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I am not sure. This is a homework for me and the purpose is not stated. Only that I have to exclude the non-significant dummy from the model, which is high school. By non-significant I mean that I already ran the model with the 3 dummies and the p-value for the highschool was very big.
I think thats something different, right? I ignore values this way, specifically the values for which diploma = high school. Ι dont want to exclude them, I basically want to run a regression with 2 dummies instead of 3. Im just not sure how to interpret the parameters for such a model.
Ok! So in general I should avoid interpreting the intercept like this? Is there a better way to do it? (Perhaps the one you noted in your answer regarding centering the data)
Thank you for the reply. My point is exactly what you are saying. So my question still remains: Do you perhaps know why, my professor at least, always interprets the intercept by saying that its the expected value of $y$ for $x=0$? Because as you just described, its not always "correct" to do estimations for values of $x$ not within your initial data range.
Isnt it "bad habit" to use linear regression model to estimate $y$ for values of $x$ that are not within your known data range? This is what I mean, and its not safe because outside of this range of $x=1,3,5,7,9$ you dont know if the point can still be modeled with a line.
