Which of these is not a possible r-value? A. -0.75 B. 1.2 C. 0.5 D. -0.1
The correct answer and explanation is:
The correct answer is B. 1.2.
Explanation:
The r-value refers to the correlation coefficient, which measures the strength and direction of a linear relationship between two variables. It is a statistic commonly used in statistics and data analysis.
Key properties of the correlation coefficient (r):
- It ranges from -1 to +1.
- An r-value of +1 means a perfect positive linear relationship.
- An r-value of -1 means a perfect negative linear relationship.
- An r-value of 0 means no linear relationship.
- Values between -1 and 1 indicate varying strengths of positive or negative correlation.
Why option B is incorrect:
- The value 1.2 is outside the allowable range of -1 to +1.
- Because correlation coefficients cannot exceed 1 or be less than -1, 1.2 is not a possible r-value.
Explanation of the other options:
- A. -0.75: This is a valid r-value, indicating a strong negative correlation.
- C. 0.5: This is also a valid r-value, indicating a moderate positive correlation.
- D. -0.1: This is valid as well, indicating a very weak negative correlation.
Additional context:
Correlation coefficients measure linear relationships only. Nonlinear relationships may exist even if r is near zero. The sign (+ or -) shows the direction of the relationship, and the magnitude (distance from zero) shows the strength.
The correlation coefficient is derived mathematically so that it cannot be outside the interval [-1, 1]. Any calculated value outside this range usually indicates an error in calculation or data.
In summary, 1.2 is not possible as a correlation coefficient because it violates the mathematical limits of correlation, making option B the correct choice.