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Which of the following statements is true of the coefficient of determination?

a. Perfect negative correlation would yield a coefficient of correlation of -1.00.
b. The value of the coefficient of determination (R2) can range between -1 and +1.
c. The lower the percentage of cost variability explained, the better job the dependent variable does of explaining the independent variable.
d. There is no cut-off point for a good versus a bad coefficient of determination.

User MikeOne
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Final answer:

The true statement is that a perfect negative correlation yields a coefficient of correlation of -1.00. R2, the coefficient of determination, ranges between 0 and 1, representing the variance in the dependent variable explained by the independent variable. There is no universal cut-off for what constitutes a 'good' R2 value.

Step-by-step explanation:

The true statement about the coefficient of determination is that a perfect negative correlation would yield a coefficient of correlation of -1.00. The coefficient of determination, denoted as R2, is the square of the correlation coefficient (r). This means that the value of R2 can only range between 0 and +1. R2 represents the proportion of variance in the dependent variable that is predictable from the independent variable.

When it comes to correlation, r is the statistic that measures the strength and direction of a linear relationship between two variables. This coefficient ranges from -1 to +1. A value of +1 indicates a perfect positive correlation, while -1 indicates a perfect negative correlation. A zero value indicates no correlation.

Lastly, it is important to note that there is not a universally accepted cut-off point for a 'good' value of R2. The interpretability of R2 depends on the context of the data and the specific field of study.

User Ger Apeldoorn
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