Does GLM return an estimate for the error term (residual standard deviation)?

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I was under the impression that if I called lm(@formula(y~x),data) from the GLM.jl package was fitting a simple linear regression of the form:

y=a+bx_i+\epsilon_i

The results from the regression being:

\hat{y}=\hat{a}+\hat{b}x

Which is our linear predictor. But we want to predict a value we have to use:

\hat{y}=\hat{a}+\hat{b}x+\epsilon_i

Why doesn’t lm return an estimate for error (\epsilon_i) in the summary of coefficients? Isn’t this an important part of the regression analysis? R returns the estimate as the auxiliary parameter. For a least squares regression wouldn’t this estimate just be the standard deviation of the residuals? Is there any way to access this information without just creating a helper function to calculate that value on my own? Im probably just missing something very dumb!

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GLM.jl doesn’t report it as part of the model summary, but you can extract it for a model with GLM.dispersion.

If you think that this should be part of the default output, please open an issue.

Also, if you want to predict a value, see GLM.predict, which can also provide prediction intervals, taking the various uncertainties in the model into account.

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This is exactly what I was looking! I guess I should have looked more closely at the documentation, but thank you for pointing it out anyway :slight_smile: