Interpreting Root Mean square Error (RMSE )when dependent variable is log transformed

So I have developed a model to predict the house prices in a county.I log transformed the target variable (home price).I split the data into training and testing sets.I trained the model on the training set and tested it on the testing set.

The R2 for this model is 0.665 and the RMSE is 0.201.How do I interpret the RMSE?How do I explain it in layman's terms? I know that its the measure of how far the predicted values are from the actual values, but as the target variable is log transformed, how can I convert the RMSE in USD form? Ideally, I would like to report that the difference between the actual home prices and the predicted home prices is xUSD.

• stats.stackexchange.com/questions/314490/… – user2974951 Oct 12 '18 at 9:19
• If the ultimate goal is to model house prices, the model does not do that until the model predictions are "de-transformed". Only then can you find the predicted price, rather than the log of the predicted price. After the de-transform you would need to recalculate R2 and RMSE on the original house prices in dollars with model predictions in dollars. Consider the regression as a part of your modeling, rather than the entirety of the modeling. – James Phillips Oct 12 '18 at 9:22
• So I fit the model on log transformed data, and test it on detransformed data? – learning_python Oct 12 '18 at 13:06
• If the purpose of taking the log was to allow linear regression to be used rather than non-linear regression, then the log is an artifact of the modeling process. In such cases, the process is: 1) take logs 2) fit linearly 3) take anti-logs. If non-linear fitting is used, this presents a different set of problems, but interpreting the fit statistics without data transformations (and de-transformations) is straightforward. Without the de-transform you have not done step 3, but rather stopped at step 2, and have a modeling process that gives the log of house price. – James Phillips Oct 12 '18 at 15:25
• A better, more modern alternativ could be to use a glm (generalized linear model) with log link function. That should give better predictions. – kjetil b halvorsen Oct 13 '18 at 23:58