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When some models state the MSE or MAE as some value, is that value in the same unit as our target variable and is it for the total model or only an observation? For example, if a model says the MAE is 4 and we are trying to predict number of oranges sold per day, it is stating we are off on average by 4 oranges per day correct?

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MAE, RMSE are in the same unit, but MSE is in unit-squares. The rules are:

  • If you add/subtract two variables of the same unit, the result will be in the same unit, i.e. $u\pm u\rightarrow u$
  • If you multiply them, it will be unit-squares, i.e. $u\times u \rightarrow u^2$
  • If you divide them, the result is unit-less, i.e. $u/u\rightarrow 1$
  • Additionally, $\sqrt{u^2}\rightarrow u$
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  • $\begingroup$ But am I correct with my logic above? $\endgroup$ Oct 16, 2020 at 20:49
  • $\begingroup$ for MAE and RMSE yes, but MSE is in orange-squares when your unit is orange $\endgroup$
    – gunes
    Oct 16, 2020 at 20:51
  • $\begingroup$ I should have specified, am I correct with it being "we are/ off on average by 4 oranges per day correct?" where 4 is measured in MAE or RMSE? $\endgroup$ Oct 21, 2020 at 2:29

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