How to interpret adjusted coefficient of determination
The adjusted coefficient of determination is a statistical measure that explains the proportion of the variance in the dependent variable that is predictable from the independent variables in a regression model, adjusted for the number of independent variables and the sample size.
To interpret the adjusted coefficient of determination, you can follow these steps:
1. Range: The adjusted coefficient of determination ranges from 0 to 1. A value of 0 means that none of the variance in the dependent variable is explained by the independent variables, while a value of 1 means that all of the variance is explained.
2. Proportion of variance explained: The coefficient of determination represents the proportion of variance in the dependent variable that is accounted for by the independent variables. For example, an adjusted coefficient of determination of 0.75 means that 75% of the variance in the dependent variable is predictable from the independent variables.
3. Adjusted for the number of variables: The adjusted coefficient of determination takes into account the number of independent variables and the sample size. It penalizes the coefficient of determination for including unnecessary independent variables, helping to avoid overfitting the model. Therefore, a higher adjusted coefficient of determination suggests a better model fit, especially when compared to the ordinary coefficient of determination.
4. Comparison: When comparing models, the higher the adjusted coefficient of determination, the better the model fits the data. However, it is important to consider other factors such as the significance of the independent variables, the residual analysis, and the theoretical plausibility of the model.
In summary, the adjusted coefficient of determination provides an estimate of how well the independent variables explain the variation in the dependent variable, taking into account the number of variables and the sample size. It allows for a more accurate interpretation of the model fit and helps in comparing different models.