If cov(x, y) = 1260, $s _ { x } ^ { 2 } = 1600$ , and $s _ { y } ^ { 2 } = 1225$ , then the coefficient of determination is:
A)0.90
B)1.23
C)0.81
D)0.006

Question

Quizplus · Accepted Answer

The coefficient of determination is the square of the correlation coefficient. The correlation coefficient $ r $ is calculated as $ r = \frac{cov(x, y)}{s_x s_y} $. Given $ cov(x, y) = 1260 $, $ s_x = \sqrt{1600} = 40 $, and $ s_y = \sqrt{1225} = 35 $, we find $ r = \frac{1260}{40 \times 35} = 0.9 $. The coefficient of determination is $ r^2 = 0.9^2 = 0.81 $.

If Cov(x, Y) = 1260 sx2=1600s _ { x } ^ { 2 } = 1600sx2​=1600

If Cov(x, Y) = 1260 $s _ { x } ^ { 2 } = 1600$