What does it mean if r = -1.00?
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A. B. C. D. E.E
All the above are properties or explanations of the coefficient of correlation being equal to -1.0.
The question pertains to the interpretation of a correlation coefficient, denoted as "r," which measures the strength and direction of the linear relationship between two variables. A correlation coefficient ranges from -1 to +1.
When the correlation coefficient is -1, it indicates a perfect negative correlation between the two variables being examined. In this scenario, option A, "High values of one variable are associated with low values of the other variable," is an accurate interpretation.
In a perfect negative correlation, as one variable increases, the other variable decreases in a consistent and predictable manner. This relationship is represented by a downward sloping straight line when the data points are plotted on a scatter plot. Therefore, when r = -1.00, high values of one variable are indeed associated with low values of the other variable.
Option B, "Dependent variable can be perfectly predicted by the independent variable," is not an accurate interpretation for a correlation coefficient of -1. While a perfect negative correlation suggests a predictable relationship, it does not imply that one variable can be perfectly predicted by the other.
Option C, "All of the variation in the dependent variable can be accounted for by the independent variable," is also incorrect. A correlation coefficient of -1 only indicates the strength and direction of the linear relationship between the variables; it does not imply that the independent variable explains all the variation in the dependent variable.
Option D, "Coefficient of nondetermination equals zero," is not applicable in this case. The coefficient of nondetermination, also known as the coefficient of alienation or coefficient of inefficiency, represents the proportion of the dependent variable's variability that is not explained by the independent variable. It is calculated as 1 minus the coefficient of determination (R-squared). Since the correlation coefficient is -1, the coefficient of determination would be 1, and the coefficient of nondetermination would be 0. However, this option is incorrect because the coefficient of nondetermination is not explicitly related to a correlation coefficient of -1.
Hence, the correct answer to the question is option A: "High values of one variable are associated with low values of the other variable."