The formula for "Relative Absolute Error" and "Root Relative Quadratic Error" used in machine learning (as calculated by Weka)

Question

In Weka's open source data mining software (written in Java), when I run some kind of data mining algorithm such as linear regression, Weka returns a model and some model score metric for the test data.

It looks like this:

Correlation coefficient 0.2978 Mean absolute error 15.5995 Root mean squared error 29.9002 Relative absolute error 47.7508 % Root relative squared error 72.2651 % 

What is the formula for "Relative Absolute Error" and "Root Square Error"? I can’t figure it out. I would like to use these metrics to evaluate my own algorithms in Matlab.

Answer 1

From this presentation, in slide 22 and quoting witt, the formulas are given:

Relative absolute error

Error of quadratic root error

from

• Actual target values: a1 a2 ... a
• Estimated target values: p1 p2 ... pn

Answer 2

The formula for Root Relative Square Error is actually a formula for relative square error. You need to take the square root of this formula to get what Weka gives out.