# How to interpret the output from the robust regression in terms of the expected value?

Regression is a way to model the relationship between the conditional expected value and the predictors. But in the robust regression we don't have the expected value (say, arithmetic mean for Gaussian response), but rather an M estimator - truncated mean, winsorized mean. So, when it comes to interpret the coefficients in a linear regression, it's simple: "a unit change in X1, holding constant all others, causes, in AVERAGE, beta change in the response". Now, how to replace the "AVERAGE" in robust regression?

• The model is predicting a summary of your response, conditional on predictors, where the summary is defined by the algorithm or recipe used. The wording need not be -- arguably cannot be -- a single short word or term. The estimand is defined by the estimator. Mar 3, 2020 at 20:47
• @Nick I don't follow your final thought, because if it were true, then why wouldn't all estimators be unbiased? If an estimator can be biased, then how exactly does an estimator determine its estimand?
– whuber
Mar 3, 2020 at 21:37
• We’ve had this discussion before. What does a trimmed mean estimate? Mar 3, 2020 at 21:44
• The allusion is to this 2013 exchange: stats.stackexchange.com/questions/63386/… Mar 4, 2020 at 15:12

With robust regression you are still estimating the conditional mean function $$E(Y|X)$$ so that the interpretation that you suggest carries over. The difference is that robust estimators require fewer assumptions on the error and the covariates than the typical least squares estimator.