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R-squared Formula:
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The Coefficient of Determination (R²) is a statistical measure that represents the proportion of variance in the dependent variable that is predictable from the independent variable(s) in a regression model. It indicates how well the regression predictions approximate the real data points.
The calculator uses the R-squared formula:
Where:
Explanation: R² measures the proportion of total variation in the dependent variable that is explained by the regression model. A value of 1 indicates perfect prediction, while 0 indicates no explanatory power.
Details: R-squared is crucial for evaluating the goodness-of-fit of regression models. It helps determine how well the model explains the variability of the response data around its mean.
Tips: Enter the sum of squared residuals and total sum of squares. Both values must be positive, and SS_res should not exceed SS_tot. The result is dimensionless and ranges from 0 to 1.
Q1: What is a good R-squared value?
A: In social sciences, R² > 0.5 is often considered good, while in physical sciences, values > 0.8 are typically expected. However, interpretation depends on the field and context.
Q2: Can R-squared be negative?
A: Yes, R² can be negative when the model performs worse than simply using the mean of the dependent variable as prediction.
Q3: What are the limitations of R-squared?
A: R² always increases with additional predictors, even if they are irrelevant. It doesn't indicate whether the regression coefficients are statistically significant.
Q4: How is R-squared different from adjusted R-squared?
A: Adjusted R² penalizes for adding unnecessary variables and is preferred when comparing models with different numbers of predictors.
Q5: When should I use R-squared?
A: Use R-squared to assess how well your regression model fits the data, but always consider it alongside other metrics like p-values and residual analysis.