What r value represents a perfect negative correlation?

What r value represents a perfect negative correlation?

• A. r = 0.25
• B. r = 0
• C. r = -1
• D. r = 1

Answer: (C)

The value that represents a perfect negative correlation is -1. In statistics, the correlation coefficient, denoted as r, ranges from -1 to 1. A correlation of -1 indicates a perfect inverse relationship between two variables, meaning that as one variable increases, the other consistently decreases in a linear fashion. This perfect negative correlation implies that there is no variability in the direction of the relationship; all points would lie exactly on a line that slopes downward. In contrast, a correlation of 0 indicates no correlation between the two variables, meaning changes in one variable do not predict changes in the other. A positive correlation value, such as 0.25 or 1, denotes a relationship where both variables move in the same direction; a correlation of 1 represents a perfect positive correlation, where both variables increase or decrease together in a completely predictable manner. Understanding the nuances of the correlation coefficient is crucial in analyzing data relationships in fields such as statistics and mathematics.

The value that represents a perfect negative correlation is -1. In statistics, the correlation coefficient, denoted as r, ranges from -1 to 1. A correlation of -1 indicates a perfect inverse relationship between two variables, meaning that as one variable increases, the other consistently decreases in a linear fashion. This perfect negative correlation implies that there is no variability in the direction of the relationship; all points would lie exactly on a line that slopes downward.

In contrast, a correlation of 0 indicates no correlation between the two variables, meaning changes in one variable do not predict changes in the other. A positive correlation value, such as 0.25 or 1, denotes a relationship where both variables move in the same direction; a correlation of 1 represents a perfect positive correlation, where both variables increase or decrease together in a completely predictable manner.

Understanding the nuances of the correlation coefficient is crucial in analyzing data relationships in fields such as statistics and mathematics.