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I need some help with the following:

I have a regression problem of income and degree type. Degree is a factor with 4 levels: high school diploma, bachelor's degree, master's and phd. In order to run a regression model for this, there is the need for 3 dummy variables in the model (say that high school diploma is the reference category).

If I want to rerun the model but this time I don't want to have 3 dummies, but only 2: one for master's and one for phd. I found a function called model.matrix(model) which I can use to extract $x_3$ and $x_4$ dummies ($x_3$ for MSc and $x_4$ for phd), and then run a regression based only on these like this:

lm(income ~ model.matrix(model)[, c(-1, -2)]

However in this case, I am not sure how to interpret the results and specifically the intercept. I guess that somehow, the intercept now incorporates both high school and bachelor's dummy variables?

Thanks in advance.

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  • $\begingroup$ Why not simply filter your dataset to include only those with a masters and PhD and rerun your model and interpret as you usually do? $\endgroup$
    – StatsStudent
    Commented Dec 11, 2020 at 21:52
  • $\begingroup$ 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. $\endgroup$
    – thenac
    Commented Dec 11, 2020 at 22:00
  • $\begingroup$ I guess it depends on what the goal of your analysis is. Can you explain more in an edit to your question what your intent/goal of your analysis is? $\endgroup$
    – StatsStudent
    Commented Dec 11, 2020 at 22:05
  • $\begingroup$ 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. $\endgroup$
    – thenac
    Commented Dec 11, 2020 at 22:58

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