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?
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1$\begingroup$ As far as I'm concerned, the standard error of a coefficient is well defined (I assume you know what that is), but "standard error of regression" looks like an imprecise term to me and I wouldn't use that term. Can't remember having seen it either. The regression is the whole thing, not a single estimator of something of which one could compute a standard error. Can you quote the context of where you've seen "standard error of regression"? $\endgroup$– Christian HennigCommented Aug 20, 2020 at 8:37
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$\begingroup$ @Lewian Hi! Thanks for the comment. I saw the term of "standard error of regression" from one blog. I just checked again, it says "Standard error of regression also called as Standard error of estimate". So, can you explain in a simple way the difference between Standard error of coefficient and standard error of estimate. Thank you! $\endgroup$– almoCommented Aug 20, 2020 at 11:31
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$\begingroup$ They are the same thing, the coefficient is estimated and hence also often called estimate $\endgroup$– stefgehrigCommented Aug 20, 2020 at 12:12
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$\begingroup$ @stefgehrig Thanks :) Was confused with those terms $\endgroup$– almoCommented Aug 20, 2020 at 12:14
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$\begingroup$ Chances are stefgehrig is right, however in general if a blog author uses imprecise terminology, it is up to them to explain it, not to us. ("Standard error of estimate" is imprecise as well as long as they don't say estimate of what.) $\endgroup$– Christian HennigCommented Aug 20, 2020 at 12:51
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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"?
answered Aug 20, 2020 at 12:18
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$\begingroup$ I’m glad to hear it isn’t just me who saw that in R and though, “I’m pretty sure this isn’t what standard error usually means.” $\endgroup$– DaveCommented Aug 20, 2020 at 12:21
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$\begingroup$ @BigBendRegion. Thanks! There are too many sources on the web. standard error, standard error of estimate, standard error of intercept, Standard error of coefficient, standard error of slope... It makes people confusing... $\endgroup$– almoCommented Aug 20, 2020 at 12:26
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1$\begingroup$ Yes, indeed. If we were to always have "standard error" refer to the estimated standard deviation of the sampling distribution of a parameter estimate, then much confusion would vanish. $\endgroup$ Commented Aug 20, 2020 at 12:35