What are the Evaluation metrics in a linear regression model?

Here are three common evaluation metrics for regression problems:

Mean Absolute Error (MAE) is the mean of the absolute value of the errors:

Mean Squared Error (MSE) is the mean of the squared errors:

Root Mean Squared Error (RMSE) is the square root of the mean of the squared errors:

Comparing these metrics:

MAE is the easiest to understand, because it's the average error.

MSE is more popular than MAE, because MSE "punishes" larger errors, which tends to be useful in the real world.

RMSE is even more popular than MSE, because RMSE is interpretable in the "y" units.

All of these are loss functions, because we want to minimize them.

We can do this in Python by the following code

from sklearn import metrics

print('MAE:', metrics.mean_absolute_error(y_test, predictions))

print('MSE:', metrics.mean_squared_error(y_test, predictions))

print('RMSE:',np.sqrt(metrics.mean_squared_error(y_test, predictions)))

Here y_test are the target values of the test data and predictions are the data predicted.