[Feature Request] Confidence bands for polynomial and nonlinear regression

[bvenn]

Is your feature request related to a problem? Please describe. Confidence and prediction bands offer a interesting insight into regression outcomes. While the fitted function (correct model selection is assumed) shows the best possibility of the current model, it does not show the confidence. While confidence and prediction bands are implemented for simple linear regression, a generalized version for linear regression and non-linear regression would be beneficial.

Additional context

• Scheffés method
• https://www.graphpad.com/guides/prism/7/curve-fitting/reg_confidence_and_prediction_band.htm
• https://www.graphpad.com/guides/prism/7/curve-fitting/reg_how_confidence_and_prediction_.htm
• https://nbviewer.org/github/gpeyre/numerical-tours/blob/master/python/ml_11_conformal_prediction.ipynb

[bvenn]

Additionally we need confidence and prediction bands for qq plots:

see: stat_qq_band and The Power to See: A New Graphical Test of Normality,Aldor-Noiman, 2013