How to interpret r²
R², also known as the coefficient of determination, is a statistical measure that indicates the proportion of the variance in the dependent variable that can be explained by the independent variable(s) in a regression model. It ranges from 0 to 1, with higher values indicating a stronger relationship and better fit of the regression model.
Here is how you can interpret R²:
1. Percentage of variance: R² represents the percentage of the variance in the dependent variable that is explained by the independent variable(s) included in the regression model. For example, if R² is 0.75, it means that 75% of the variance in the dependent variable can be accounted for by the independent variable(s).
2. Goodness of fit: R² provides an indication of how well the regression model fits the observed data points. A higher R² value indicates a better fit and suggests that the independent variable(s) have a strong explanatory power for the dependent variable. Conversely, a lower R² value suggests a weaker fit and indicates that the independent variable(s) do not explain much of the variation in the dependent variable.
3. Predictive power: R² can also be interpreted as a measure of the predictive power of the regression model. A higher R² suggests that the model can more accurately predict the values of the dependent variable based on the independent variable(s). However, it is important to note that a high R² does not guarantee accurate predictions, as it primarily reflects the relationship between the variables used in the model.
It is important to keep in mind that R² has limitations. It cannot determine causality, as it only identifies the strength and magnitude of the relationship between variables. Additionally, R² can be influenced by the number of independent variables included in the model. It is always recommended to consider other statistical measures and evaluate the overall context when interpreting R².