Model summary table for Random Forests^® Regression

R² is the percentage of variation in the response that the model explains.

Interpretation

Use R² to determine how well the model fits your data. The higher the R² value, the better the model fits your data. R² is always between 0% and 100%.

You can graphically illustrate the meaning of different R² values. The first plot illustrates a simple regression model that explains 85.5% of the variation in the response. The second plot illustrates a model that explains 22.6% of the variation in the response. The more variation that is explained by the model, the closer the data points fall to the fitted values. Theoretically, if a model can explain 100% of the variation, the fitted values would always equal the observed values and all of the data points would fall on the line y = x.

Note

Because Random Forests® use out-of-bag data to calculate R², but not to fit the model, overfitting of the model is not a concern.

The root mean square error (RMSE) measures the accuracy of the model. Outliers have a greater effect on RMSE than on MAD and MAPE.

The mean square error (MSE) measures the accuracy of the model. Outliers have a greater effect on MSE than on MAD and MAPE.

The mean absolute deviation (MAD) expresses accuracy in the same units as the data, which helps conceptualize the amount of error. Outliers have less of an effect on MAD than on R², RMSE, and MSE.

The mean absolute percent error (MAPE) expresses the size of the error relative to the size of the response value. Thus, the same size error will have a larger MAPE value for a smaller value of the response variable than for a larger value. Because the MAPE is a percentage, it can be easier to understand than the other accuracy measure statistics. For example, if the MAPE, on average, is 0.05, then the average ratio between the fitted error and the actual value across all cases is 5%. Outliers have less of an effect on MAPE than on R², RMSE, and MSE.

However, sometimes you may see a very large MAPE value even though the model appears to fit the data well. Examine the fitted vs actual response value plot to see if any data values are close to 0. Because MAPE divides the absolute error by the actual data, values close to 0 can greatly inflate the MAPE.