What degree of relationship do values of the correlation coefficient (r) with magnitudes close to 1.00 indicate?
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A. B. C. D.B
The closer to 1, the stronger the relationship.
In the context of correlation coefficient (r), values close to 1.00 indicate a strong degree of relationship between the variables being analyzed. Therefore, the correct answer is B. Strong.
The correlation coefficient (r) is a statistical measure that quantifies the strength and direction of the linear relationship between two variables. It ranges from -1.00 to +1.00. The closer the value of r is to +1.00 or -1.00, the stronger the relationship between the variables.
When the correlation coefficient is close to +1.00, it signifies a strong positive linear relationship. This means that as one variable increases, the other variable tends to increase as well. For example, if you observe a correlation coefficient of +0.95 between the price of a stock and its earnings per share, it suggests a strong positive relationship, indicating that as the earnings per share increase, the price of the stock tends to increase as well.
Conversely, when the correlation coefficient is close to -1.00, it indicates a strong negative linear relationship. This means that as one variable increases, the other variable tends to decrease. For instance, if you find a correlation coefficient of -0.90 between the average temperature and the sale of winter coats, it implies a strong negative relationship. As the average temperature decreases, the sale of winter coats tends to increase.
On the other hand, when the correlation coefficient is close to 0, it suggests a weak or no linear relationship between the variables. A value of 0 indicates no linear relationship, while values closer to 0 (but not close to 1 or -1) suggest a weak linear relationship. This implies that the variables being analyzed do not have a strong linear association with each other.
To summarize, a correlation coefficient (r) with a magnitude close to 1.00 (either positive or negative) indicates a strong degree of relationship between the variables, implying that they have a strong linear association with each other.