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.
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$R^2$ values close to 1 indicate that a large proportion of variance in the dependent variable is explained by the model.
$R^2 = 0$ means that the independent variables do not explain any of the variability in the dependent variable.
$R^2$ can never be negative since it represents a squared term.
$R^2$ alone cannot indicate whether a regression model is appropriate; other diagnostics are also needed.
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.