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

1) If the coefficient of correlation is negative, then the two variables move together in the same direction.
2) Perfect negative correlation would yield a coefficient of correlation of -1.00.
3) It is the cube root of the coefficient of determination when there is one independent variable.
4) It is an alternative measure of the hypothesis test of cost parameters.

User Scrameri
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Final answer:

The true statement about the coefficient of correlation is that perfect negative correlation yields a coefficient of -1.00, indicating a perfect inverse linear relationship between two variables.

Step-by-step explanation:

The coefficient of correlation is a measure that indicates the strength and direction of the linear relationship between two variables. Among the given options regarding the coefficient of correlation, statement 2) 'Perfect negative correlation would yield a coefficient of correlation of -1.00.' is true. When the correlation coefficient, often represented by the letter r, is -1, it indicates a perfect negative correlation. This means as one variable increases, the other variable decreases, and this relationship is consistently linear.

It's important to remember that the coefficient of correlation ranges between -1 and 1. The closer the value of r is to -1 or 1, the stronger the correlation. A value of r that is exactly -1 or 1 indicates a perfect linear relationship. If r is negative, an increase in one variable corresponds with a decrease in the other, which is the inverse relationship also known as negative correlation.

As for the coefficient of determination, represented as r², it is the square of the correlation coefficient. This tells us what percentage of the variation in the dependent variable can be explained by the independent variable, using the best fit linear line.

User Xedo
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