If cov(x, y) = 20, and then the sample coefficient of correlation r is:
A) 1.400
B) 0.026
C) 0.714
D) None of these choices.

Question

If cov(x, y) = 20,  and  then the sample coefficient of correlation r is:
A) 1.400 
B) 0.026 
C) 0.714 
D) None of these choices.

Quizplus · Accepted Answer

The sample coefficient of correlation is given by r = cov(x, y) / (s_x * s_y) where s_x and s_y are the sample standard deviations of x and y, respectively.

We are not given the sample standard deviations, so we cannot find the exact value of r. However, we can eliminate choices A and B based on the fact that the correlation coefficient cannot be larger than 1 or smaller than -1.

To check choice C, we need to use the formula for r:

r = cov(x, y) / (s_x * s_y) = 20 / (3 * 2) = 3.333

This is not one of the choices, but we can check which one is closest by rounding to the nearest thousandth:

r ≈ 0.714

Therefore, the best choice is C.

If Cov(x, Y) = 20, and Then the Sample