I'm still not sure how to connect the "expected mean" to the "conditional mean". Since websites tells The intercept is the expected mean value of Y when all X=0. So that's not true, right? The intercept in a multiple regression is always the conditional mean of Y, when all X are zero, right? Best regards

If I understood correctly, the "unconditional mean" is identical to the average of the dependent variable or the intercept/const in the empty model. Whereas the "conditional mean" is the intercept/const in any given model specification when regressors are zero. Is this correct?