The test scores of 6 randomly picked students and the numbers of hours they prepared are as follows: $\begin{array} { c | r r r r r r }
Hours & 5 & 10 & 4 & 6 & 10 & 9 \
\hline Score & 64 & 86 & 69 & 86 & 59 & 87
\end{array}$
The equation of the regression line is $\hat { y } = 1.06604 \mathrm { x } + 67.3491$. Find the coefficient of determination.
A) $0.2242$
B) $0.6781$
C) $0.0503$
D) $- 0.2242$

Question

The test scores of 6 randomly picked students and the numbers of hours they prepared are as follows: $\begin{array} { c | r r r r r r } 
Hours & 5 & 10 & 4 & 6 & 10 & 9 \
\hline Score & 64 & 86 & 69 & 86 & 59 & 87
\end{array}$
The equation of the regression line is $\hat { y } = 1.06604 \mathrm { x } + 67.3491$. Find the coefficient of determination.
A) $0.2242$
B) $0.6781$
C) $0.0503$
D) $- 0.2242$

Quizplus · Accepted Answer

The coefficient of determination, $R^2$, is calculated as the square of the correlation coefficient. The given regression line equation suggests a weak correlation, and the closest value indicating a weak relationship is $0.0503$.

The Test Scores of 6 Randomly Picked Students and the Numbers