I have been told that you must consider the context of a problem in order to determine what your error metrics are telling you.
Question:
What thought process would you go through to determine how good these numbers are in the exact context of this data-set?
Context:
I have created a linear regression model of two variables of the Iris data-set. The independent variable is "Petal Length" and the dependent variable is "Sepal Length". The error metrics have been calculated:
- Average Sepal Length: 5.843333
- R-squared: 0.703197
- Mean Absolute Error: 0.313679
- Mean Squared Error: 0.150961
- Root Mean Squared Error: 0.388537
- Mean Error: -0.88352
Some answers I am not looking for:
I am comfortable with the math behind some of the error metrics of linear regression, and I'm comfortable with what they represent in a big picture sort of way. For example, mean squared error is going to penalize large outliers by squaring the error. I realize that Mean Absolute Error does not do that. I also realize that Mean Absolute Error doesn't tell us which way our model is biased because it only counts magnitude, not direction. I know $R^2$ tells us how much better our model is than just predicting the average value. So these sorts of things are pretty clear and won't answer my question.
Types of answers I am looking for:
Based on $R^2$ it looks like my model is at least slightly better than just predicting the average. But how much better. What is the scale here?
I see that my model tends to under-estimate by 0.88 centimeters. That's about 20% of the average value, so that seems pretty bad to me. Is it really?
The mean squared is 2.5% of the average. What does that mean to me (I've seen this calculation done in example problems with no explanation of why)?