What does R-squared indicate in a regression model?

What does R-squared indicate in a regression model?

• A. The accuracy of the predictions made by the model
• B. The relationship between independent and dependent variables
• C. The proportion of variance in the dependent variable explained by the independent variable(s)
• D. The standard deviation of the residuals

Answer: (C)

R-squared, also known as the coefficient of determination, is a key metric in regression analysis that quantifies how well the independent variable(s) account for the variability in the dependent variable. Specifically, it represents the proportion of the total variance in the dependent variable that can be explained by the model's independent variable(s). A higher R-squared value implies that a greater proportion of variance is explained by the model, indicating a potentially better fit. It ranges from 0 to 1, where 0 means that the model explains none of the variability, and 1 indicates that it accounts for all of it. This makes R-squared a valuable indicator of the effectiveness of the model in explaining the variation in the outcome being measured. Understanding R-squared helps in evaluating the strength of the relationship between the independent and dependent variables. While it does provide insight into the relationship, its primary role remains rooted in variance explanation rather than merely indicating the strength or accuracy of predictions. Other options touch on related concepts, but without capturing the essence of R-squared's role in the context of statistical modeling.

R-squared, also known as the coefficient of determination, is a key metric in regression analysis that quantifies how well the independent variable(s) account for the variability in the dependent variable. Specifically, it represents the proportion of the total variance in the dependent variable that can be explained by the model's independent variable(s).

A higher R-squared value implies that a greater proportion of variance is explained by the model, indicating a potentially better fit. It ranges from 0 to 1, where 0 means that the model explains none of the variability, and 1 indicates that it accounts for all of it. This makes R-squared a valuable indicator of the effectiveness of the model in explaining the variation in the outcome being measured.

Understanding R-squared helps in evaluating the strength of the relationship between the independent and dependent variables. While it does provide insight into the relationship, its primary role remains rooted in variance explanation rather than merely indicating the strength or accuracy of predictions. Other options touch on related concepts, but without capturing the essence of R-squared's role in the context of statistical modeling.