What range does correlation take to indicate the strength and direction of a linear relationship?

What range does correlation take to indicate the strength and direction of a linear relationship?

• A. -1 to 0
• B. 0 to +1
• C. -1 to +1
• D. 0 to –1

Answer: (C)

The correct range for correlation coefficients, which indicates both the strength and direction of a linear relationship between two variables, is from -1 to +1. A correlation of -1 signifies a perfect negative linear relationship, meaning that as one variable increases, the other decreases in a perfect linear fashion. Conversely, a correlation of +1 indicates a perfect positive linear relationship, where both variables increase together in a perfect linear manner. A correlation of 0 reflects no linear relationship between the variables. Understanding this scale is essential for interpreting the results of correlation analysis in statistics. A value close to -1 or +1 suggests a strong relationship, while values closer to 0 imply a weaker relationship. This range captures the full spectrum of linear associations, making it critical for data analysis and interpretation.

The correct range for correlation coefficients, which indicates both the strength and direction of a linear relationship between two variables, is from -1 to +1. A correlation of -1 signifies a perfect negative linear relationship, meaning that as one variable increases, the other decreases in a perfect linear fashion. Conversely, a correlation of +1 indicates a perfect positive linear relationship, where both variables increase together in a perfect linear manner. A correlation of 0 reflects no linear relationship between the variables.

Understanding this scale is essential for interpreting the results of correlation analysis in statistics. A value close to -1 or +1 suggests a strong relationship, while values closer to 0 imply a weaker relationship. This range captures the full spectrum of linear associations, making it critical for data analysis and interpretation.