Given that cov(x,y) = 8.5, $s _ { y } ^ { 2 }$ = 8 and $S _ { x } ^ { 2 }$ = 10, the value of the coefficient of determination is 0.95.

Question

Quizplus · Accepted Answer

The coefficient of determination is the square of the correlation coefficient, which is calculated as $ r = \frac{cov(x,y)}{\sqrt{s_x^2 \cdot s_y^2}} $. Here, $ r = \frac{8.5}{\sqrt{10 \cdot 8}} \approx 0.95 $, so $ r^2 \approx 0.9025 $, not 0.95.

Given That Cov(x,y) = 8 sy2s _ { y } ^ { 2 }sy2​

Given That Cov(x,y) = 8 $s _ { y } ^ { 2 }$