linear regression and logistic regression global p values aren't associated to the same test? How to interpret them? I'm using the package statsmodels in Python 3.9.10.
When I carry out a linear regression model, I get this:

Am I right when I say:
The F-statistic checks how likely the sample if all coefficients are 0. In this particular case, it's the same as the p value associated to the categorical variable VHD. This is because when there's only one variable, the F-statistic (testing if the coefficients are 0) is the same as the t-statistic associated to VHD (testing if the coefficient VHD is 0).
Now I want to have the same p values when carrying out a logistic regression. However, I have this:

And I can't find Prob (F-statistic) anymore.
I have however LLR p-value. Why is that? Should I interpret it the same way as the F-statistic p-value when doing a linear regression?

There are three tests of nested regression models that get covered in a typical statistical theory class, such as one taught from the Casella/Berger textbook Statistical Inference.

*

*Wald test


*Likelihood ratio test


*Score test (sometimes called a “Lagrange multiplier test”)
In linear regression, the F-test is an example of a Wald test. When you get to logistic regression, however, there are issues with Wald testing. Consequently, there are arguments to be made that likelihood ratio testing is more appropriate.
That’s what your printout is giving.
