So I know what Root Mean Square Error (RMSE) is — you take the difference between all respective predicted and actual values, square the differences and sum them, then take the mean and square root it.

In simple terms, without all the fancy equations and mathematical jargon, what’s MCRMSE? I take that it’s an extension of RMSE, but what does Mean Columnwise mean?

I’m doing a Kaggle competition where the metric used is MCRMSE. You can view the metric in the competition here.

In the Kaggle competition you are referring to, there are six target variables - cohesion, syntax, vocabulary, phraseology, grammar, and conventions. MCRMSE simply takes the average of the RMSE for each target variable, that is, it would be equivalent to (rmse(pred_cohesion, targ_cohesion) + rmse(pred_syntax, targ_syntax) + ... + rmse(pred_conventions, targ_conventions)) / 6.