Problem statementSend feedbackWhy is the average of the difference between the errors for each data point, not a suitable way to evaluate a regression model?

The average of the difference between the errors for each data point is not a suitable way to evaluate a regression model for several reasons:

1. Cancellation of Errors: If we simply average the errors, positive and negative errors could cancel each other out. This could lead to a misleadingly low average error even if the model is performing poorly. For example, if for two data points, the errors are +5 and -5, the average error would be 0, which suggests a perfect model, but in reality, the model is off by 5 units for each prediction.

2. Lack of Squaring: The average of the differences does not square the errors. Squaring the errors, as done in Mean Squared Error (MSE), is beneficial because it penalizes larger errors more than smaller ones, which is usually desirable in a regression context.

3. Absence of Absolute Value: Unlike Mean Absolute Error (MAE), averaging the differences does not take the absolute value of the errors. This means that it does not represent the average magnitude of the errors, which is often what we care about in a regression context.

4. No Standardization: The average of the differences is not standardized, meaning it can be hard to compare across different datasets or models. Other metrics like R-squared or Adjusted R-squared are standardized from 0 to 1, making them easier to interpret and compare.

In summary, while the average of the differences between the errors for each data point can provide some information about a model's performance, it is not a comprehensive or reliable way to evaluate a regression model.