Coefficient of determination

Definition

The coefficient of determination, denoted as $R^2$, measures the proportion of the variance in the dependent variable that is predictable from the independent variable(s) in a regression model. It provides an indication of the goodness-of-fit for the model.

5 Must Know Facts For Your Next Test

1. $R^2$ values range from 0 to 1, where 0 indicates no explanatory power and 1 indicates perfect explanatory power.
2. An $R^2$ value of 0.85 means that 85% of the variance in the dependent variable is explained by the independent variables.
3. $R^2$ can be used to compare different regression models; a higher $R^2$ suggests a better fit.
4. A high $R^2$ does not imply causation or that the model is appropriate; other statistical tests are needed to validate the model.
5. $R^2$ can be adjusted (Adjusted $R^2$) to account for the number of predictors in the model, which helps prevent overfitting.

Review Questions

• What does an $R^2$ value close to 1 signify in a regression model?
• How can you use $R^2$ to compare different regression models?
• Why might a high $R^2$ not necessarily indicate a good regression model?

Related terms

Regression Equation: An equation that describes the relationship between one dependent variable and one or more independent variables.

Correlation Coefficient: A measure that determines the degree to which two variables' movements are associated.

Adjusted R-Squared: A modified version of $R^2$ that adjusts for the number of predictors in a model, providing a more accurate measure when multiple predictors are used.