When I built the model, I applied the log transformation to all variables including the dependent variables. Now, I'm calculating the RMSE for the evaluation, and the result is in the log format, which is pretty small, around 0.48.
However, I don't think the number is correct to evaluate the model under this situation. For example, if one actual value is 10.1 after log transformation, and its predicted value is 10; another actual value is 1.1, and its predicted value is 1, the residuals under the log transformation of these two numbers are both 0.1. But if I convert them back to the original format and calculate the residuals: the residuals of
exp(10.1)-exp(10) is way too different from the
My question is: How to I fix this problem? (ex.manually calculate the RMSE after converting the predicted value in log format to the original format?)