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). It ranges from 0 to 1, where a higher value indicates a better fit of the model.

5 Must Know Facts For Your Next Test

1. $R^2$ values close to 1 indicate that a large proportion of variance in the dependent variable is explained by the model.
2. $R^2 = 0$ means that the independent variables do not explain any of the variability in the dependent variable.
3. $R^2$ can never be negative since it represents a squared term.
4. $R^2$ alone cannot indicate whether a regression model is appropriate; other diagnostics are also needed.
5. Adjusted $R^2$ accounts for the number of predictors and adjusts for their impact on the overall fit.

Review Questions

• What does an $R^2$ value close to 0 signify?
• Why can’t $R^2$ be negative?
• How does adjusted $R^2$ differ from $R^2$?

Related terms

Adjusted $R^2$: 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.

Linear Regression: A statistical method that models the relationship between two or more variables by fitting a linear equation to observed data.

Correlation Coefficient: A measure that determines the degree to which two variables' movements are associated, ranging from -1 to +1.