Find the Least-Squares Regression Line and Use the Line to Make Predictions
-The data below are the number of absences and the final grades of 9 randomly selected students from a literature class. Find the equation of the regression line for the given data. What would be the predicted final grade if a student was absent 14 times? Round the predicted grade to the nearest whole number.
$\begin{array}{|l|c|c|c|c|c|c|c|c|c|}
\hline \text { Number of absences, } \mathrm{x} & 0 & 3 & 6 & 4 & 9 & 2 & 15 & 8 & 5 \
\hline \text { Final grade, } \mathrm{y} & 98 & 86 & 80 & 82 & 71 & 92 & 55 & 76 & 82
\end{array}$

A) $\hat { y } = - 2.75 \mathrm { x } + 96.14 ; 58$
B) $\hat { y } = 96.14 \mathrm { x } - 2.75 ; 1343$
C) $\hat {y} = - 2.75 x - 96.14 ; 134.64$
D) $\hat { y } = - 96.14 \mathrm { x } + 2.75 ; 1343$

Question

Find the Least-Squares Regression Line and Use the Line to Make Predictions
-The data below are the number of absences and the final grades of 9 randomly selected students from a literature class. Find the equation of the regression line for the given data. What would be the predicted final grade if a student was absent 14 times? Round the predicted grade to the nearest whole number.
$\begin{array}{|l|c|c|c|c|c|c|c|c|c|}
\hline \text { Number of absences, } \mathrm{x} & 0 & 3 & 6 & 4 & 9 & 2 & 15 & 8 & 5 \
\hline \text { Final grade, } \mathrm{y} & 98 & 86 & 80 & 82 & 71 & 92 & 55 & 76 & 82
\end{array}$

A) $\hat  { y } = - 2.75 \mathrm { x } + 96.14 ; 58$
B) $\hat  { y } = 96.14 \mathrm { x } - 2.75 ; 1343$
C) $\hat {y} = - 2.75 x - 96.14 ; 134.64$
D) $\hat   { y } = - 96.14 \mathrm { x } + 2.75 ; 1343$

Quizplus · Accepted Answer

The least-squares regression line is calculated using the formula $\hat{y} = mx + b$, where $m$ is the slope and $b$ is the y-intercept. The correct equation, based on the given data, is $\hat{y} = -2.75x + 96.14$. To predict the final grade for a student with 14 absences, substitute $x = 14$ into the equation to get a predicted grade, which rounds to 58.