RMSE and MAE

Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) are two common metrics used to measure the accuracy of a predictive model, particularly in regression analysis and time series forecasting. Both metrics quantify the difference between the actual (observed) values and the predicted (forecasted) values, but they do so in slightly different ways.

Root Mean Square Error (RMSE):

RMSE is the square root of the average of the squared differences between the predicted and actual values. It can be mathematically represented as:

Characteristics of RMSE:

• RMSE gives more weight to larger errors due to the squaring operation. Therefore, it may be more sensitive to outliers.
• The unit of RMSE is the same as the original data, making it relatively interpretable.
• Generally, a lower RMSE indicates a better fit of the model to the data.

Mean Absolute Error (MAE):

MAE is the average of the absolute differences between the predicted and actual values. It can be mathematically represented as:

Characteristics of MAE:

• Unlike RMSE, MAE treats all errors equally, regardless of their size. Therefore, it is less sensitive to outliers.
• The unit of MAE is the same as the original data, and it is straightforward to interpret.
• A lower MAE indicates a better fit of the model to the data.

Comparison:

• Sensitivity to Outliers: RMSE is more sensitive to outliers, whereas MAE treats all errors equally.
• Interpretation: Both are easy to interpret as they are in the same units as the original data.
• Computation: RMSE involves squaring and square rooting, making it slightly more computationally intensive than MAE.

In general, both RMSE and MAE are valuable metrics for assessing the accuracy of a model. The choice between them may depend on the specific needs of the analysis, such as whether large errors are particularly concerning or whether a more robust measure is preferred.