# Interpreting RMSE of log-values

I am modelling a regression with a GBM and evaluate by RMSE. My model input & target is log-transformed which results in an RMSE that is also on log-scale.

How can i interpret this in an intuitive way, e.g. as deviation from the mean price or sth. equal, that is easy to understand?

As the RMSE is in log-space it behaves like a multipicative factor. So you are finding the square root of the mean of the squared ratio between the model values and the true values.

I.e. if the RMSE were 0.693 (=ln 2) the model values would be roughly a factor of two out on average (in either direction) from the true values in the original (non-log) space.

Also, by taking the mean in log space you are less sensitive to large valued outliers.

• so, meaning that the predicted values are roughly a factor of two out on average from the true values on the log scale or "normal" scale? Commented Oct 14, 2018 at 16:16
• On the 'normal' (non-log) scale Commented Oct 15, 2018 at 7:46

great answer by @stuart10 above. I'd like to add that if you transform your y_pred and y variables back from logspace (say, using np.exp) you can in addition calculate RMSE where the results is the mean error in the original units.

so if y was in dollars, after transforming back from logspace, RMSE would give average error in dollars

• Sure, but this would be a bad idea. If the fit was going to work in non-log space you wouldn't transform to log space. Since you transformed to log space, it implies you don't expect a very good/meaningful fit in non-log space. For example when the data ranges over several orders of magnitude. Commented Apr 8, 2020 at 19:29