If cov(x, y) = 20, $s _ { x } ^ { 2 } = 16$ and $s _ { y } ^ { 2 } = 49$ then the sample coefficient of correlation r is:
A)1.400
B)0.026
C)0.710
D)None of these choices.

Question

Quizplus · Accepted Answer

The sample coefficient of correlation $ r $ is calculated using the formula $ r = \frac{\text{cov}(x, y)}{s_x s_y} $. Here, $ s_x = \sqrt{16} = 4 $ and $ s_y = \sqrt{49} = 7 $. So, $ r = \frac{20}{4 \times 7} = \frac{20}{28} = 0.714 $, which rounds to 0.710.

If Cov(x, Y) = 20 sx2=16s _ { x } ^ { 2 } = 16sx2​=16

If Cov(x, Y) = 20 $s _ { x } ^ { 2 } = 16$