The R² (coefficient of determination) and Adjusted R² are both measures of how well a regression model explains the variability of the dependent variable. Here’s a breakdown of their differences: 1. R² (Coefficient of Determination): • Definition: Measures the proportion of variance in the dependent variable that is explained by the independent variables in the model. • Formula:  Where: •  = Sum of squared residuals (errors) •  = Total sum of squares • Key Characteristics: • Ranges from 0 to 1 (sometimes negative for poor models in specific cases). • A higher value indicates a better fit. • Increases (or stays constant) as you add more predictors, even if the predictors are irrelevant. 2. Adjusted R²: • Definition: Adjusts R² for the number of predictors in the model. It penalizes the addition of predictors that do not improve the model significantly. • Formula:  Where: •  = Number of observations •  = Number of predictors (independent variables) • Key Characteristics: • Can decrease if an added predictor doesn’t improve the model. • Provides a more accurate measure of model performance, especially for multiple regression. • Can be negative if the model performs worse than just using the mean of the dependent variable. Key Differences: Aspect R² Adjusted R² Penalizes for Overfitting No Yes Value Behavior Always increases or stays constant when more predictors are added. Can decrease if unnecessary predictors are added. Usefulness Good for simple regression or initial assessment. Better for multiple regression when comparing models with different numbers of predictors. When to Use: • Use R² to understand how much of the variance is explained. • Use Adjusted R² to compare models with a different number of predictors or when there is a risk of overfitting.