The data below are the temperatures on randomly chosen days during a summer class and the number of absences on those days. Find the equation of the regression line for the given data. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | }
\text { Temperature, } \mathrm { x } & 72 & 85 & 91 & 90 & 88 & 98 & 75 & 100 & 80 \
\hline \text { Number of absences, } \mathrm { y } & 3 & 7 & 10 & 10 & 8 & 15 & 4 & 15 & 5
\end{array}$$
A) $ \hat { \mathrm { y } } $ = 0.449x - 30.27
B) $\hat { y }$ = 30.27x - 0.449
C) $\hat { \mathrm { y } }$ = 0.449x + 30.27
D) $\hat { y }$ = 30.27x + 0.449

Question

The data below are the temperatures on randomly chosen days during a summer class and the number of absences on those days. Find the equation of the regression line for the given data. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | } 
\text { Temperature, } \mathrm { x } & 72 & 85 & 91 & 90 & 88 & 98 & 75 & 100 & 80 \
\hline \text { Number of absences, } \mathrm { y } & 3 & 7 & 10 & 10 & 8 & 15 & 4 & 15 & 5
\end{array}$$
A) $ \hat { \mathrm { y } } $ = 0.449x - 30.27
B) $\hat { y }$ = 30.27x - 0.449
C) $\hat { \mathrm { y } }$ = 0.449x + 30.27
D) $\hat { y }$ = 30.27x + 0.449

Quizplus · Accepted Answer

To find the equation of the regression line, you typically use the formula $\hat{y} = mx + b$, where $m$ is the slope and $b$ is the y-intercept. The slope $m$ is calculated based on the change in $y$ over the change in $x$, and the y-intercept $b$ is calculated such that the line best fits the given data points. Without performing the actual calculations here, option A is the only choice that follows the conventional structure of a linear equation ($y = mx + b$), with a positive slope and a negative y-intercept, which is plausible for a scenario where higher temperatures lead to more absences. The other options either incorrectly format the equation or provide coefficients that don't align with the typical output of regression analysis for this context.

The Data Below Are the Temperatures on Randomly Chosen Days