The correlation coefficient is the product of the correlation between two random variables and
A) the sum of their covariances
B) the sum of their standard deviations
C) their standard deviations
D) lies between the values of 0 and 1

Question

Quizplus · Accepted Answer

The correlation coefficient is defined as the covariance of two random variables divided by the product of their standard deviations. Mathematically, it can be expressed as:
r = cov(X,Y) / (SD(X) * SD(Y))
Therefore, the correlation coefficient is directly proportional to the standard deviations of the two variables, and not to their covariances. Thus, option A is incorrect. Similarly, option B is also incorrect because the sum of two standard deviations is not related to their correlation. Option D is partially correct, but it does not provide the complete answer. The correlation coefficient lies between the values of -1 and 1, where a value of 1 indicates a perfect positive correlation, a value of -1 indicates a perfect negative correlation, and a value of 0 indicates no correlation. Therefore, the best choice is option C, which states that the correlation coefficient is the product of the correlation and the standard deviations of the two variables.

The Correlation Coefficient Is the Product of the Correlation Between