# Better to Minimize Absolute Error or Sum of Squared Error?

I have an Excel model which predicts the number of customers for a given month. The prediction depends on a churn rate. I have the absolute error (actual vs predicted), along with squared error and sum of square error.

My question is:

Would it better to find a churn rate that minimizes the absolute for each period (year, month) or find a churn rate that minimizes the sum of squared errors? Does the former even make sense to do?

• This depends on your loss function, I think. – Richard Hardy Nov 28 '18 at 19:07

A-priori arguments aside, train a model using least squares, and then plot a histogram of your prediction errors $$y_{i} - \hat{y}_{i}$$. Does this distribution look normal? Train the model using absolute error and plot $$y_{i} - \hat{y}_{i}$$, does this distribution look Laplacian?