Correlation Coefficient and Its Impact on Variables X and Y

B

r ranges from -1 to +1. The closer it is to -1 or +1, the stronger the relationship. Closer it is to zero, the weaker.

If the correlation coefficient between two variables equals zero, it means that there is no linear relationship between the variables X and Y. In other words, the variables are not linearly correlated.

Option B, "Not correlated," is the correct answer in this case. A correlation coefficient of zero indicates that there is no linear association between X and Y. It does not imply that there is no relationship at all between the variables; it just means that the relationship is not linear.

Option A, "Highly correlated," is incorrect because a correlation coefficient of zero implies no correlation, not a high correlation.

Option C, "Dependent on each other," is also incorrect. The absence of a linear relationship (correlation) does not provide any information about the dependence or independence of the variables.

Option D, "None of these answers are correct," is incorrect because option B, "Not correlated," is indeed the correct answer.

Option E, "All of these answers are correct," is incorrect because only option B, "Not correlated," accurately describes the relationship between the variables.

To summarize, when the correlation coefficient between two variables is zero, it indicates that the variables are not linearly correlated.