The data below are the final exam scores of 10 randomly selected statistics students and the number of hours they studied for the exam. Find the equation of the regression line for the given data. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | c | }
\text { Hours, } \mathrm { x } & 3 & 5 & 2 & 8 & 2 & 4 & 4 & 5 & 6 & 3 \
\hline \text { Scores, } \mathrm { y } & 65 & 80 & 60 & 88 & 66 & 78 & 85 & 90 & 90 & 71
\end{array}$$
A) $\hat{y}$ = 5.044x + 56.113
B) $\hat { \mathrm { y } }$ = 56.113x - 5.044
C) $\hat { \mathrm { y } }$ = -56.113x - 5.044
D) $\hat { \mathrm { y } }$ = -5.044x + 56.113

Question

The data below are the final exam scores of 10 randomly selected statistics students and the number of hours they studied for the exam. Find the equation of the regression line for the given data. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | c | } 
\text { Hours, } \mathrm { x } & 3 & 5 & 2 & 8 & 2 & 4 & 4 & 5 & 6 & 3 \
\hline \text { Scores, } \mathrm { y } & 65 & 80 & 60 & 88 & 66 & 78 & 85 & 90 & 90 & 71
\end{array}$$
A) $\hat{y}$ = 5.044x + 56.113
B) $\hat { \mathrm { y } }$ = 56.113x - 5.044
C) $\hat { \mathrm { y } }$ = -56.113x - 5.044
D) $\hat { \mathrm { y } }$ = -5.044x + 56.113

Quizplus · Accepted Answer

The equation of the regression line is calculated using the least squares method, which involves finding the line that minimizes the sum of the squares of the vertical distances of the points from the line. The correct equation, $\hat{y} = 5.044x + 56.113$, indicates that for each additional hour studied, the expected increase in the exam score is approximately 5.044 points, starting from a base score of 56.113 when no hours are studied.

The Data Below Are the Final Exam Scores of 10