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Answer: The movement in one variable will result in the exact opposite proportional movement in the other variable.
A correlation of -1 indicates a perfect negative linear relationship between two variables. This means that when one variable increases by a certain proportion, the other variable decreases by exactly the same proportion, and vice versa. The variables move in opposite directions with perfect consistency. **Key points:** - **Correlation of -1**: Perfect negative linear relationship - **Correlation of +1**: Perfect positive linear relationship (variables move together in the same direction in the same proportion) - **Correlation of 0**: No linear relationship between variables Option A is incorrect because it describes a correlation of 0, not -1. Option B is misleading because while both variables move in negative directions relative to each other, the key distinction is the exact opposite proportional movement. Option C correctly captures the precise mathematical meaning of a -1 correlation coefficient.
Author: Nikitesh Somanthe
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Which of the following is the most appropriate explanation of a -1 correlation between two random variables?
A
There is no correlation between two random variables.
B
Both variables move together in a negative direction.
C
The movement in one variable will result in the exact opposite proportional movement in the other variable.
D
None of the above.