Hopefully I'm asking this in the correct section. So I've got a graph with a linear trend of data and a best fit line plotted. The data points on the main graph obviously each have their own error bars. I've also made a subplot of residuals.

My question is: do the residual subplot's data points normally have to have error bars and if so, are these error bars the same ones as those on the main graph? I ask because I thought that perhaps the error on the gradient and the error on the intercept (calculated by Excel's LINEST in my case) contribute to the error on the residual data point which would mean I can't use the same error bars as those used on the main graph? Or am I wrong here?

Note: in my case, only the dependent variable has error - the independent variable, i.e. x axis does not have error.

Many thanks for any help.

  • $\begingroup$ I see what you mean, yes. The reason why I asked this question is because I found images on the internet, e.g. i.stack.imgur.com/ajXYY.png which appear as though they have error bars on the residuals. Are these people simply wrong, or are these special cases? $\endgroup$ – mathphys Mar 17 '16 at 2:20
  • $\begingroup$ Ok, that sounds reasonable. So to double check, you'd recommend just doing plain residual data points with no error bars and leaving the error bars on the main graph if I'm simply considering one set of data with simple independent and dependent variables? $\endgroup$ – mathphys Mar 17 '16 at 2:30
  • $\begingroup$ In particle physics it is common if plotting residual against a fit or model result to keep the raw error bars on the data and draw the fit or model error bars symmetrically around 0 (for absolute residual) or 1 (for "as a fraction of" plots whatever they should be called). $\endgroup$ – dmckee --- ex-moderator kitten Mar 17 '16 at 2:34

Yes, residuals should have error bars.

If your residuals are the difference between your data and your model, and your data are well-described by your model except for independent, normally-distributed errors which you have modeled correctly with your uncertainties, then your residuals should be (a) randomly distributed, without any leftover shape, and (b) about two thirds of the error bars on the residuals should touch zero. A residual plot without error bars only lets you evaluate the first of these criteria.

Sometimes you'll see plots of "normalized residuals", where each (data-model) difference has been scaled so that the associated error bar is 1. This is closely related to the computation of the $\chi^2$ statistic used for goodness-of-fit tests.


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