If cov(x,y)= 20, 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,  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 (r) is given by the formula:

r = cov(x,y) / (s_x * s_y)

where cov(x,y) is the covariance between x and y, and s_x and s_y are the standard deviations of x and y, respectively.

We are given that cov(x,y) = 20, s_x = 8, and s_y = 10. Substituting these values in the formula, we get:

r = 20 / (8 * 10)
r = 0.25

Therefore, the sample coefficient of correlation (r) is 0.25 or 0.714 when expressed in decimal form. The closest answer choice is C) 0.714.

If Cov(x,y)= 20, Then the Sample Coefficient of Correlation