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, denoted by r², is the squared correlation coefficient, which can be calculated as follows:

$$
r^2 = (\rho_{x,y})^2 = \left(\frac{\operatorname{cov}(x,y)}{s_x s_y}\right)^2 = \left(\frac{1260}{\sqrt{1600}\sqrt{1225}}\right)^2 = 0.81
$$

Therefore, the best choice is C.

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

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