R Squared

calender iconUpdated on June 11, 2024
corporate finance and accounting
financial analysis

R-squared (R²) is a measure of how much variability in the dependent variable is explained by the independent variables in a regression model. It is a coefficient of determination that ranges from 0 to 1, with values closer to 1 indicating a better fit of the model to the data.

Formula:

R² = 1 - (SSres / SStotal)

where:

  • is the coefficient of determination
  • SSres is the sum of squares of residuals
  • SStotal is the total sum of squares

Interpretation:

  • R² = 0: The model does not explain any variability in the dependent variable.
  • R² = 1: The model explains all variability in the dependent variable.
  • 0 < R² < 1: The model explains a certain percentage of variability in the dependent variable.

Example:

R² = 0.85

This means that the model explains 85% of the variability in the dependent variable.

Uses:

  • To assess the overall fit of a regression model.
  • To compare different models and select the best-fitting model.
  • To evaluate the predictive power of a model.

Limitations:

  • Overfitting: If the model is too complex, it can lead to an inflated R-squared value.
  • Sensitive to outliers: Outliers can significantly impact R-squared values.
  • Not a perfect measure: R-squared does not necessarily reflect the accuracy of a model’s predictions.

Additional Notes:

  • R-squared is a commonly used metric in regression analysis.
  • It is a popular measure of model fit, but it should not be the only factor considered when selecting a model.
  • Other factors, such as the model’s complexity and the presence of outliers, should also be taken into account.

FAQ's

What does R-squared tell you?

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R-squared tells you the proportion of the variance in the dependent variable that is explained by the independent variables in a regression model. It measures the model’s goodness-of-fit.

How do you interpret R-squared?

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What is a good R-squared value?

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Is a higher R-squared better?

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