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How do we decide whether mean absolute error or mean square error is better for linear regression? Are there other loss functions that are commonly used for linear regression?

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Generally, MAE is more robust to outliers, so if your data set has outliers, then you can use MAE. But if the outliers represent anomalies in data and it is important that you want to find these anomalies and report it, then we should use MSE. But, if the outliers are just the corrupt data that acts as noise in the data set, then you can use MAE.

RMSE is another very common loss function that can be used for the linear regression :

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