### What is residual standard error?

• When running a multiple regression model in R, one of the outputs is a residual standard error of 0.0589 on 95,161 degrees of freedom. I know that the 95,161 degrees of freedom is given by the difference between the number of observations in my sample and the number of variables in my model. What is the residual standard error?

This question and its answers might help: Why do we say residual standard error?

A quick question: Is "residual standard error" the same as "residual standard deviation"? Gelman and Hill (p.41, 2007) seem to use them interchangeably.

7 years ago

A fitted regression model uses the parameters to generate point estimate predictions which are the means of observed responses if you were to replicate the study with the same \$X\$ values an infinite number of times (and when the linear model is true). The difference between these predicted values and the ones used to fit the model are called "residuals" which, when replicating the data collection process, have properties of random variables with 0 means.

The observed residuals are then used to subsequently estimate the variability in these values and to estimate the sampling distribution of the parameters. When the residual standard error is exactly 0 then the model fits the data perfectly (likely due to overfitting). If the residual standard error can not be shown to be significantly different from the variability in the unconditional response, then there is little evidence to suggest the linear model has any predictive ability.

This may have been answered before. See if this question provides the answers you need. [Interpretation of R's lm() output][1] [1]: http://stats.stackexchange.com/questions/5135/interpretation-of-rs-lm-output