A Freakonometrics blog post shows how to use a LOESS regression of the residuals of a logistic model on the predicted values of the logistic model to assess the linearity of the predictors used in the logistic regression model.
If the green interval contains zero, this indicates that the model is correctly specified (or close enough).
My question is, should I use a confidence interval or a prediction interval around the LOESS fitted curve?
I am interested in whether the estimate of $\text{E}[y \mid x]$ is correctly specified - so that makes me think confidence interval. However, normally prediction intervals are used for individual observations.
For reference:
Difference between confidence intervals and prediction intervals