Question

Two independent variables are-

• A. Correlated
• B. Uncorrelated
• C. Linearly Correlated
• D. Nonlinearly Correlated

Hint:

Independence of variables always implies zero correlation, but zero correlation does not always imply independence.

Answer 1

The Correct Option is B

Step 1: Definition of Independence.
Two variables are independent if the occurrence of one does not influence the probability distribution of the other.
Step 2: Independence and Correlation.
Independent variables exhibit no correlation, neither linear nor nonlinear.
Consequently, independent variables are always uncorrelated.
Step 3: Evaluation of Choices.
- (1) Correlated: Incorrect. Independence implies the absence of a relationship.
- (2) Uncorrelated: Correct. Independence is equivalent to the absence of correlation.
- (3) Linearly correlated: Incorrect. This implies a linear relationship, contradicting independence.
- (4) Nonlinearly correlated: Incorrect. Any form of correlation signifies dependence.
Step 4: Final Determination.
Thus, independent variables are invariably uncorrelated.