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Which of the following is the most reasonable estimate of the correlation coefficient? −1.0 −0.9 −0.7 −0.5

User Myong
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Final answer:

A correlation coefficient of -0.9 indicates a stronger relationship between two variables than a coefficient of -0.5, with -0.9 being closer to the perfect correlation values of -1 or 1. Additionally, a correlation of 0.71 or higher is necessary for at least a 0.50 coefficient of determination.

Step-by-step explanation:

The correlation coefficient is a statistical measure that describes the extent to which two variables are related. A correlation coefficient of -1 or 1 indicates a perfect linear relationship, whereas a coefficient of 0 indicates no linear relationship at all. When comparing -0.90 and -0.50, the value that is closest to -1 or 1 would indicate the strongest relationship.

Therefore, a correlation coefficient of -0.90 is stronger than -0.50, indicating a more predictable relationship between the two variables. The sign before the correlation coefficient (- or +) indicates the direction of the relationship; in this case, both -0.90 and -0.50 are negative, signifying negative correlations, but -0.90 is stronger.

To achieve a coefficient of determination of at least 0.50, which explains 50% of the variance in one variable predicted from the other, you would need a correlation of approximately 0.71 or higher.

User CalvinR
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