R-squared in Regression Analysis
How to Interpret R-squared in Regression Analysis
R-squared is a measure used in linear regression to show how well the model explains the variation in the dependent variable. It’s expressed as a percentage, ranging from 0% to 100%.
What Does R-squared Represent?
0% R-squared: The model does not explain any variation in the dependent variable.
100% R-squared: The model explains all the variation.
Higher R-squared values generally mean the model fits better, but this is not always the case!
Key Points About R-squared
Goodness-of-Fit
R-squared indicates how close the data points are to the regression line. A higher value often suggests a better fit, but the fit should always be evaluated with residual plots to ensure there’s no bias.Residuals and Bias
Residuals are the differences between observed and predicted values. An unbiased model has residuals randomly scattered around zero. If residual plots show patterns, the model might be biased, even if R-squared is high.Low R-squared Values
In fields like social sciences, low R-squared values are common due to the complexity of human behavior.
Even with a low R-squared, significant independent variables can provide useful insights.
High R-squared Values
A high R-squared doesn’t always mean the model is good. For instance:
The model could miss key variables, leading to systematic errors (bias).
Overfitting or mining random patterns can artificially inflate R-squared.
Always check residual plots to confirm the model’s quality.
How to Use R-squared Effectively
Combine R-squared with other statistics, residual plots, and domain knowledge.
Adjusted R-squared and predicted R-squared can provide better insights, especially for comparing models or assessing predictive accuracy.
R-squared is a helpful tool, but it’s not the full story. Always look deeper to ensure your model is reliable and unbiased
.