Sir, we are creating a regression equation for prediction, not for comparison of two groups.
Okay, then why the concern about the different intercepts? As you said, the models are equivalent. Either will give you the same predicted values. As I have pointed out, and now as Steve seems to be pointing out, you can create models for prediction, or you can create models for understanding the individual terms (or both). Do NOT confuse the two. If you want a predictive model, then you choose either, and you report the Overall F as its level of significance. If you want to understand the individual terms, you report the tests of the individual model coefficients, with appropriate interpretation. (and of course you can do both) You keep wandering back and forth between obtaining predictive model, and obtaining understanding of the individual terms.
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