Which correlation coefficient represents a moderate negative correlation?
r=-0.04
r=-0.24
r=-0.64
r=-0.94
Answer (2)
Correlation coefficients range from -1 to 1, where -1 is a perfect negative correlation, 0 is no correlation, and 1 is a perfect positive correlation.
Moderate negative correlations typically fall between -0.3 and -0.7.
Examining the given options, r = − 0.64 falls within this range.
Thus, the correlation coefficient representing a moderate negative correlation is − 0.64 .
Explanation
Understand the problem and provided data We are given four correlation coefficients: r = − 0.04 , r = − 0.24 , r = − 0.64 , and r = − 0.94 . We need to identify which of these represents a moderate negative correlation.
Understanding Correlation Coefficients Correlation coefficients range from -1 to 1. A correlation coefficient of -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation. Moderate negative correlations are typically between -0.3 and -0.7.
Analyze each option Let's examine each given correlation coefficient:
r = − 0.04 : This is close to 0, indicating a very weak negative correlation (almost no correlation).
r = − 0.24 : This indicates a weak negative correlation.
r = − 0.64 : This falls within the range of -0.3 to -0.7, indicating a moderate negative correlation.
r = − 0.94 : This is close to -1, indicating a strong negative correlation.
Final Answer Therefore, the correlation coefficient that represents a moderate negative correlation is r = − 0.64 .
Examples
Understanding correlation coefficients is crucial in many real-world scenarios. For instance, in marketing, a moderate negative correlation might be observed between the price of a product and the quantity sold. As the price increases, the quantity sold moderately decreases. This information helps businesses make informed decisions about pricing strategies. Similarly, in healthcare, a moderate negative correlation might exist between exercise frequency and blood pressure levels, indicating that increased exercise is associated with moderately lower blood pressure.
The correlation coefficient that represents a moderate negative correlation is r = − 0.64 . This value falls within the range of -0.3 to -0.7, indicating a moderate negative relationship between two variables. Therefore, the correct answer is r = − 0.64 .
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