What does a lower R-squared value suggest about the fitted line?

What does a lower R-squared value suggest about the fitted line?

• A. It perfectly fits the data
• B. It captures most of the variation
• C. It does not capture much of the variation
• D. It indicates a strong relationship

Answer: (C)

A lower R-squared value indicates that the fitted line does not capture much of the variation in the dependent variable that can be explained by the independent variable(s) in the model. R-squared is a statistical measure that represents the proportion of the variance for the dependent variable that's explained by the independent variables in a regression model. When the R-squared value is low, it suggests that the independent variables have a limited ability to account for the variability in the dependent variable. This often means that the model may not be the best fit for the data, indicating that other factors or variables not included in the model may be influencing the dependent variable. Therefore, a lower R-squared value reflects a weaker explanatory power of the regression model regarding the relationship between the variables, aligning well with the idea that it does not capture much of the variation.

A lower R-squared value indicates that the fitted line does not capture much of the variation in the dependent variable that can be explained by the independent variable(s) in the model. R-squared is a statistical measure that represents the proportion of the variance for the dependent variable that's explained by the independent variables in a regression model.

When the R-squared value is low, it suggests that the independent variables have a limited ability to account for the variability in the dependent variable. This often means that the model may not be the best fit for the data, indicating that other factors or variables not included in the model may be influencing the dependent variable.

Therefore, a lower R-squared value reflects a weaker explanatory power of the regression model regarding the relationship between the variables, aligning well with the idea that it does not capture much of the variation.