Standard error of estimate and standard error of coefficient I am doing self-study/review of the above mentioned topics. I am a little bit confused with these two terms. Are they the same thing? If not, could you please show me the formula?
 A: The term "standard error" is used by EXCEL to denote the residual root mean square. It is also used by R (egads!) in the term "Residual standard error" to denote the same thing. It is probably used by other software, too.
Use of "standard error" to refer to the estimated conditional standard deviation of the regression model is bad statistical practice. It is also bad for statistics education. Since "standard error" is most commonly thought of as an estimate of the standard deviation of the sampling distribution of a parameter estimate, the term "standard error" as a reference to the estimate of a regression model parameter (and not its sampling distribution) should be abandoned. It would be just like calling an estimated $\beta$ in regression a "standard error" because both are estimates of parameters, not estimates of the sampling distribution of parameter estimates.
Hey R developers! Can you change "Residual standard error" to, say "root mean square error"?  If the problem is with the word "mean" because of the df adjustment, then how about "Est condl sdev"?
