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Im trying to show how both linear regression and classification tree performed on a dataset. I know by this and this that RMSE or MAPE are adequate metrics to assess goodness of fit, but Im in a working enviroment where people can understand the concepts of correlation and average only.

I thought comparing the correlation of predicted values and the observed ones for each model would be ok for my purpose, but I don't know if there is a huge mistake I'm comitting in doing so.

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Computing the correlation is not strong enough. It will tell you there is a linear relationship between the predictions of the model and the observed values, but it ignores scale and location which are important. Frankly, if you're working group is willing to understand correlation but not RMSE or MAPE, then your problem sounds more likely a social or educational problem than a statistical one.

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