Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE)


Mean absolute error (MAE)
The MAE measures the average magnitude of the errors in a set of forecasts,
without considering their direction.
It measures accuracy for continuous variables.
The equation is given in the library references.
Expressed in words, the MAE is the average over the verification sample of the
absolute values of the differences between forecast and the corresponding observation.
The MAE is a linear score which means that all the individual differences are
weighted equally in the average.
Root mean squared error (RMSE)
The RMSE is a quadratic scoring rule which measures the average magnitude of the error.
The equation for the RMSE is given in both of the references.
Expressing the formula in words, the difference between forecast and corresponding
observed values are each squared and then averaged over the sample.
Finally, the square root of the average is taken.
Since the errors are squared before they are averaged, the RMSE gives a relatively
high weight to large errors.
This means the RMSE is most useful when large errors are particularly undesirable.
The MAE and the RMSE can be used together to diagnose the variation in the errors
in a set of forecasts.
The RMSE will always be larger or equal to the MAE; the greater difference
between them, the greater the variance in the individual errors in the sample.
If the RMSE=MAE, then all the errors are of the same magnitude
Both the MAE and RMSE can range from 0 to ∞. They are negativelyoriented scores:
Lower values are better.
Loading Questions
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You read that a set of temperature forecasts shows a MAE of 1.5 degrees
and a RMSE of 2.5 degrees. What does this mean?
Choose the best answer:
This is true, but not the best answer. If RMSE>MAE, then
there is variation in the errors.
This is true too, the RMSEMAE difference isn't large enough to indicate
the presence of very large errors.
This is true, by the definition of the MAE, but not the best answer.
This is the best answer. See the other choices for more feedback.