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I understand the concept of a confidence interval for the mean response (fitted line) for simple linear regression $y$ = $\beta_{0}$+$\beta_{1}$$X_{i}$. It is that taken over many times, with 95% probability the CI will contain the true regression line.

However, I am not sure how to compare this to a working-hoteling confidence band. The latter has the interpretation that it contains "the entire true regression line with probability 1-$\alpha$

Could someone explain how the two are different? thank you.

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I think one is conditional to x (at one value of x, you confidence statement is correct), and the other is simultaneous for the entire regression line support. The second should be larger due to "multiplicity".

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  • $\begingroup$ This doesn't look correct--but perhaps it requires a specific interpretation of "one" and "the other." Could you elaborate on what these refer to? $\endgroup$
    – whuber ♦
    Apr 16, 2022 at 20:15

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