# Understanding Mean Squared Error

When determining the quality of an estimator, I understand a simple metric such as, if the expected and predicted are close, then we consider this instance to be correct. Then sum up all correct and divide by total. This will give you a measure of accuracy.

But mean squared error is harder for me to understand. What is a good value of MSE? How close to 0 does it need to be to consider it as "good"? Is it only the relative values of MSE which we need to consider to determine if one estimator is "better" than another?

Is there any way to normalize MSE so that it more closely represents an accuracy as a percentage of total instances?

• A bare MSE arguably has no interpretation. For one thing it depends on the units that are being used for measurement. It also gives no notion of how much variation is being accounted for by the model. – dsaxton Mar 11 '16 at 19:32
• You can normalized RMSE by the mean value to offer some comparison within and between case studies. – Cyrille Mar 11 '16 at 19:44
• Your "if expected and predicted are close, Then sum up all correct and divide by total." suggests that you are truncating your data, throwing away all the sample values that do not meet your criterion regarding the interpretation of "close" and averaging only the "good" samples. Can you have a rational conversation with someone whose standards of "close" are laxer than yours, or, for that matter with someone "holier than thou"? Also, what do you do if none of the samples meet your stringent interpretation of "close"? – Dilip Sarwate Sep 3 '17 at 14:37