# Interpreting RMSE and MAE

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?

• 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, $$\sqrt{u^2}\rightarrow u$$