What does r² measure in a correlation analysis?

What does r² measure in a correlation analysis?

• A. the variance not shared by the two variables
• B. the strength of the positive relationship of the two variables
• C. the variance shared by the two variables
• D. none of the above

Answer: (C)

In correlation analysis, r², known as the coefficient of determination, specifically measures the proportion of variance in one variable that can be explained by its relationship with another variable. This statistic provides insight into how closely the two variables are related. When r² is calculated, it represents the extent to which changes in one variable are associated with changes in another. A higher r² value indicates that a significant portion of the variance in the dependent variable can be predicted from the independent variable. Consequently, this shared variance is indicative of the strength and directionality of their relationship. The correct choice emphasizes this shared variance, establishing that r² is not merely a reflection of correlation strength but specifies how much of the variability in one variable is accounted for by the other. This is crucial in both statistical analysis and practical applications, as it helps to determine how well the independent variable serves as a predictor for the dependent variable.

In correlation analysis, r², known as the coefficient of determination, specifically measures the proportion of variance in one variable that can be explained by its relationship with another variable. This statistic provides insight into how closely the two variables are related.

When r² is calculated, it represents the extent to which changes in one variable are associated with changes in another. A higher r² value indicates that a significant portion of the variance in the dependent variable can be predicted from the independent variable. Consequently, this shared variance is indicative of the strength and directionality of their relationship.

The correct choice emphasizes this shared variance, establishing that r² is not merely a reflection of correlation strength but specifies how much of the variability in one variable is accounted for by the other. This is crucial in both statistical analysis and practical applications, as it helps to determine how well the independent variable serves as a predictor for the dependent variable.