How to interpret coefficient of determination
The coefficient of determination, denoted as R² or R-squared, is a statistical measure that indicates the proportion of the variance in the dependent variable that is predictable or explained by the independent variables in a regression model. It ranges from 0 to 1, where 0 indicates that the independent variables have no explanatory power, and 1 indicates that the independent variables perfectly explain the variance in the dependent variable.
To interpret the coefficient of determination:
1. Accounted Variation: R² represents the percentage of variation in the dependent variable that can be explained by the independent variables in the regression model. For example, an R² value of 0.75 implies that 75% of the variation in the dependent variable can be explained by the independent variables.
2. Goodness of Fit: R² also serves as a measure of how well the regression model fits the observed data. A higher value of R² indicates a better fit, meaning that the model explains a larger proportion of the variability in the dependent variable.
3. Comparisons: R² can be used to compare different regression models to determine which one provides a better fit to the data. The model with a higher R² value is generally preferred as it explains a larger proportion of the variation in the dependent variable.
4. Limitations: It is important to note that R² does not provide information about the statistical significance of the relationship between the independent and dependent variables. Therefore, it should be used in conjunction with other statistical measures, such as p-values, to assess the overall reliability and significance of the regression model.
Overall, the coefficient of determination helps to quantify the extent to which the independent variables explain the variation in the dependent variable and evaluate the goodness of fit of a regression model.