MATLAB: Confidence and Prediction Bounds Documentation: How do the “confidence bounds for the fitted coefficients” relate to the “prediction bounds of a new function value”

Question

I have a question regarding the Confidence and Prediction Bounds Documentation page . The page lists three types of confidence and prediction bounds. I am trying to figure out if the information contained in the confidence bounds for the fitted coefficients is basically the same as in the prediction bounds for a new functions value. I can see that the first is purely numerical and the second is also displayed graphically, but do they hold the same information from a statistical point of view?

Answer 1

After reading the chapter on predictions in Chatterjee and Hadi, I see the difference between confidence bounds on the parameters and confidence bounds on a prediction a little clearer. Confidence bounds on the parameters make a statement about an interval where the true (but unknown) parameters are located with a certain probability. Confidence bounds on a prediction, on the other hand, tell you in which interval a new observation (if sampled again) or a new regression fit (of the new samples) will probably lie.

So to answer my initial question, they are indeed different things from a statistical point of view.