 12$ absences; $\mathrm { Yes }$, it is reasonable.
C) $\hat  { y } = 0.45 \mathrm { x } + 30.27 ; 48$ absences; Yes, it is reasonable.
D) $\hat  { y } = 0.45 \mathrm { x } + 30.27 ; 48$ absences; No, it is not reasonable. 40 minutes is well outside the scope of the model.

Quizplus · Accepted Answer

Without the actual calculation of the regression line and the predicted value for a 40-minute commute, it's impossible to directly verify the correct equation and prediction. However, predicting -12 absences is not reasonable because the number of absences cannot be negative. The statement about the 40-minute commute being outside the scope of the model is valid because the given data do not include commute times as low as 40 minutes, making extrapolation to this value potentially inaccurate.

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